Picking Funds with Confidence

⇤

Niels S. Grønborg Aarhus University, CREATES and DFI

Asger Lunde Aarhus University and CREATES

Allan Timmermann UCSD

Russ Wermers University of Maryland

Abstract

We present a new approach to selecting actively-managed mutual funds that uses both portfolio

holdings and fund return information to eliminate funds with predicted inferior performance

through a sequence of pairwise fund comparisons. Our methodology determines both the number

of skilled funds and their identities, and locates funds with substantially higher risk-adjusted

returns than those identified by conventional alpha ranking methods. We find strong evidence

of time-series variation in both the number of funds identified as superior using our approach,

as well as in their performance across di↵erent economic states.

Key words: Fund confidence set; equity mutual funds; risk-adjusted performance

JEL codes: G2, G11, G17

⇤We thank an anonymous referee for several constructive comments and suggestions on an earlier version of thepaper. We are grateful to conference participants at the 2016 SoFiE and 2018 EFA conferences, and thank seminarparticipants at Erasmus, Georgetown, Purdue, Texas A&M, University of Hawaii, University of Illinois at Urbana-Champaign, University of Maastricht, Tilburg, and CREATES for comments on the paper. Grønborg gratefullyacknowledges support from the Danish Council for Independent Research, Social Sciences (4091-00190/FSE).

1. Introduction

Each year, large sums of money and vast amounts of e↵ort are dedicated towards selecting the

best mutual funds.1 Yet, despite decades of academic research, forecasting which mutual funds will

go on to produce the best performance remains an elusive goal. While many studies have singled

out di↵erent characteristics of individual funds that are correlated with future performance, it is

unclear how to e↵ectively identify the set of funds that is most likely to outperform in the future.2

Indeed, the identification of a superior set of funds, rather than an individual fund, involves a

considerably more complicated statistical problem and requires testing multiple hypotheses against

a number of reasonable alternatives.3

Consider the problem of selecting a menu of actively managed funds for a Defined-Contribution

(DC) plan by a fiduciary (perhaps assisted by an investment consultant). This problem is very com-

mon, and a↵ects the investments of millions of workers in the United States. Further, thousands of

investment alternatives, including numerous open-end mutual funds, are available for consideration

by such a fiduciary. Two main issues plague the identification of the set of funds deemed most

likely to provide the best future risk-adjusted performance for such a DC plan, net of fees. First,

members of this set can change substantially as broad economic conditions evolve, resulting in the

set dramatically expanding or shrinking, as well as containing di↵erent component funds during

di↵erent years.4 Specifically, the nature of a fund’s information–and the fund’s strategies for acting

on such information–can depend on the competitiveness in the fund’s peer-group as well as the

state of the economy, both of which evolve and can lead to changes in the set of funds that outper-

form. For example, the ability of a fund to outperform may be short-lived, as evidence of successful

strategies attracts competitors (Hoberg, Kumar, and Prabhala, 2018) as well as additional investor

flows.

A second major issue is whether an investor can, ex-ante, locate the number and identity

of the set of active funds that will outperform in the future (with a high level of probability).

1As of year-end 2016, over $4.6 trillion was invested in actively managed U.S. equity mutual funds (seehttp://www.icifactbook.org/deployedfiles/FactBook/Site%20Properties/pdf/2017/17 fb table42.pdf). A large indus-try of investment advisors and consultants is engaged in advising retail and institutional clients on how to select funds.For instance, according to the 2015 Cerulli RIA Marketplace 2015 report, there were more than 56,000 registeredinvestment advisors in the U.S. in 2014.

2See, e.g., Cremers and Petajisto (2009), Kacperczyk, Sialm, and Zheng (2005, 2008), and Wei, Wermers, and Yao(2015).

3See Barras, Scaillet, and Wermers (2010) for a discussion of the complexity of a multiple testing problem in thecontext of the actively managed mutual fund space.

4Recent studies suggest that the ability of individual mutual funds to outperform varies over time. For example,Kacperczyk, van Nieuwerburgh, and Veldkamp (2014) find that the investment strategies of mutual funds, as well astheir ability to outperform, depend on whether the economy is in an expansion or in a recession state. Similarly, Glode,Hollifield, Kacperczyk, and Kogan (2011) find evidence of strong (weak) predictability of mutual fund returns followingperiods of high (low) market returns. Ferson and Schadt (1996), Christopherson, Ferson, and Glassman (1998),Avramov and Wermers (2006), and Banegas, Gillen, Timmermann, and Wermers (2013) show that macroeconomicstate variables can be used to better predict the future performance of individual equity mutual funds.

1

Estimates of funds’ risk-adjusted returns (alphas) tend to be surrounded by large sampling errors,

as outperforming fund managers tend to carry a greater level of idiosyncratic risk (Kacperczyk,

Sialm, and Zheng, 2005). As a result, the estimation error in using past fund data renders any fund-

by-fund analysis as resulting in a large number of “false discoveries” of funds with disappointing

future performance. The model of Kacperczyk, van Nieuwerburgh, and Veldkamp (2016) implies

that dispersion in return performance across active fund managers increases during periods with

high uncertainty, which both heightens the need for an e�cient identification of the best funds and

makes this task more challenging.5

Mutual funds’ fleeting competitive advantage–and the ensuring challenge in identifying transient

skills–has been noted and discussed in both empirical and theoretical studies. Empirically, Carhart

(1997) finds that the performance of top-ranked funds reverts towards the mean after about one

year, while Bollen and Busse (2004) find abnormal performance that lasts for one quarter, but

disappears at longer horizons. Berk and Green (2004) propose a theoretical model in which fund

alphas converge toward zero as a result of decreasing returns to scale and investors chasing past

fund performance as a (noisy) signal of fund manager skills. Mamaysky, Spiegel, and Zhang (2008)

develop a model in which managers observe private information signals which revert toward being

uninformative. Similarly, Glode, Hollifield, Kacperczyk, and Kogan (2011) present a flow-based

model in which diseconomies-of-scale at the fund level remove any abnormal performance over time

as investors allocate more money to small funds with high past alphas and allocate less money to

large funds with negative past alphas.

This paper introduces an e�cient approach to identifying (ex-ante) the set of funds with superior

performance, as well as identifying how large the selected set of funds is, what types of investment

strategies they adopt, and how this set of funds (along with its risk-adjusted performance) evolves

over time. Our approach to identifying the set of “best” (or superior) funds requires not only

that we compare each fund’s performance against a single benchmark (or a set of risk factors, as

is common practice), but that we also conduct a large set of pairwise comparisons across funds

to eliminate those funds whose performance is dominated by at least one other fund.6 Since our

stepwise approach for selecting a set of superior funds accounts for estimation error, investors can

be confident that the funds that remain after the elimination process are most likely to genuinely

have positive future alphas.

5That is, the model predicts that, during periods with high aggregate volatility, individual fund managers dependmore on their private signals, and less on common, aggregate signals. The result is increased cross-sectional hetero-geneity in fund-manager beliefs and, as a consequence, in their investment strategies and portfolio returns exactlywhen investors more highly value significant active investment skills that may increase portfolio expected returnwithout a commensurate increase in portfolio risk.

6As we will show, this pairwise comparison is e�cient, in part, because it discards all funds deemed to be the”worst fund” in comparison with any of the other funds, eliminating one ”worst fund” per round of comparisons.With traditional multiple hypothesis tests, the full (estimated) covariance matrix must be employed, which requiresthe estimation of the covariance of each fund with every other fund—a monumental task.

2

The sequence of pairwise tests seemingly ignores potential portfolio diversification benefits from

considering funds with positive but slightly smaller alphas than those in the chosen set. Fund

alphas are, however, not observed, and so investors must rely on estimated alphas when forming

portfolios. This is important because alpha estimates tend to be estimated with considerable noise.

This matters particularly for funds whose alpha estimates are positive but close to zero so that

their true alphas are more likely to be negative or zero. Conversely, the true alphas of funds with

large and positive t-statistics of alpha estimates are less likely to be zero or negative. We show

that the tests we use in our pairwise elimination rule can be viewed as the information ratio of a

long position in one fund and a short position in another, with positions chosen according to the

predicted sign of the risk-adjusted return. The test statistic used by our approach will be high when

the average risk-adjusted return on one fund is significantly higher than that of another fund and,

also, when the two funds’ returns are highly correlated. Both conditions indicate that the worse

fund contributes little to the portfolio’s information ratio. It follows that our stepwise approach can

be seen as an elimination rule for deciding whether a fund is so unlikely to improve the information

ratio of the overall portfolio, that it is tossed out. Thus, the FCS helps in controlling estimation

error in the final portfolio formation process. Essentially, the FCS approach can be viewed as a first

(selection) step used to identify those funds whose alphas we can most confidently trust are truly

positive. From this perspective, the FCS approach can be viewed as a first step towards forming

a portfolio of funds with positive alphas. The second step then applies mean-variance optimal

weights to the funds included in the FCS.

Besides providing valuable information for investors, DC fiduciaries, and consultants, our ap-

proach also sheds new light on the nature of competition in the mutual fund industry. Specifically,

by singling out the set of funds with superior performance and showing how this set evolves through

time, we are able to analyze how many funds are in this set, for how long they can maintain their

competitive edge, and, thus, how rapid turnover is among funds included in the set.7

Conventional approaches in the finance literature are not well-designed to handle such compar-

isons, nor do they control for the “size” of the test, i.e., the probability of wrongly eliminating truly

superior funds.8 To deal with such issues, our analysis adopts a new approach for the selection of

mutual funds that makes use of the Model Confidence Set (MCS) methodology of Hansen, Lunde,

7We note that our search for funds with superior performance uses only simple and widely available data on pastreturns and publicly reported holdings—both of which are readily available to the public at the time a decision onwhether to invest in the fund is made by our empirical tests.

8While the “False Discovery Rate” (FDR) procedure used by Barras, Scaillet, and Wermers (2010) provides ane�cient approach to estimating the Type I error (size) associated with identifying a set of outperforming funds, itsays little about the error rate in identifying individual funds within a given set that are expected to outperform.Indeed, Barras, Scaillet, and Wermers (2010) apply a simple approach that examines the set of funds with the bestestimated alphas (or t-statistics), with no mechanism to winnow out individual funds within this set that are unlikelyto be skilled according to a desired level of Type I error. That is, the simplicity of the FDR approach compromisesthe selection of the most-skilled funds by stopping the analysis at the level of the initially chosen set of funds, e.g.,all those having an alpha p-value lower than 5%.

3

and Nason (2011), HLN henceforth, which, in turn, is designed to select the most accurate predic-

tion models from a large set of candidate models. In our context, the set of “candidate models” is

the set of alpha forecasts, one for each equity mutual fund in existence at a given point in time; these

individual fund alpha forecasts are generated by a particular risk model (e.g., the four-factor model

of Carhart, 1997). Using the MCS methodology, our approach undertakes a series of pairwise tests

to sequentially eliminate funds with inferior performance. If at least one fund with significantly

inferior performance, relative to any other fund, is identified, this fund is eliminated, and the elim-

ination process continues on the reduced set of funds.9 The procedure continues until no further

funds with inferior performance, relative to any other fund, can be identified and eliminated. We

label the set of funds remaining at the end–the funds forecasted to have superior performance–as

the “Fund Confidence Set” (FCS).

The FCS is designed to choose the best among a set of funds using a particular forecasting

model. The successful implementation of the FCS is therefore closely linked to how accurate the

underlying performance model is in estimating and predicting fund performance. In particular, if

the approach used to estimate fund performance is very noisy, the FCS is unlikely to have much

power to discern di↵erences between mutual funds and isolate the best funds. To overcome this

issue, we propose a novel (yet, parsimonious in its data requirements) performance model that (i)

allows for time-varying alphas using the latent skill approach of Mamaysky, Spiegel, and Zhang

(2008); and (ii) extracts alpha estimates, pooling information from past fund returns and fund

holdings. Empirically, we find that the FCS approach can be used to select a set of funds with

considerably better average performance than techniques that employ a fixed proportion (e.g., 5%

or 10%) of top ranked funds. In particular, a portfolio of funds included in the top FCS generates a

four-factor alpha of more than 65 bps/month which is highly statistically significant and far higher

than the performance achievable by a range of existing approaches.

The performance of most funds is estimated with large sampling errors. Our approach therefore

works best if we use a relatively stringent criterion for inclusion of funds in the FCS–resulting in a

relatively narrow set of superior funds and a reduced probability of wrongly including funds with

inferior performance. Using this stringent approach, we find that the set of funds identified as

superior fluctuates considerably over time. Sometimes, only a few funds (or even a single fund) are

selected; at other times, the approach identifies a large set of funds as being superior. As we relax

this stringent inclusion criterion, we still find that the FCS identifies a superior set of funds, but

with slightly weaker economic and statistical significance. In further tests, we find that the fraction

of superior funds is larger in low-volatility states, and smaller in high-volatility states, suggesting

that funds’ ability to outperform is state-dependent.

We also find that dispersion in fund performance is greater during times with high levels of

9Note that the e�ciency of this approach exploits the fact that we wish to generate a set of funds forecasted tohave the best performance, and not, e.g., an optimized portfolio of funds with the best mean-variance properties.

4

market volatility, leading to the best funds–as identified by our FCS approach–performing better

during such periods, relative to calmer times.10 This is consistent with the model of Kacperczyk,

van Nieuwerburgh, and Veldkamp (2016), which suggests that the rewards to skilled investors from

processing information are higher when market risk is high.

The FCS methodology can also be used to identify funds with inferior performance. When

applied to select inferior funds, we find that the set of “worst” funds is somewhat wider than

the equivalent set of superior funds. This reflects the greater persistence of factors giving rise

to underperformance, such as high trading costs and management fees (relative to skills). Funds

identified as being inferior by our FCS go on to produce large negative and highly significant risk-

adjusted returns, indicating that the FCS e↵ectively identifies funds with poor skills rather than

funds that have simply experienced a spell of bad luck.

Our analysis di↵ers from previous studies in several important dimensions. Kosowski, Timmer-

mann, Wermers, and White (2006) ask whether any fund is capable of genuinely outperforming

on a risk-adjusted basis. However, their methodology cannot be used to endogenously determine

the size of the set of funds with superior performance or the identity of the individual funds, a

much tougher econometric problem. In fact, a strategy of only investing in the fund whose alpha

is deemed highest can sometimes backfire, because such a fund might have been “lucky,” and its

performance could reflect very high idiosyncratic risk taking. Barras, Scaillet, and Wermers (2010)

develop an approach that controls for funds whose high alpha estimates are due to “luck.” However,

unlike us, they do not address the identification of individual funds deemed to have the highest

(positive) alphas. This is a highly relevant question from an investor’s perspective, because not

all funds, even those with truly positive alphas, should be expected to perform equally well. In

addition, and of great relevance to a fiduciary charged with selecting a set of active funds, indi-

vidual investors typically wish to invest in only one or a few funds, and not a larger set. Thus,

the identification of the refined set of superior funds is of great value to such investors. Further,

Barras, Scaillet, and Wermers (2010) find evidence that the set of funds with positive alphas has

been shrinking over time, making it more di�cult to identify truly superior fund managers. This

result highlights the importance of identifying individual funds that are predicted to outperform in

order to form a precise set, rather than starting with a set and conducting inference on the entire

set (equal-weighted) as is done by Barras, Scaillet, and Wermers (2010).11

We show empirically that our approach, which endogenously builds the set of funds (starting

with pairwise individual fund comparisons) with superior expected performance, is better at identi-

10This result highlights the di�culty in identifying, ex-ante, superior funds in a recession setting–even though theaverage performance of active funds is better during recessions–due to the short time-series nature of recessions. Forinstance, there are only 34 months of NBER-identified recessions during our entire sample period.

11Harvey and Lui (2018) propose a novel random e↵ects approach that exploits cross-sectional information onalpha estimates in a way that reduces the e↵ect of estimation error in individual fund alphas. While their approachis distinctly di↵erent from ours, like us they use information on the population of alpha estimates to identify fundswith superior performance.

5

fying truly superior funds and forming portfolios of such funds. Compared to existing alternatives,

our approach helps to discard individual funds that lie in the top past-performance fractile due to

luck. Moreover, our approach helps to adjust the search for superior active managers in accordance

with the breadth of active management skills during a particular period of time, broadening or

narrowing the set of chosen funds as market conditions evolve. We show that these advantages

translate into superior fund alphas, as well as better identification of inferior funds. The key to our

approach is its e�cient pairwise comparisons of funds to separate luck from skill.

The outline of our paper is as follows. Section 2 introduces the FCS methodology, while Section

3 describes our data and the model used to measure the performance of individual funds. Section 4

presents performance results for the FCS portfolios and Section 5 provides details on which funds

get selected to be among the superior or inferior funds and how this set varies through time. Section

6 concludes.

2. The Fund Confidence Set

This section introduces our approach to fund selection that endogenously determines the set of

funds with superior performance, allowing the range of this set to vary over time. Our approach

reflects how a sophisticated investor with access to historical data on individual fund returns and

periodic security holdings could go about identifying superior funds, mimicking the search for skill

described in papers such as Garleanu and Pedersen (2018).

Before formally introducing our Fund Confidence Set approach, we first provide a motivating

example in which the set of funds is small enough that we can gain intuition for how the approach

works. Next, we formally describe the approach, characterize its properties, and provide details on

how we implement the approach on our mutual fund data.

2.1. Selecting funds with superior performance: A motivating example

To illustrate the central idea of our FCS approach and demonstrate how it di↵ers from other

possible approaches for fund selection, we initially consider an example with only four funds, namely

Shearson Appreciation, Growth Fund of America, Sogen International Fund, and Pioneer II. We

assume that an investor has obtained alpha estimates for these funds based on data available in

November 1990 and wants to determine which, if any, of these funds to hold.

A simple way to select funds would be to look at their average alphas. For the four funds

under consideration, alpha estimates are presented in Panel A of Table 1. Because all estimates are

positive, the four funds could be regarded as worthy of investment as indicated by the checkmarks in

the table. This logic ignores sampling errors, however, and fails to assess the statistical significance

of the alpha estimates. To account for sampling error, the investor could instead test the statistical

6

significance of the alpha estimates by means of a simple t-test. The values of the associated t-

statistic are presented for each fund in Panel B of Table 1. Using conventional levels of significance,

Shearson Appreciation, Growth Fund of America, and Sogen International Fund would be identified

as having abnormally good performance.

The advantage of using the t-statistics for the alpha estimates rather than the alpha estimates

themselves is that t-statistics account for the uncertainty in estimation of the alphas. t-statistics

are not well suited, however, for comparing the performance across di↵erent funds, as they ignore

the correlation in performance between di↵erent funds. In other words, they do not address the

possibility that two funds have significantly positive alpha estimates, but one fund clearly dominates

the other. In this situation, it may not be optimal to invest in both funds.

To address this possibility and distinguish between superior, neutral and inferior funds, one can

conduct pairwise comparisons of the funds’ performance. If, for example, two funds have a very

similar focus, the di↵erence in their average alpha might be very small and this could lead to similar

t-statistics. However, if two funds produce di↵erent alphas and have very similar risk exposures,

we would not want to label both as superior, even if both alphas are significantly positive. In fact,

a high correlation between two funds’ returns (induced by similar risk exposures) should help us in

identifying situations where one fund dominates the other. Panel C of Table 1 presents the outcome

of a stepwise procedure for comparing the performance of the four funds under consideration.12 In

Step 1, all six pairwise t-statistics for the four funds are presented. The largest (in absolute terms)

test statistic (-2.04; reported, in the table, for the funds in the rows relative to the funds in the

columns) stems from comparing Sogen International Fund and Pioneer II.13 Using a bootstrap

methodology described below, we conclude that the performance of Pioneer II is significantly worse

than that of Sogen International Fund, and we, therefore, eliminate Pioneer II.14 In Step 2, we

consider the three test statistics for pairwise comparisons of the remaining funds. The largest test

statistic (2.03) arises from the comparison of Growth Fund of America and Shearson Appreciation.

Using bootstrapped critical values, we can eliminate Shearson Appreciation. In Step 3 we only have

one comparison left. The comparison of the Sogen International Fund and Growth Fund of America

results in a test statistic of 0.29, which would not lead to elimination of any of the remaining funds

at most conventional levels of significance.

Note from this example that Pioneer II, which has a positive but statistically insignificant

alpha, could not be eliminated based on a pairwise comparison with Growth Fund of America

alone. Instead this fund was eliminated through its pairwise comparison with Sogen International

Fund. Likewise, Shearson Appreciation, which has a significantly positive alpha, could only be

eliminated after a pairwise comparison with Growth Fund of America. The fact that the two

12This stepwise approach is similar to what we will be using in our subsequent analysis.13The tests use the range statistic of Hansen, Lunde, and Nason (2011), which we discuss further below.14A key contribution of Hansen, Lunde, and Nason (2011) is to calculate p-values for all the pairwise test statistics

that remain valid in spite of the stepwise comparisons.

7

remaining funds each eliminate one of the other funds, but that neither of them can eliminate

both, is explained by the di↵erences in return correlations between the funds. Returns on Growth

Fund of America are much higher correlated with returns on Shearson Appreciation than with

returns on Sogen International Fund, while Sogen International Fund is much higher correlated

with Pioneer II than with Growth Fund of America. Hence, this example shows that both the

absolute (alpha) performance, but also the correlation in returns matter to our ability to identify

funds with superior performance.

The elimination step of the FCS uses a t-test that divides di↵erences in funds’ abnormal returns

by the standard error of this di↵erence, which tends to be lower, the higher the correlation between

the funds’ idiosyncratic returns. Hence, the ability of the FCS to eliminate inferiors fund will be

higher, (i) the lower the funds’ risk-adjusted returns relative to that of at least one other fund; and

(ii) the more highly correlated the inferior funds’ returns are with other fund returns. Conversely,

the approach is less likely to eliminate inferior funds whose returns are only weakly correlated

with that of other funds–unless, of course, their expected return is far smaller. From a portfolio

perspective, it is desirable to eliminate low-alpha funds whose returns are highly correlated with

those of at least one other fund while keeping funds whose returns are only weakly correlated with

those of other funds since it preserves diversification gains.

2.2. Predictive Alpha

For a fund to be attractive to investors, it must have a high expected risk-adjusted performance,

relative to the benchmark model that those investors use. This requires that the fund’s performance

be at least modestly predictable. Our objective is, therefore, to identify funds whose risk-adjusted

performance can be reliably predicted.

Following common practice, we compute fund i’s risk-adjusted return in period t by adjusting

its excess returns, net of the T-bill rate, Ri,t, for its exposure to a set of risk factors, zt :

Ri,t = ↵i,t + �0i,tzt + "i,t. (1)

Here "i,t ⇠ (0,�2

"i) is the fund’s idiosyncratic return, �i,t measures the fund’s exposure to the

common risk factors, while ↵i,t measures its risk-adjusted (abnormal) performance at time t. The

model in equation (1) is quite general as it allows both ↵it and �it to vary over time. If a fund’s

alpha is constant over time, the fund’s average historical performance can be used to compute its

expected future performance. Conversely, if a fund’s abnormal performance changes over time, we

need to model how such changes evolve.

Let ↵̂i,t|t�1

be the expected value of fund i’s alpha during period t based on information available

at time t � 1. To determine if ↵̂i,t|t�1

reliably predicts fund i’s performance in period t, consider

8

the following “predictive alpha”:

Pi,t = (Ri,t � �̂0i,tzt)⇥ sign(↵̂i,t|t�1

). (2)

Here the sign function sign(•) equals +1 if the argument is positive, -1 if the argument is negative,

or 0 if the argument is zero. Pi,t is the risk-adjusted return an investor would earn at time t

from using ↵̂i,t|t�1

as a buy or sell signal at time t � 1. Pi,t will be large for fund i if either

(i) a positive risk-adjusted return (Ri,t � �0i,tzt > 0) is anticipated by a positive alpha estimate

(↵̂i,t|t�1

> 0), or (ii) a negative risk-adjusted return (Ri,t � �0i,tzt < 0) is anticipated by a negative

alpha estimate (↵̂i,t|t�1

< 0). Conversely, the objective in (2) penalizes funds with positive alpha

forecasts but negative future risk-adjusted returns, or vice versa. Predictive alpha measures the

risk-adjusted return an investor would have earned from following the “directional” information in

the alpha forecast, buying if the alpha forecast is positive, otherwise selling. It preserves scale as it

is measured in return units and rewards (penalizes) alpha forecasts associated with higher returns

(larger losses) for the investor.15

The predictive alpha measure can also be interpreted as the realized alpha, conditional on the

sign of its predicted value. The measure is symmetric as it rewards correct forecasts of both positive

and negative excess returns. When we apply the measure to select funds with superior performance,

we therefore limit our attention to funds whose future predicted alphas are positive.

We estimate fund i’s predictive alpha at time t using the sample average of (2):

P̄i,t =1

t� ti0

tX

⌧=ti0+1

Pi,⌧ =1

t� ti0

tX

⌧=ti0+1

(Ri,⌧ � �̂0i,⌧z⌧ )⇥ sign(↵̂i,⌧ |⌧�1

). (3)

Here, ↵̂i,⌧ |⌧�1

is the forecast of ↵i,⌧ based on information available at time ⌧ � 1, and �̂0i,⌧ are

least-squares estimates of �0i, using data only up to time ⌧ . Finally, ti0 + 1 is the starting point

of the sample used to estimate the ith fund’s predictive alpha performance up to time t, P̄i,t. We

estimate the average predictive alpha on at least 12 monthly return observations, but allow up to

60 observations to be included in the estimate if available.

2.3. Fund Confidence Set

Our data contain almost 3,000 funds whose performance needs to be pairwise compared at each

point in time. This introduces a complicated multiple hypothesis testing problem, which we address

by applying the model confidence set (MCS) approach of HLN. This approach is designed to choose

the set of “best” forecasting models from a larger set of candidate models and so needs to be modified

15Appendix A considers a range of alternative specifications for the predictive alpha measure.

9

for our setting. Most obviously, the object of interest in our analysis is not a model, but a model

applied to a fund’s return performance, and, so, we label our approach the Fund Confidence Set

(FCS). We next describe how the approach works.

Our goal is to select a set of funds which, with a certain probability, contains the best fund–or

set of funds, if multiple funds are believed to have identical performance. The approach relies on

an equivalence test and an elimination rule. Let F0

t = {F1t, ..., Fnt} be the initial set of funds under

consideration while Pi,t, given by equation (2), measures fund i’s performance in period t. The

di↵erence between the performance of funds i and j at time t is then

dij,t = Pi,t � Pj,t , i, j 2 F0

t . (4)

Defining µij = E[dij,t] as the expected di↵erence in the performance of funds i and j, we prefer fund

i to fund j if µij > 0; both funds are judged to be equally good if µij = 0. The set of “superior”

funds at time t, F⇤t , consists of those funds that are not dominated by any other funds in F0

t , i.e.,

F⇤t = {i 2 F0

t : µij � 0 for all j 2 F0

t }. The FCS approach identifies F⇤t by means of a sequence of

tests, each of which eliminates the fund deemed to be worst relative to another fund in the current

set of surviving funds, Ft ✓ F0

t –provided that this di↵erence is statistically significant. Each round

of this procedure tests the null hypothesis of equal performance

H0,Ft : µij = 0, for all i, j 2 Ft, (5)

against the alternative hypothesis that the expected performance di↵ers for at least two funds:

HA,Ft : µij 6= 0 for some i, j 2 Ft. (6)

Following HLN, we define the Fund Confidence Set (FCS) as any subset of F0

t that contains F⇤t

with a certain probability, 1� �, where � is the size of the test.

With these definitions in place, we next explain how the algorithm for constructing the FCS

works. The first step sets Ft = F0

t , the full list of funds under consideration at time t. The second

step uses an equivalence test to test H0,Ft : µij = 0 for all i, j 2 F0

t at a critical level �. If H0,Ft

is accepted, the FCS is F̂⇤t = Ft. If, instead, H

0,Ft gets rejected, the elimination rule ejects one

fund from Ft, and the procedure is repeated on the reduced set of funds. The procedure continues

until the equivalence test does not reject, and, so, no additional funds need to be eliminated. The

remaining set of funds in this final step is F̂⇤t .

To choose whether or not to eliminate individual funds, we use equations (3) and (4) and

estimate the performance of fund i relative to fund j as d̄ij = t�1

Pt⌧=1

dij,⌧ . Next, we divide this

10

measure by its standard error,qdvar(d̄ij), to obtain a t-test16

tij =d̄ijqdvar(d̄ij)

. (7)

As in HLN, we base the test of H0,Ft on the range statistic

TFt = maxi,j2Ft

|tij |, (8)

which finds the largest t-statistic, chosen among the many pairwise t-tests in (7).

Under assumptions listed in HLN, the set of pairwise t-tests, tij , are asymptotically joint-

normally distributed with unknown covariance matrix, ⌦. Because so many pairwise test statistics

are being compared, the resulting test statistic, TFt , has a non-standard asymptotic distribution

whose critical values can be bootstrapped using the approach of White (2000). From these draws,

the following sequential elimination rule is used to identify the fund (i) with the worst estimated

performance measured relative to some other fund (j) as the candidate for elimination:17

argmini2Ft

supj2Ft

tij . (9)

Based on (8) and (9), we purge any fund whose performance looks su�ciently poor, relative to that

of at least one other fund currently included in the FCS.18

Carrying out a large number of possibly dependent tests makes it far from trivial to control the

coverage probability of this stepwise procedure. Notably, if each round conducts a test at a fixed

critical level, �, then the final FCS will have a very di↵erent coverage probability than 1��. A key

contribution of HLN is to design a sequential procedure that can be used to control the coverage

probability, 1� �, of the FCS by dynamically adjusting the bootstrapped critical values employed

in each elimination step.19

Funds may be included in the FCS because they have a precisely estimated positive average

performance. Indeed, when the performance data allow for sharp inference, the equivalence tests

first eliminate the poor funds before questioning the superior funds. However, funds with negative

16Dividing d̄ij by its standard error gives us a pivotal test statistic with better sampling properties.17Our objective is to eliminate funds for whom our risk model has poor forecasting power, while HLN’s objective is

to eliminate the least accurate forecasting models. Accordingly, we alter the elimination rule, as compared to HLN,who use argmaxi2Ft supj2Ft

tij .18Specifically, if the FCS p-value for the fund identified by (8) is smaller than the �-quantile of the bootstrapped

distribution, then this fund is deemed inferior to at least one other fund and is eliminated.19Theorem 1 in Hansen, Lunde, and Nason (2011) establishes conditions under which the probability that a truly

superior fund is contained in the estimated FCS is greater than or equal to 1 � �, while the probability of wronglyincluding an inferior fund in F̂⇤

t asymptotically goes to zero.

11

alphas may fail to be eliminated from the FCS because their alphas are estimated with large

standard errors, which reduces tij in (7) and makes it hard to reject the null. When the performance

data does not support sharp inference, the FCS algorithm will tend to eliminate too few funds,

resulting in an over-sized set that includes many inferior funds. The trade-o↵ between these e↵ects

depends on the choice of � as we next discuss.

2.4. Choosing �

As with any inference problem, the FCS approach requires us to trade o↵ type I and type II errors.

Type I errors (false positives) are incorrect rejections of a true null, i.e., wrongly eliminating any

funds whose performance is as good as that of the best fund. Type II errors, conversely, are failures

to reject a false null hypothesis, i.e., failing to exclude a poor fund from the FCS. How these errors

are traded o↵ is controlled by the choice of the size of the equivalence test (�) used by the FCS

approach, which, therefore, is an important parameter.

Setting � high means reducing the probability of wrongly including inferior funds (i.e., increasing

the power of the equivalence test), but also implies that we stand a reduced chance of including

funds with truly superior performance. Conversely, setting � low means increasing the probability of

including both truly inferior and truly superior funds as we become more cautious about eliminating

individual funds, and the algorithm becomes less selective.

In practice, the alpha estimates of many of the funds in our sample are quite noisy and so we

choose relatively high values of �. Our choice reflects that returns data often do not have much

power to distinguish between the performance of di↵erent funds.20

In trading o↵ these e↵ects, our goal is to identify a set of funds whose expected risk-adjusted

performance is genuinely superior. We believe that this goal is especially useful for retirement plan

fiduciaries, who seek to provide, with a high level of statistical confidence, a menu of the most

promising funds for their investors, as well as fiduciaries who select managers for pension funds,

endowments, sovereign wealth funds, and other trusts.21

We, therefore, opt for a relatively high value of �, choosing � = 0.90 as our benchmark. However,

to illustrate how sensitive our results are to our particular choice of �, in robustness tests, we also

consider three alternative values (� = 0.75, 0.50, 0.10) which result in fewer funds being eliminated.

We refer to the four sets of �-values as tight (� = 0.90), medium-tight (� = 0.75), medium

(� = 0.50), and wide (� = 0.10).

20See also Harvey and Lui (2018) for a thorough discussion of the trade-o↵s between type I and type II errors infinancial decisions.

21Such fiduciaries generally wish to minimize Type 2 error (the probability of including an unskilled fund) at theexpense of allowing higher Type 1 error (the probability of not including a skilled fund).

12

2.5. Candidate set of funds

The MCS approach requires conducting all possible pairwise comparisons to determine if any model

is inferior and, if so, which model gets eliminated. A key contribution of HLN is to show that this

exhaustive protocol for testing and comparing models controls the size of the resulting step-wise

approach. This assures us that the FCS approach has well-defined properties for identifying superior

funds and eliminating inferior ones.

With almost 3,000 funds in our sample, it is, however, not feasible to conduct all possible

pairwise performance comparisons.22 One could consider alternative approaches to reducing the

number of pairwise comparisons such as picking the fund with the highest estimated P̄it (“top

fund”) and comparing other funds against this.23 This approach is likely to eliminate a large

number of funds without requiring nearly as many pairwise comparisons. Relative to this simple

and intuitive approach, the stepwise FCS approach seems quite ine�cient. A limitation of the “top

fund” approach is that its theoretical properties (e.g., controlling the size of the test) have not been

established and so it is unclear how well it would perform in practice. In Appendix B, we therefore

conduct a Monte Carlo simulation study that explores the properties of this simpler approach. We

find that the level of the associated sequence of tests cannot be controlled by this simple algorithm.

In particular, the probability of correctly including all superior funds in the set drops towards zero

as the number of superior funds increases. Comparing other funds’ alpha estimates only to the

top-ranked fund disregards that this fund’s performance is, itself, the result of random sampling

variation. Intuitively, the alpha estimate of the top-ranked fund is more likely to be biased upwards,

as a result of random sampling variation, than that of a fund ranked in the middle. The “top

fund” approach is, therefore, likely to eliminate too many funds from the equivalence (FCS) set.

Conversely, by conducting all pairwise comparisons, including seemingly redundant ones, the FCS

approach avoids anchoring the performance on a single fund’s alpha estimate and, thus, properly

accounts for the e↵ect of sampling variation on the funds’ alpha estimates.

Given these findings, as a simple way to reduce the number of comparisons, we only consider

funds with positive estimates of predictive alpha in the initial set of funds (F0

t ). Heuristically, this

can be thought of as a simple nonparametric way to eliminate funds with poor predictive alphas.

2.6. Summary of the FCS procedure

We briefly summarize the di↵erent steps that make up the FCS algorithm:

22For example, a cross-section of 3,000 funds observed over 313 months requires over 1.4 billion pairwise compar-isons. We estimate the fund confidence set using the MulCom 2.0 package for Ox; see Hansen and Lunde (2010) andDoornik (2006).

23We are grateful to a referee for suggesting this alternative method.

13

Step 1: For all funds, i, satisfying the minimal data requirements, compute alpha forecasts for

period t+ 1, ↵̂i,t+1|t.

Step 2: Discard funds with negative or zero alpha forecasts, ↵̂i,t+1|t 0.

Step 3: Evaluate the predictive alpha, Pi,t for the remaining funds.

Step 4: Select funds with positive estimates, P̄i,t.

Step 5: Estimate the FCS based on the candidate set of funds from Step 4.

Step 6: Construct a portfolio based on the funds included in the FCS.

Step 7: Obtain the return for this portfolio.

We repeat these steps at each point in time, t, during our sample.

2.7. FCS and portfolio formation

Assuming that returns are generated by a factor model, Treynor and Black (1973) show that mean-

variance e�cient portfolios of risky assets weight individual assets in proportion with their alphas,

↵i, divided by the variance of their idiosyncratic risk, �2

i , relative to that of all included funds.

Specifically, for funds i = 1, ..., n with positive alphas, ↵i > 0, the optimal weights, !⇤i , are

!⇤i /

↵i

�2

i

=IRi

�i, (10)

so the optimal portfolio weights are proportional to the information ratio, IRi, scaled by the

idiosyncratic standard deviation.

Portfolio e↵ects are seemingly ignored by the FCS approach which considers individual funds’

performance without accounting for possible diversification benefits from including funds with

small, but positive, alphas. However, the weights in (10) are idealized and, in practice, investors

must rely on estimated alphas when forming portfolios. This matters particularly for funds whose

alpha estimates are positive but close to zero so that their true alphas are more likely to be negative.

Conversely, it is less likely that the true alphas are negative for funds with large and positive alpha

t-statistics.

The t-test we use in our pairwise elimination rule in equation (7) can be viewed as the infor-

mation ratio of a long position in one fund (fund i) and a short position in another (fund j), with

positions chosen according to the sign of the predictive alpha. If the test statistic is high, either the

risk-adjusted return on fund i is high compared to that of fund j or the two are highly correlated,

or both. The low return of fund j and/or the high correlation will indicate that fund j contributes

little to the mean-variance e�cient portfolio’s information ratio. It follows that the FCS can be

seen as an elimination rule that decides whether a fund is so unlikely to improve the information

ratio of the overall portfolio, that it is tossed out. Thus, the FCS helps in controlling estimation

14

error in the portfolio formation process and it can be viewed as a natural first step in forming a

portfolio of funds with positive alpha estimates that, moreover, accounts for cross-fund correlation

in residual risk. The second step then applies mean-variance optimal weights to the funds selected

in the first-step FCS, assigning greater weight to funds with large IR values per unit of idiosyncratic

risk.

To directly assess these arguments and evaluate the practical usefulness of the FCS approach in

a portfolio context, we conduct three experiments. First, we compare the performance of the FCS

portfolio to that of a portfolio applying mean-variance optimal weights to all funds with positive

alpha estimates. If the FCS fund performs better than this broader portfolio, this suggests that

using the FCS as a first step to select those funds most likely to have positive alpha values works

well.

Second, comparing the performance of portfolios of FCS-selected funds that apply (i) optimal

weights from (10) to (ii) equal weights, we can see if di↵erences in scaled IRs (IRi/�i) across funds

included in the FCS are large enough to be exploited to improve portfolio performance. If the

di↵erences in scaled IRs are su�ciently large and can be estimated su�ciently precisely, we would

expect the optimally-weighted portfolio to produce notably larger gains than the equal-weighted

portfolio.

Third, many investors have constraints on the number of funds they can invest in. This could

force them to either select a smaller subset of the funds in the FCS (in periods where the FCS

contains many funds) or, conversely, to add more funds (in periods where the FCS contains very

few funds). We therefore also consider portfolios that are subject to holding a minimum number

of funds (e.g., n � 10) or a maximum number of funds (e.g., n 10).

In each case we use information from the fund elimination process adopted by the FCS approach

to construct a list of funds investors can choose from. Because our approach is structured around

a number of equivalence tests, if the FCS list is too long, without loss of generality, investors can

simply choose a subset of the funds selected. Conversely, if the list is too short, they could include

the last funds to be eliminated from the FCS.

3. Performance measurement model

This section introduces our approach to estimate the risk-adjusted performance of individual funds.

The performance measurement model plays an important role in the empirical analysis as no

approach can be expected to work well without accurate signals about individual funds’ future

performance. As we show below, an approach that uses both returns and fund holdings data can

provide sharper inference about alphas than an approach which uses only returns data. This, in

turn, translates into an improved ability to discriminate between truly skilled and truly unskilled

fund managers.

15

In common with much of the existing literature on mutual fund performance, we use as our

benchmark a four-factor model that, in addition to the market factor, adjusts for the size and value

factors of Fama and French (1993) and the momentum factor of Carhart (1997): The benchmark

four-factor model takes the form

Rit = ↵i + �0izt + "it. (11)

Here Rit is the monthly return on fund i, measured in excess of a 1-month T-bill rate, and zt =

(Rmt, SMBt, HMLt,MOMt)0 where Rmt is the return on the market portfolio in excess of a 1-

month T-bill rate, SMBt and HMLt are the small-minus-big equity market capitalization and

value-minus-growth factors of Fama and French (1993), and MOMt is the momentum factor of

Carhart (1997), constructed as the return di↵erential on portfolios comprising winner versus loser

stocks, tracked over the previous 12 months.

Following common practice, we allow for slowly-evolving shifts in mutual fund performance and

risk exposures by estimating ✓i = (↵i �0i)0 on a rolling 60-month data window.

3.1. Time-varying skills

We generalize (11) in two ways. First, following Mamaysky, Spiegel, and Zhang (2007, 2008), we

assume that managers receive information (unobserved to the econometrician) that is correlated

with future returns and gives rise to a time-varying component in fund performance. Second, we

introduce a generalized framework that combines information from past returns with holdings data

to more accurately extract an estimate of fund performance.

Individual funds’ alphas are value-weighted averages of their stock-level alphas, so our analysis

starts by decomposing the excess return of each stock, rjt, into a risk-adjusted return component,

↵jt, a systematic return component �0jzt, and an idiosyncratic return component, "jt.24 We stack

these return components into Nt⇥1 vectors ↵t and "t and an Nt⇥4 matrix of betas, �, where Nt is

the number of stocks in existence at time t. Because abnormal returns are likely to be temporary,

we allow individual stocks’ alphas to vary over time.

Fund returns can be computed by summing across individual stock returns, rt, weighted by the

funds’ ex-ante portfolio weights measured at the end of time t� 1, !t�1

. The excess return of fund

i, net of the risk-free rate, transaction costs, fees and expenses, ki, is given by

Rit = !0it�1

(↵t + �zt + "t)� ki ⌘ ↵it + �0itzt + "it, "it ⇠ iidN(0,�2

"), (12)

where ↵it = !0it�1

↵t � ki, �it= !0it�1

�, and "it = !0it�1

"t.

24Following Mamaysky, Spiegel, and Zhang (2008), we assume that stock betas are constant, although this assump-tion can be relaxed. Note that although individual stock betas are assumed constant, fund betas will be time-varyingbecause of changes in the portfolio weights.

16

Following Mamaysky, Spiegel, and Zhang (2008), we capture individual funds’ private informa-

tion through a private (fund-specific) signal, Fit, which follows an autoregressive process,

Fit = ⌫iFit�1

+ ⌘it, ⌘it ⇠ iidN(0,�2

⌘), for ⌫i 2 [0; 1), (13)

Following Mamaysky, Spiegel, and Zhang (2008), assume that (i) fund portfolio weights are linear in

the private signal, !it�1

= !̄i+�iFit�1

; (ii) Cov("it, ⌘it) = 0; and (iii) there is a constant mapping

↵̄i from fund i’s private signal to its ability to identify abnormal performance, ↵it = ↵̄iFit�1

.

These assumptions and equation (12) imply that fund i’s beta and alpha are linear and quadratic

functions of the signal, Fit�1

, respectively:

↵it = !̄0i↵̄iFit�1

+ � 0i↵̄iF

2

it�1

� ki ⌘ aiFit�1

+ biF2

it�1

� ki, (14)

�it = !̄0i� + � 0

i�Fit�1

⌘ �̄i + ciFit�1

. (15)

Individual funds’ signals, Fit, are unobserved to the econometrician who can, however, extract an

estimate of the signal from fund returns by writing (13)-(15) in state space form:

Rit = aiFit�1

+ biF2

it�1

� ki + (�̄0i + c0iFit�1

)zt + "it (16)

Fit = ⌫iFit�1

+ ⌘it.

As explained by Mamaysky, Spiegel, and Zhang (2008), the parameters of this model can be

estimated fund-by-fund using an extended Kalman Filter that accounts for the presence of the

squared value of the state variable, Fit�1

, in equation (16).25

3.1.1. Information in fund holdings

Conventional approaches to estimating fund performance use data on past returns, which can be

very noisy and, thus, reduces our ability to identify funds with superior performance. We therefore

augment our model with information from portfolio holdings which, as is clear from equation (14),

can be used to track how a fund’s alpha evolves through time. Building on this idea, we next

generalize the methodology in Mamaysky, Spiegel, and Zhang (2008) and show that holdings-based

information can be added in the form of an additional measurement equation in the state space

representation of the model in (16). Moreover, this model can be estimated by means of an extended

Kalman filter.

Data on fund holdings allow us to perform risk-adjustment at the individual stock level by

matching each stock to a portfolio of stocks with similar sensitivity to book-to-market, market

25After normalizing one of the elements, the four-factor model requires 13 parameters to be estimated.

17

capitalization, and price momentum factors. The di↵erence between an individual stock’s return

and the return on its characteristics-matched portfolio can be used as a measure of that stock’s

abnormal return. Weighting individual stocks’ abnormal returns across all stock positions held

by a fund, we obtain the fund-level characteristic-selectivity (CS) measure of Daniel, Grinblatt,

Titman, and Wermers (1997):

CSit = !0it�1

(rt � rbt). (17)

Here, rt and rbt are vectors of excess returns on the stocks held by the fund (rt) and the cor-

responding benchmark portfolios (rbt), respectively. Benchmark portfolios are chosen to match,

as closely as possible, the characteristics of the individual stocks and so �it = �bt. Because the

characteristics-matched stocks are chosen mechanically, the average stock can be expected to have

zero alpha, ↵bt = 0. Using (14) and (17) we, therefore, have

CSit = !0it�1

�↵t + �0zt + "t �

�↵bt + �0

bzt + "bt��

= !0it�1

(↵t �↵bt) + !0it�1

(� � �b)0zt + !0

it�1

("t � "bt)

= ↵it + ki � !0it�1

↵bt + (�it � �bt)0zt + "it � "bt

= aiFit�1

+ biF2

it�1

+ "it � "bt. (18)

Because the CS measure does not depend on sample estimates of risk factor loadings, it has the

potential to generate a more accurate estimate of fund performance and, thus, to improve inference

based on the return-only models.26

Our generalized latent skill, holding-based model can be summarized as

Rit

CSit

!=

aiFit�1

+ biF 2

it�1

� ki

aiFit�1

+ biF 2

it�1

!+

�̄i + ciFit�1

0

!zt +

"it

"it � "bt

!(19)

Fit = ⌫iFit�1

+ ⌘it.

Compared to the model of Mamaysky, Spiegel, and Zhang (2008) in (16), our model uses the

additional information contained in CSit. This has the potential to make estimation and extraction

of funds’ private information component, Fit, more precise. We estimate the parameters of (19)

using the extended Kalman filter with two measurement equations; Appendix C provides further

details.26The CS measurement equation is “idealized,” in the sense that the CS performance measure will not capture

intra-quarter trading returns. The CS and return-based measures can be viewed as di↵erent estimates of the sameunderlying fund performance, observed with di↵erent measurement errors.

18

4. Performance results

This section introduces our data and analyzes the empirical performance of FCS portfolios.

4.1. Data

Our empirical analysis uses monthly returns on a sample of U.S. equity mutual funds over the

32-year period from 1980:07 to 2012:12. Individual fund returns are taken from the Center for

Research in Security Prices (CRSP) mutual fund data base, and are computed net of transaction

costs and fees.

We use quarterly holdings data from Thomson Financial to construct a three-month estimate

of CS.27 We merge the returns and holdings data using the MFLINKS files of Wermers (2000),

updated by the Wharton Research Data Services, which allows us to map the Thomson holdings

data to CRSP returns using the funds’ WFICN identifier. To reduce estimation error, we require

each fund to have at least six months of contiguous returns data and 72 months of concurrent

observations on returns and CS (not necessarily contiguous). In total, we have returns and holdings

data on 2,991 actively managed U.S. domiciled equity mutual funds.28 The number of funds

included in the analysis peaks at above 2,500 in 2005 before declining to around 1,800 in 2012.

We use time-series data on individual funds’ historical returns to obtain alpha estimates. Table 2

provides summary statistics for the cross-sectional distribution of individual fund (ex-post) alphas.

Consistent with previous academic studies (e.g., Carhart, 1997), the median fund has a negative

alpha–minus 78 bps/year for our sample. The bottom 5% of funds, ranked by alpha performance,

have a negative alpha estimate of about -44 bps/month, or just under -5.2%/year. The top 5% of

funds have an alpha estimate of 26 bps/month, or 3%/year. The cross-sectional distributions of

Sharpe and information ratios for the funds (shown in the second and third columns) also suggest

that only a small subset of funds is capable of outperforming.29

4.2. Performance of alpha-sorted portfolios

To establish a reference point for our FCS results, we consider both portfolio sorting alternatives

from the existing literature as well as new strategies chosen for their comparability with our FCS

approach in at least one dimension, e.g., the average number of funds held.

27Prior to 2004, funds were only required to report holdings every six months. However, the majority of fundsdisclosed holdings every three months to Thomson. See Wermers (1999) for details.

28Sector funds, defined as funds whose R2 is less than 70% in a four-factor regression, are excluded because thesimple four-factor risk-adjustment approach is not appropriate for these funds.

29Similar estimates of the cross-section of alphas (not reported here) are obtained for a conventional four-factormodel with constant alphas and for the basic model proposed by Mamaysky, Spiegel, and Zhang (2008).

19

First, we consider a portfolio of all funds with positive alpha forecasts. Second, to more directly

evaluate the e↵ect of applying the FCS approach for fund selection, we consider a portfolio of the

same funds from which the FCS is determined, i.e., funds with positive alpha forecasts and positive

average predictive alphas. Third, we consider subsets of the candidate set of funds which each

month rank funds on their alphas ↵̂i,t+1|t and form optimally-weighted portfolios.

We record the returns on each of these portfolios over the subsequent month. Each month, as

new data arrive, we repeat this sorting routine, form optimally-weighted portfolios based on the

funds’ updated alpha estimates, then, again, record their next-month returns. Using five years

of data to initiate the portfolio sorts and another year to obtain an estimate of the predictive

alpha, we get a time series of portfolio excess returns, Rpt, spanning the 26-year period from July

1, 1986 to December 31, 2012. This approach, while requiring 6 years of returns history for each

fund under consideration, does not induce substantial survival bias, as we do not require funds to

survive beyond a single month into the future.30

To evaluate the performance of the portfolios, we follow conventional practice and estimate

four-factor alphas on the (out-of-sample) portfolio returns, Rpt,

Rpt = ↵p + �0pzt + "pt, t = 1, . . . , T. (20)

The resulting estimates, ↵̂p, can be interpreted as the “average” portfolio alphas.

Table 3 presents performance estimates for the alpha- and predictive alpha sorts based on three

di↵erent alpha models, namely the latent skill holdings (LSH, top panel), latent skill (LS, middle

panel) and the conventional constant-alpha Carhart model (bottom panel). The table shows results

for both optimally- and equal-weighted portfolios.

We find notably weaker performance of the alpha-sorts applied to the top-ranked funds com-

pared to the predictive-alpha sorts for the latent skill and latent skill holdings models that are set

up to capture time-variation in the underlying alphas. For example, under the LS model, the alpha

of the optimally weighted portfolio consisting of the top 5% of funds goes from 2 bps/month to 33

bps/month once we move from ranking on alphas to ranking on predictive alphas. For the LSH

model we see a rise from 2 bps/month to 25 bps/month.

In turn, for the Carhart alpha estimates, there is little di↵erence between the performance

results that use the regular alpha measure (left columns) and the results based on our predictive

alpha measure (right columns).31 If alphas are genuinely constant (as assumed by the conventional

Carhart specification), the predictive alpha measure simply adds a bit of noise from the idiosyncratic

shocks. Hence, we should expect the di↵erences in the performances of the alpha and predictive

30See also Carhart (1997) for a discussion of survivorship bias.31Our estimates of the top-5-10% ranked funds’ Carhart alphas are very similar to those reported in Mamaysky,

Spiegel, and Zhang (2007) for a portfolio of similar size.

20

alpha specifications to be quite small and perhaps a little weaker for the predictive alpha measure.

This is exactly what we find.

We conclude from this evidence that using our proposed predictive alpha approach can help

improve the empirical performance of portfolios constructed using models that allow for time-

varying alphas. However, the empirical performance estimates remain relatively weak. As we next

show, much stronger results can be obtained by relaxing the assumption that the proportion of

funds used to form portfolios is fixed through time and across economic states.

4.3. Performance of superior funds

Figure 1 illustrates how, at a single point in time (November 1994), the FCS approach selects supe-

rior funds from the larger set of funds with positive forecasts of alpha. In each case, distributions

refer to average predictive alphas. Gray bars plot the distribution for the full set of eligible funds

in existence at that point. This distribution is centered close to zero, and has a wide dispersion.

We also show distributions for funds with positive forecasts of alphas (green) for next month (De-

cember 1994) and for funds with positive alpha forecasts as well as positive estimates of average

predictive alpha (red). Finally, the blue bars capture the distribution for funds included in the FCS.

Note that the FCS distribution lies to the right of the distribution for the more inclusive candidate

set of funds with positive average predictive alphas and the FCS methodology is markedly more

discriminating than an approach that simply selects funds with positive alphas.

Turning to the formal analysis, the left columns in Table 4 present performance measures for

portfolios formed each month by applying either optimal- (top four rows), equal- (middle four

rows), or winsorized optimal-weights to the set of funds included in the FCS. As in Table 3, the

sample runs from 1986:07 to 2012:12. We consider a range of values for the size of the equivalence

tests, � = {0.90, 0.75, 0.50, 0.10}, corresponding to tight, medium-tight, medium, and wide fund

confidence sets.

First, consider the results for the latent skill holdings approach (top panel). As we move from

� = 0.10 to � = 0.90, we observe a monotonically increasing pattern in alpha performance, rising

from minus 1 bps/month for the wide FCS to 66 bps/month for the tight FCS, the latter being

highly statistically significant with a t-statistic of 3.25.

These findings suggest that the marginal funds included in the wider FCS perform worse than

the funds identified by the more selective approach. Because the alpha estimates of many funds

are surrounded by large standard errors, choosing a small value of � means that the equivalence

test used to eliminate inferior funds has insu�cient power to reject the null that fund alphas are

identical; we analyze this finding in more detail below.

The sequential elimination of funds from the candidate set, Step 5 in Section 2.6, is important

to the FCS results. In particular, the alpha estimate of a portfolio consisting of the entire candidate

21

set from which our FCS is determined, is zero bps/month–much lower than the alpha of the tight

FCS specification. For comparison, we can consider a portfolio composed of the same average

proportion of funds from the candidate set ranked on average predictive alpha. This portfolio,

constructed to have the same average “breadth” as the tight FCS generates a performance of 13

bps/month–much lower than the tight FCS portfolio even though the number of funds is the same.

Selecting a narrow set of funds is, therefore, not su�cient to achieve superior performance.

Next, consider the results for the latent skill and constant alpha (Carhart) models. Using

equally-weighted portfolios, these approaches generate FCS-tight alphas of 20 and 34 bps/month

which is economically sizeable, though not statistically significant and notably lower than the values

produced by the tight FCS portfolio constructed from the latent skill holdings model (67 bps/month

with a t-statistic above three). Using portfolio weights chosen to optimize the information ratio, we

find similar performance results for the Carhart alphas, though somewhat weaker performance for

the latent skill model. This deterioration is again consistent with Mamaysky, Spiegel, and Zhang

(2007) who find that an unfiltered latent skill model can get dominated by outliers which is the

reason they introduce two filters on the alpha estimates to obtain more stable results. Consistent

with their finding, when we winsorize the portfolio weights to limit the influence of the funds with

the ten percent highest information ratios, the performance results improve substantially for the

latent skill model. Conversely, winsorization has little e↵ect on the portfolios constructed from the

LSH model, strengthening the case for using holdings information to obtain alpha estimates that

are less sensitive to outliers.

Overall, the improvements in alpha estimates observed as we move from the FCS-wide to the

FCS-tight portfolio are smaller for the constant-alpha Carhart model (an increase from 3 bps/month

to 32 bps/month) than what we observe for our more accurate latent skill holdings model (an

increase from 4 bps/month to 67 bps/month). Using more accurate alpha estimates with stronger

predictive power over future fund returns thus clearly helps the performance of the FCS approach.

These observations suggest that the large alpha values of our tight FCS approach result from

the joint e↵ect of using a more accurate approach to estimating alphas (pooling return and holdings

data) as well as using the sequential FCS fund selection approach to eliminate inferior funds. Inter-

estingly, the performance of the FCS portfolios is robust to whether these portfolios are constructed

using weights proportional to funds’ IRs or using equal weights. This confirms the importance of

the selection step conducted by the FCS–choosing the right set of superior funds is more important

than how they are weighted in a portfolio going forward.

Table 4 also reports Sharpe ratios and information ratios for the optimally-weighted and equal-

weighted portfolios. Before interpreting these measures, note that the Sharpe ratios of the portfolios

that choose weights to maximize the information ratio need not exceed the Sharpe ratios of the

equal-weighted portfolios. Conversely, in the absence of estimation error, we would expect the

information ratios of the IR-weighted portfolios to be higher than the information ratios of the

22

equal-weighted portfolios. In general, we do not find that this holds – in fact, the Sharpe ratios

and information ratios of the portfolios weighted to maximize the IR tend to be slightly smaller

than the information ratios of the equal-weighted portfolios.

To shed light on whether this finding is due to estimation errors in alphas and idiosyncratic

risk levels, we also consider a weighting scheme that winsorizes the IR-based portfolio weights,

thus reducing the weights on funds with the very largest IR estimates as explained in Appendix

A. These weights are less sensitive to estimation error than the weights that are proportional to

the funds’ estimated information ratios. Consistent with estimation error in information ratios

being the chief reason for why the IR-weighted portfolios fail to increase the information ratio of

the equal-weighted portfolios, we find that the winsorized IR-weighted portfolios tend to generate

higher information ratios than the portfolios that use weights that are proportional to the estimated

IRs. As a final data point consistent with this explanation, the average ex-ante IR-values of the

optimally-weighted, optimally IR-weighted and winsorized, and equal-weighted FCS-tight portfolios

are 1.30, 1.15, and 0.78, whereas the actual (ex-post) IR values of these three portfolios are 0.74,

0.76, and 0.77. This shows that the information ratio of the optimally weighted portfolio is more

sensitive to estimation error (i.e., sees a larger percentage decline from ex-ante to ex-post IRs) than

the winsorized and equal-weighted portfolios.

4.4. Performance of Inferior FCS Funds

Next, we analyze whether the FCS approach can be used to identify funds with inferior performance.

To this end we need only to redefine the candidate set of funds from Step 4 to consider funds with

negative alpha forecasts and positive average predictive alpha–the latter to ensure that a fund’s

performance is actually predictable.

The right columns in Table 4 consider the performance of a strategy that identifies funds with

negative alpha forecasts and positive average predictive alphas, followed by the use of the FCS

approach to select the set of worst-performing funds. Again, we start with the results for the latent

skill holdings model. The tight FCS portfolio generates the smallest alpha estimates–around -34

bps/month–while the medium and wide FCS portfolios generate alphas around -15 bps/month.

Similar results are obtained when we use other performance benchmarks such as the constant-

alpha, four-factor model of Carhart (1997) or the Mamaysky, Spiegel, and Zhang (2008) model that

does not use holdings information, although the results are a little less sharp for the constant-alpha

approach. Because the left tail of the performance distribution is thicker than the right tail, the

performance of the portfolios of inferior funds is less sensitive to our choice of � than portfolios of

superior funds. For inferior funds, the main e↵ect of varying � is to include or exclude funds with

slightly smaller negative performance than the worst-performing funds.

23

4.5. Time variation in fund performance

The values reported in Tables 3 and 4 are estimates of average alpha performance and thus do not

reveal if the performance of di↵erent funds is concentrated in certain states or occur over certain

periods of time. Addressing this point can help provide us with further insights into the nature

of the performance of the selected funds. Accordingly, we next explore this issue using a non-

parametric methodology designed to capture “local” time variation in portfolio alphas. Appendix

D provides further details of this approach.

Figure 2 shows the evolution through time in the risk-adjusted performance (alpha) of superior

funds included in the tight FCS portfolio (in blue), along with the performance of a portfolio of

the top 5% predictive alpha-ranked funds in the candidate set (in purple) from which we select

the FCS. The red line tracks the performance of the candidate set of funds. Finally, the green line

tracks the performance of the set of funds with positive alpha forecasts, while the black line tracks

the performance of the average fund at a given point in time. Each portfolio uses weights that are

proportional to the individual funds’ information ratios in accordance with equation (10).

In the first part of the sample (until 1994), the local alpha estimates of the FCS portfolio

fluctuate around zero. Starting in 1994, the performance of the FCS portfolio increases markedly,

before peaking at about 150 bps/month in 1999-2001. Over the same five-year period the top 5%

of funds from the candidate set also performs well, though with alphas that clearly are lower than

those of the FCS. The performance of the FCS portfolio decreases to around 40 bps/month in 2003,

fluctuates between 40 and 60 bps/month for until 2010 before briefly decreasing to zero in 2011

and bouncing back to 40 bps/month at the end of the sample. The increase in the performance

of funds included in the FCS towards the end of the sample is particularly noteworthy given the

evidence of intensified competition in the fund industry (Pastor, Stambaugh, and Taylor, 2015).

Figure 3 plots the time-series evolution in the local alpha estimates for the tight FCS portfolio

of inferior funds. This portfolio succeeds in generating negative risk-adjusted returns in the entire

sample. For most of the sample, the inferior FCS funds generate negative returns between -40 and

-20 bps/month. However, the performance of the FCS portfolio of inferior funds is particularly

poor between 1996 and 2000 and at times falls below 70 bps/month.

4.6. Technology factor

Our results up to this point use a four-factor model to compute the fund-level alpha forecasts,

compare fund performances using the FCS methodology, and, finally, evaluate fund performance.

One concern that is commonly raised when assessing results based on factor models is that they

could be a↵ected by an omitted risk factor. As we show in Section 5.1, there are times when the

FCS of superior funds is quite concentrated and loads up on technology-heavy funds, so a concern

here might be that our results are not robust to the presence of a technology factor.

24

To address this issue, and as a robustness check, we therefore include a fifth, technology index,

factor in the evaluation of the FCS portfolio.32 Funds selected by the tight FCS (� = 0.9) go on

to produce five-factor alpha estimates of 47 bps/month with a t-stat of 2.36, suggesting that our

performance results are quite robust to including a technology factor.

4.7. Alternative portfolio approaches

Earlier, we argued that the FCS can be viewed as a first step for determining the set of funds

whose alphas are most likely to truly be positive. Having identified such funds, this step can be

followed by a portfolio formation step which assigns weights on each fund so as to maximize the

overall information ratio.

Because a information-ratio maximizing investors would want to hold some money in funds with

positive alpha estimates, it is still a concern that this two-step procedure eliminates too many funds

that could have been used to enhance diversification gains and increase portfolio performance.

To address this concern, we consider two alternative portfolios. First, we consider a portfolio

that includes all funds with positive alpha forecasts. Ignoring estimation error, mean-variance

theory suggests that such funds should obtain positive weights in the optimal portfolio (equation

(10)). Panel A in Table 5 reports the performance of portfolios comprising all funds with positive

alpha estimates. Regardless of whether the funds are weighted by their scaled IR estimates or

are assigned equal weights, the risk-adjusted return performance of these portfolios is very low.

This suggests that, in practice, alpha estimation error poses an important obstacle towards the

successful implementation of mean-variance portfolio theory.

Second, we consider an iterative portfolio approach that directly determines whether funds with

small but positive alpha estimates should be included (albeit with smaller weights) in an optimal

portfolio due to diversification gains. This iterative fund-weighting approach works as follows.

First, we form a portfolio of the n funds in the FCS, using weights that are proportional to their

information ratio and, thus, designed to optimize the resulting portfolio’s information ratio. Next,

we test if this portfolio has a higher IR estimate than that of a portfolio of funds that includes

the n + 1 ranked fund–the last fund to be eliminated from the FCS–and re-calculate the optimal

portfolio weights on this expanded set of funds. If the IR of this augmented portfolio exceeds

that of the FCS portfolio by a certain threshold, we include the marginal (n+ 1) fund and form a

portfolio of n + 1 funds. Next, we repeat this step, comparing an optimally-weighted portfolio of

n+ 1 funds to an optimally-weighted portfolio of n+ 2 funds. We proceed until we can reject that

the portfolio formed by including n+ k funds fails to increase the ex-ante IR value of the portfolio

32Including the fifth factor in the forecasting and selection steps (Step 1 and Step 3 in Section 2.6) is possible, butnot practical. Our performance model already requires estimation of 14 parameters and the inclusion of an additionalfactor increases this number to 16. This poses a serious challenge to obtaining reliable parameter estimates and wouldrequire us to expand the estimation window for the five-factor model.

25

comprising n + k � 1 funds (k � 1) by the threshold value. We choose the threshold value to be

1% but also consider alternative values of 5% and 10%.

Adding another fund with a non-negative alpha estimate should not, of course, reduce the ex-

ante information ratio of the Treynor-Black weighted optimal portfolio. Due to estimation error,

however, in practice the ex-post information ratio of the iterative approach may not be higher than

that of the (one-shot) FCS approach.

Panel B in Table 5 presents results for this iterative approach using a threshold value of 1%.

Empirically, we find that the iterative approach fails to improve on the information ratios of the tight

and medium-tight FCS portfolios. However, we now find some (economically modest) improvements

in the ex-post information ratios of the medium and wide FCS portfolios constructed using our

iterative IR approach compared to the baseline FCS approach. Using higher thresholds such as a

5% or 10% to trigger the addition of funds excluded from the FCS results in portfolios that are

very similar to the original FCS portfolios.

To see if estimation error continues to explain these findings, note that the ex-ante expected IR-

value for the iterative approach applied to the tight FCS portfolio is 19% higher than the expected

IR value for the portfolio based on the original (one-shot) FCS. Hence, we might expect the iterative

approach to improve the performance of the FCS-tight portfolio by a sizeable amount (19%). In

fact, the actual information ratio of the tight FCS portfolio is lower under the iterative approach

as compared to the value for the regular FCS portfolio. This suggests that the additional funds

included by the iterative approach have alphas which are estimated with considerable error (and

thus do not get included in the FCS set). Such funds may not genuinely have positive alphas even

though they are given positive weights by the iterated IR-optimal approach.

These results highlight again that, in practice, estimation error in the information ratios used

to form optimal weights makes it di�cult to improve on the actual (ex-post) performance of the

portfolio constructed from funds included in the FCS.

As discussed previously, institutional investors frequently have restrictions on the number of

funds they can invest in. We therefore also consider two portfolio strategies that impose upper

or lower bounds on the number of funds, in each case using the ranking information from the

sequential FCS approach to determine the identity of the funds held.

For the portfolio restricted to holding a minimum of five funds (Panel C), we find a statistically

significant alpha estimate of 33 bps/month for the tight FCS portfolio.33 The alpha estimate of

the portfolio restricted to hold a minimum of 10 funds (20 bps/month; Panel D), is a bit lower, but

remains statistically significant in the equal-weighted case and is on the border of being significant

(t-statistic of 1.95) with optimal weights. Although investors clearly would have been better o↵

33Note that there is a tradeo↵ between (1) allowing the FCS to completely dictate the elimination, and (2) restrictingthe FCS to eliminate only up to a certain number of funds, then using a more restrictive (”tight”) comparison protocolbetween remaining funds.

26

without these restrictions, our FCS approach thus can be used to provide guidance for choosing

which funds to include even for investors with constraints on the minimum number of funds to

hold.

We next investigate the e↵ect of imposing a cap on the maximum number of funds allowed in

the portfolio, nmax

. At each point in time, if the number of superior funds is smaller than nmax

, the

constrained portfolio consists of all such superior funds. If the number of superior funds exceeds

nmax

, we pick nmax

funds at random, repeating this procedure to generate 1,000 portfolios. Panel

E reports results in the form of quantiles of the performance distribution of these capped FCS

portfolios. Interestingly, the median fund does better when the FCS approach is applied without

restricting the number of funds. As shown by the left-tail alpha estimates, the FCS portfolios

capped to include one fund are slightly riskier than the wider FCS portfolios capped to hold a

maximum of three or five funds. For the FCS portfolios capped at one, three and five funds,

respectively, there is a 5% chance of getting an alpha estimate of 48, 57, and 59 bps/month or

less. The narrower FCS portfolios also have slightly greater upside, with a 5% chance of obtaining

an alpha estimate of at least 85, 78, and 74 bps/month for the FCS portfolios capped at one,

three and five funds, respectively. The wider spread of the narrower portfolios is what we would

expect due to the e↵ect of diversification across the actively-managed funds. Interestingly, all

alpha quantiles–even those in the far left tail (5%)–of these concentrated portfolios remain highly

statistically significant. Furthermore, the capped portfolios obtain attractive performance with

Sharpe ratios and information ratios of 0.46 or higher even in the far left tail.

In addition to restrictions on the number of funds, some managers are also restricted to certain

investment styles. Our approach can also be applied to such cases. For example, applying our

approach to choose from large growth funds, the tight FCS set of superior funds generates an alpha

estimate of 47 bps/month with a t-statistic of 2.17. Choosing funds from this narrower style set,

on average, the superior FCS portfolio includes nine large growth funds.

We conclude from these results that our FCS methodology can be combined with a variety of

common constraints on portfolio compositions to produce attractive performance results.

4.8. Fund performance in high and low volatility states

Kacperczyk, van Nieuwerburgh, and Veldkamp (2016) analyze mutual funds’ allocation of attention

in a setting with multiple risky assets. Assuming that uncertainty about the aggregate risk factors

is su�ciently large, their analysis shows that an increase in the variance of the aggregate risk

factors increases (i) dispersion in fund portfolio holdings; (ii) dispersion in fund excess returns

(Proposition 3); and (iii) excess returns for skilled funds (Proposition 5). Intuitively, rewards from

processing information are higher in states where asset payo↵s are highly volatile, giving skilled

investors stronger incentives to allocate extra attention to their portfolio decisions in such states.

27

Conversely, unskilled investors can either not increase their attention (noise traders) or face higher

costs from doing so, with the result that performance di↵erentials between skilled and unskilled

funds increases during periods of high volatility.

To test the first two predictions (wider dispersion in portfolio holdings and returns), we compute

the cross-sectional dispersion in industry exposure across the funds in our sample. At each point

in time, the dispersion measure is computed relative to the average industry exposure across all

funds. We then sort the sample into three groups, according to whether the aggregate (market)

volatility is low, medium or high, assigning one-third of the total sample to each volatility bin.

Panel A in Table 6 (left column) shows that the dispersion in industry concentration–computed

using holdings in 48 industries–across funds is marginally higher in high-risk than in low-risk

states.34 However, with a p-value of 0.27, the di↵erence in mean industry concentration across

states with high and low aggregate volatility is not statistically significant.

Consistent with the prediction that excess returns should be more dispersed across funds during

times of high volatility, the right column of Panel A in Table 6 shows that during periods with

high aggregate risk the dispersion in the CS measure is more than three times greater (9.02 versus

2.57) than during periods with low aggregate risk. Moreover, this di↵erence in dispersion across the

high and low volatility states is highly statistically significant. Since the CS measure is constructed

from funds’ individual security holdings, this finding is consistent with the cross-sectional dispersion

increasing during times of high volatility due to more dispersion in individual funds’ stock holdings.

Our FCS approach is ideally suited for testing the third prediction–that excess returns should

be higher among the most skilled funds during times with high volatility–as it seeks to identify the

set of funds with superior performance and thus, as we have seen, provides a direct estimate of the

breadth of skill among mutual funds at a given point in time. Even so, it can be challenging to

identify, ex-ante, outperforming active equity funds during periods of high stock market volatility.

Although the greater separation in fund alphas in high-volatility states should enhance our ability

to identify superior funds, test procedures are hindered by a larger level of noise in alpha point

estimates during periods with high volatility. Which of these two influences dominates depends on

how much the skilled fund managers’ performance increases during periods with higher volatility.

Panel B1 in Table 6 reports four-factor alpha estimates computed for the low, medium and high

risk samples, using a 12-month rolling window to determine the underlying volatility state. The

FCS alphas are notably higher (88 bps per month) during periods with high aggregate volatility

(left columns) than during periods with low volatility (17 bps/month), and their di↵erence (72

bps/month) is highly statistically significant and more than three times greater than the spread

computed using the portfolio of the top 5% alpha-ranked funds (“top 5%”). A similar result holds

when we sort by idiosyncratic volatility (right columns) as the alpha of the FCS portfolio is 31

34A number of 25 corresponds to an average deviation of an industry’s weight in a given fund of about 0.7%,relative to the industry’s average portfolio weight across funds.

28

bps/month in low-risk episodes but 75 bps/month during periods with high idiosyncratic risk. The

resulting high-low spread (44 bps/month) is more than twice as large as the corresponding spread

(17 bps/month) identified using the top 5% of funds.

Panel B2 of Table 6 reports the same results for a 36-month volatility forecast. The results

are very similar to those reported for the one-month horizon and the link between volatility and

performance is much stronger for the FCS-sorted funds than for portfolios of the top-5% ranked

funds.

We conclude from this evidence that performance among superior funds is notably higher during

periods with high aggregate or idiosyncratic volatility and that this e↵ect dominates any increased

noise a↵ecting the estimated alphas during such periods. The FCS approach e↵ectively identifies

the set of superior equity funds during periods when they produce their greatest risk-adjusted

return performance. Compared to these findings, the simple alpha-ranked portfolio approach yields

notably weaker results in high-volatility states.35

5. Selection of superior and inferior funds

Section 4 shows that the FCS approach can be used to endogenously identify the set of funds with

superior or inferior risk-adjusted performance. This section provides details of both the number of

funds selected by the FCS approach and of their identify.

5.1. Identifying superior funds

The top panel of Figure 4 shows the number of funds included in the FCS portfolio at each point in

time. Because this set depends on the size of the test, �, we present results for the tight, medium-

tight, medium, and wide sets, � = {0.9, 0.75, 0.5, 0.1}, but focus on the tight set (� = 0.90) in most

of our discussion. The number of funds included in the FCS fluctuates considerably over time.

Relatively few funds get selected during the 17-year period from 1993-2010 which coincides with

the best risk-adjusted performance of the superior FCS portfolio. At least for this historical period,

the FCS methodology thus succeeded in identifying a narrow set of funds with high subsequent

performance. During the last 18 months of the sample, the superior FCS set grows in size to

include more than 300 funds. This increase is caused by a large number of new funds entering our

sample in 2005 and our data requirement of a six-year initial training and estimation sample. On

average, across the full sample, the tight FCS (� = 0.90) includes 29 funds, while the medium-tight

35Kacperczyk, van Nieuwerburgh, and Veldkamp (2016) compare fund performance during recession and expansionperiods, noting that recessions tend to be periods with higher stock market volatility. We also considered splittingthe data sample using the NBER recession indicator, but found that fund performance was imprecisely estimated,partly due to the small number of recession months in our sample (34), which made the estimated recession alphaimprecise.

29

(� = 0.75), medium (� = 0.50) and wide (� = 0.10) FCS include 47, 76 and 145 funds, respectively.

Because the number of funds in our data increases over time, the bottom panel in Figure 4

plots the percentage of funds identified by the FCS approach as being superior. For the tight FCS

(� = 0.90), the percentage of included funds fluctuates between a number close to zero and 20%.

For smaller values of �, the percentage of funds included is, of course, a bit higher. On average, the

tight FCS includes 3.5% of the funds, while the medium-tight, medium and wide FCS portfolios

include 5.8, 9.5 and 17.0% of the funds, respectively.

For each fund that gets selected at least once during the sample, Figure 5 shows when this

particular fund is chosen by the medium tight (top panel) and tight (bottom panel) FCS. (The

labeling on the y-axis is arbitrary, but maps one-to-one to the fund ID, and is sorted chronologically

according to the first appearance of a particular fund in the FCS.) Regardless of the value of

�, we see examples of a single fund being selected for long spells of time. For example, only

Fidelity Select Software gets selected during 1993 and 1994 while only T-Rowe Price Media and

Telecommunications is selected between 2005 and 2007. For most of the remaining periods a broader

set of funds is selected.

We conclude that the set of superior funds identified by our approach fluctuates significantly

over time. Sometimes this set is quite broad, containing up to 20% of the funds, at other times,

the set is very narrow and contains less than a handful of funds–or even just a single fund.

5.2. Identifying inferior funds

Figure 6 shows that the set of funds with inferior performance fluctuates considerably through time,

peaking at close to 30% for the narrow FCS portfolio (� = 0.90), at other times containing 1% or

fewer of the funds. On average, the tight FCS (� = 0.90) includes 89 funds, while the medium-tight

(� = 0.75), medium (� = 0.50) and wide FCS (� = 0.10) portfolios on average include 137, 201

and 326 funds, respectively. These figures correspond to 7.6%, 12.9%, 20.1% and 33.4% of the total

number of funds, respectively. Thus, across all values of �, the set of inferior funds is broader and

includes more funds than the equivalent FCS for superior funds.

Figure 7 shows inclusion plots for individual funds with inferior performance for the medium

tight (� = 0.75, top panel) and tight (� = 0.9, bottom panel) FCS approach. We continue to see

periods during which only a single inferior fund is selected. For example, only the Alger Small Cap

Fund gets included by the tight FCS in 1996 and 1997, while, from 1999 and 2000, the tight FCS

predominantly consists of the Pacific Advisors Small Cap Fund.

Interestingly, passive index funds, such as the Vanguard S&P500, are never included by either

the (tight) superior or inferior FCS portfolios. This suggests that there always exist funds with

genuinely better or genuinely worse expected performance than a passive low-cost strategy.

30

5.3. Market volatility and breadth of the set of superior funds

The model of Kacperczyk, van Nieuwerburgh, and Veldkamp (2016) implies that skilled fund man-

agers should perform better in times of high market volatility. We may therefore expect clearer

performance signals and possibly be able to identify a narrower set of superior funds during such

times. To see whether the proportion of funds identified to have superior performance depends on

the state of the economy, we divide the sample into equal-sized terciles according to the level of

market volatility.

Panel C of Table 6 shows that more funds are identified as being superior during times of

low volatility. Conversely, and consistent with the theoretical predictions of Kacperczyk, van

Nieuwerburgh, and Veldkamp (2016), the set of superior funds is narrower in times of high volatility.

Moreover, the di↵erence in the proportions of funds selected during high and low volatility states

is statistically significant and is robust in the sense that the results hold for both aggregate and

idiosyncratic risk measures and regardless of whether we use 12- or 36-months volatility estimates.

5.4. Turnover of funds included in the FCS

As a way to illustrate how often individual funds enter and exit the FCS, we next compute the

turnover in the set of funds included in the tight FCS portfolio, and compare this to the turnover

among funds in the top and bottom decile portfolios. Specifically, we compute

Turnovert =1

2

NtX

i=1

|�wit|, (21)

where wit is the portfolio weight on fund i at time t, and �wit = wit � wit�1

measures the change

in the portfolio weight on fund i from month t� 1 to month t.

The average monthly turnover for the superior FCS portfolio is 0.38, while the corresponding

figure for the inferior FCS portfolio is 0.50. For comparison, the monthly turnover of the portfolios

of the top 5% of the candidate sets of top and bottom funds are 0.24 and 0.19, respectively. Thus,

the turnover is somewhat higher for the FCS portfolios, than for the fractile-based counterparts,

which is to be expected as the FCS portfolios consist of more funds on average.

6. Conclusion

This paper presents a new approach to selecting funds with superior performance which goes well

beyond earlier studies in that we predict the set of funds most likely to outperform in the future.

This goal is very di↵erent from predicting whether an individual fund might outperform in the

future. By conducting a large set of pairwise performance comparisons across a large set of mutual

31

funds, our approach iteratively eliminates funds with inferior performance. Our results suggest that

it is important to choose a stringent procedure that is capable of eliminating funds with inferior

performance.

Several insights emerge from our analysis. First, consistent with recent studies we find that

only a relatively narrow set of funds is capable of outperforming on a risk-adjusted basis. Second,

we find that the set of funds identified ex-ante to have superior performance subsequently goes

on to generate risk-adjusted returns that are substantially higher than those obtained from simple

alpha-ranked portfolios of funds. Clearly there is substantial heterogeneity in performance even

among the funds with the highest alpha estimates.

Third, because of the considerable sampling error surrounding estimates of individual funds’

alphas, our results show that it can be beneficial to combine funds’ return records with informa-

tion obtained from their holdings to obtain su�ciently accurate performance estimates making it

possible to discriminate superior from inferior funds.

Fourth, the proportion of funds–as well as the identify of the individual funds–deemed to be

superior varies considerably over time. Consistent with predictions from the theoretical analysis in

Kacperczyk, van Nieuwerburgh, and Veldkamp (2016), we find that the cross-sectional dispersion

in fund performance increases in states with high market volatility and that the performance of

funds identified as being superior also rises when aggregate (or idiosyncratic) volatility is high.

This suggests that the payo↵s to mutual funds from allocating more attention to the stock market

is higher during such periods.

Fifth and finally, the performance of the funds included in the superior fund confidence set is

notably higher during periods with high aggregate or idiosyncratic volatility than during periods

with low volatility, suggesting that the best managers are able to exploit more volatile markets to

enhance their risk-adjusted returns.

32

Internet Appendix A: Performance for di↵erent alpha specifications

This appendix shows results for di↵erent specifications of the predictive alpha measure in (2). We

consider a number of specifications in order to better understand the importance of each component

of the predictive alpha specification and their combination. The alternative specifications are listed

below with empirical results presented in Table A.1.

P (1)

i,t = ↵̂i,t|t�1

P (2)

i,t = Ri,t � �̂0i,tzt

P (3)

i,t =

8<

:↵̂i,t|t�1

⇥ sign(Ri,t � �̂0i,tzt) if � 0.02 < ↵̂i,t|t�1

< 0.02

�1 otherwise

P (4)

i,t = ↵̂i,t|t�1

⇥ sign(Ri,t � �̂0i,tzt) where

8<

:↵̂i,t|t�1

= q↵̂(0.05) if q↵̂(0.05) > ↵̂i,t|t�1

↵̂i,t|t�1

= q↵̂(0.95) if q↵̂(0.95) < ↵̂i,t|t�1

P (5)

i,t = (Ri,t � �̂0i,tzt)⇥

✓2

1 + exp(��↵̂i,t|t�1

)� 1

◆

P (6)

i,t = (Ri,t � �̂0i,tzt)⇥ sign(↵̂i,t|t�1

)⇥ exp(��|↵̂i,t|t�1

|)

P (7)

i,t = (Ri,t � �̂0i,tzt)⇥

�2�(↵̂i,t|t�1

)� 1�

P (8)

i,t = (Ri,t � �̂0i,tzt)↵̂i,t|t�1

where

8<

:↵̂i,t|t�1

= q↵̂(0.05) if q↵̂(0.05) > ↵̂i,t|t�1

↵̂i,t|t�1

= q↵̂(0.95) if q↵̂(0.95) < ↵̂i,t|t�1

Here q↵̂(p) denotes the p-th quantile of the cross-sectional distribution of ↵̂, �(x) is the CDF

of a standard normal distribution, and � is a tuning parameter.

The first specification only uses the alpha forecast. This model performs poorly and leads to a

very small number of funds being selected with estimation noise and outliers dominating the fund

selection process. The second specification simply uses the risk-adjusted fund return, controlling

for common risk factors. Again, this approach performs poorly because there is no signal about

manager skill. The third and fourth specifications are based on the alpha forecast multiplied by

the sign of the realized return and thus represent di↵erent ways of dealing with outliers. The third

model eliminates funds with large forecasts, using the elimination rule introduced in Mamaysky,

Spiegel, and Zhang (2007). This improves results considerably, but the performance remains in-

significant in statistical terms. The fourth model uses a winsorization strategy which produces

significant performance for the tight and medium-tight specifications. These results indicate that

it is important to limit the influence of outliers in the alpha estimates. Our predictive alpha spec-

ification in (2) accomplishes this by utilizing only the sign of the forecast, thus clearly limiting

33

the influence of outliers in alpha forecasts since all positive (negative) forecasts receive the same

weight. Models 5-8 present alternatives ways to reduce the sensitivity to extreme alpha estimates.

Model 5 places smaller weights on the returns of funds with low alpha forecasts while also ensuring

that funds with implausibly high alpha forecasts do not receive too large weights. Model 6 puts

lower weights on very high forecasts of alpha. Model 7 uses the CDF of the normal distribution

to assign weights, ensuring that small alpha forecasts receive a low weight while, conversely, large

alpha forecasts are not weighted too heavily. Finally, Model 8 uses a winsorization scheme in place

of the sign function used in our specification in (2). Specifications 5-8 perform very similarly to

our preferred specification. Some perform better and some perform worse. We conclude from this

that the performance documented in the main part of the manuscript is not unique to the speci-

fication in (2), but reflects a broader finding about the importance of exploiting predictability in

risk-adjusted returns while simultaneously controlling for outliers in the alpha forecasts.

As illustrated in this appendix, it is important to limit the influence of the largest alpha esti-

mates. This can also be true when forming portfolios based on funds with extreme IRs which tend

to receive very large weights. A simple way to deal with this issue is to winsorize the distribution

of IRs included in the FCS to limit the influence of the funds with the largest ratios. This win-

sorization scheme is only used if explicitly stated by labelling the results as ”optimally weighted

portfolio (winsorized).”

Internet Appendix B: Alternative fund selection algorithm

This appendix considers the properties of the MCS approach–which requires conducting an all

possible pairwise model comparisons–and the simpler “top fund” approach which identifies the

best-performing model and eliminates as many models as it can by comparing them against this

fund.

Since analytical results are generally not feasible, we use Monte Carlo simulations to compare

the two approaches. Our simulation study uses the following setup. Consider 100 funds whose mean

returns are chosen such that Ns of the funds are superior in the sense that they have higher means.

We accomplish this by letting the first Ns funds have a mean return of 1 while the remaining

100 � Ns funds have a mean return of 0.25. All fund returns are normally distributed with a

standard deviation of 1 and are uncorrelated across funds. Our analysis assumes a 10% significance

level (size).

Our simulations check whether the first Ns funds—those whose mean returns are genuinely

higher—are selected as being superior by the MCS methodology. For the “top comparison” proce-

dure, we first identify the fund with the highest mean return, then calculate all 99 t–statistics by

comparing the top fund to the remaining ones. Finally, we eliminate all funds with a t�statistic

significantly greater than the critical value of a one-sided t�test; since we use the highest mean

return, we know that all t�statistics are positive and so can apply a one-sided test. Next, we

34

consider the fund with the second highest mean and repeat the elimination steps. We continue

until no more funds are eliminated. Finally, we check whether the first Ns funds remain in the set

of funds that have not been eliminated. We repeat this procedure 100 times to construct 100 sets

of selected funds for the two methods.

Figure B.1 shows the fraction of the 100 simulations in which all the truly superior funds (Ns)

are included as we vary the number of truly superior funds (shown on the x-axis) from Ns = 1 to

Ns = 10. The top and bottom panels assume sample sizes of 60 and 120 observations, respectively.

The red line tracks the level of the FCS; the blue line tracks the level of the iterative elimination

procedure. The green line is simply one minus the nominal level of 10% (0.90) and serves as a

reference point as tests with the right size should closely mirror this line.

We observe the following. In the presence of a single superior fund (Ns = 1), both the FCS and

the “top comparison” methods perform very well. However, as the number of truly superior funds

(Ns) increases, the performance of the iterative elimination approach deteriorates in the sense that

it fails to correctly include all Ns funds. Conversely, the FCS approach continues to perform well

regardless of whether Ns is small or large.

Internet Appendix C: Estimation and prediction of fund performance

This appendix explains how we estimate the unknown parameters of the latent skill models and

generate predictions of the conditional alpha.

For each fund, i, we observe a sample of excess returns, Rit. We cast the return model into

state space form as follows:

Rit = aiFit�1

+ biF2

it�1

� ki + (�̄0i + c0iFit�1

)zt + "it

= Git(Fit�1

) + "it,

Fit = ⌫iFit�1

+ ⌘it.

We focus on models where Rit is a linear function of the signal. Define F̂it|t�1

and Pit|t�1

as

the conditional mean and variance of the ith fund’s signal, given information at time t � 1. The

extended Kalman filter relies on a linear approximation of Git(Fit�1

) around F̂it�1|t�2

,

Git(Fit�1

) ⇡ Git(F̂it�1|t�2

) +GF,it(Fit�1

� F̂it�1|t�2

),

where

GF,it =@Git(Fit�1

)

@Fit�1

�����Fit�1=

ˆFit�1|t�2

.

Given starting values for F̂i1|0 and Pi1|0, the following recursions constitute the extended Kalman

35

filter:

vit = Rit �Git(F̂it�1|t�2

),

F̂i,t�1|t�1

= F̂it�1|t�2

+ Pit�1|t�2

G0F,it�1

K�1

it�1

vit�1

,

F̂it|t�1

= ⌫iF̂i,t�1|t�1

,

Kit = GF,itPit�1|t�2

G0F,it + "2it,

Pi,t�1|t�1

= Pit�1|t�2

� Pit�1|t�2

G0F,it�1

K�1

it�1

GF,it�1

Pit�1|t�2

,

Pit|t�1

= ⌫2iPi,t�1|t�1

+ ⌘2it�1

.

Using information up to time t � 1, we can estimate the parameters of the latent skill models

presented in Section 3. Let ✓̂i,t�1

denote the parameter estimates based on time t� 1 information.

We use the Kalman filter to forecast the signal one step ahead:

F̂i,t|t�1

= F̂i,t|t�1

(✓̂i,t�1

).

For each fund, i = 1, ..., Nt, we also predict the alpha one step ahead

↵̂i,t|t�1

= ↵̂i,t|t�1

(F̂i,t|t�1

).

The forecast of alpha at time t, given information at time t � 1, is therefore a function of the

forecast of the signal and the parameter estimates available at time t� 1.

Internet Appendix D: Local estimates of fund performance

This appendix shows how we generate non-parametric estimates of local (in time) return perfor-

mance.

To track variation in the performance of portfolios over time, we use a flexible, nonparametric

approach that allows for time-varying alpha performance, as well as time-varying factor exposures

through the following smooth time-varying parameter model:

Rpt = ↵p(t/T ) + �0p(t/T )zt + "pt, t = 1, . . . , T. (22)

Here ↵p(·) and �p(·) are unknown smooth functions that are allowed to depend on the sample

“fraction”, t/T , and, thus, can vary over time.36 To see how we can nonparametrically estimate

the parameters, define the vector of regressors Xt = (1 zt) and parameters ✓p(t/T ) = (↵p(t/T )

36Technically, the ↵p(·) and �p(·) functions allow for a finite number of discontinuities.

36

�0p(t/T ))

0, and rewrite equation (22) as

Rpt = X0t✓p(t/T ) + "pt. (23)

The parameters ✓p(t/T ) can be estimated by means of a two-step procedure that first considers

the OLS estimator �̂p = (�̂p0, �̂p1)0 of the transformed model

k1/2st Rps = k1/2st X0s�p0 + k1/2st

✓s� t

T

◆X0

s�p1 + "ps, s = 1, . . . , T, (24)

where kst = k( s�tTh ) is a kernel function, and h is the bandwidth.37 In the second step, we construct

an estimator of ↵pt = ↵p(t/T ) as

↵̂pt = (e⌦ I)�̂p, (25)

where e = (1,0), I is an identity matrix, and ⌦ denotes the Kronecker product; see Cai (2007)

and Chen and Hong (2012) for further discussion of this approach, and its ability to capture time

variation in parameter estimates.

The estimate ↵̂p,t from (25) portrays the evolution in the performance of the di↵erent portfolios

in a way that does not “average out” potentially interesting time-variation in ↵p. This can be

contrasted with the conventional full-sample approach or even a rolling-window procedure which

does not take into account how much the performance varies over time.

37Following Chen and Hong (2012), we set h = T�1/5/p12.

37

References

Avramov, D., Wermers, R., 2006. Investing in mutual funds when returns are predictable. Journal

of Financial Economics 81, 339–377.

Banegas, A., Gillen, B., Timmermann, A., Wermers, R., 2013. The cross-section of conditional

mutual fund performance in European stock markets. Journal of Financial Economics 108, 269–

726.

Barras, L., Scaillet, O., Wermers, R., 2010, False discoveries in mutual fund performance: Measur-

ing luck in estimated alphas. The Journal of Finance 65, 179-216.

Berk, J.B., Green, R.C., 2004, Mutual fund flows and performance in rational markets. Journal of

Political Economy 112, 1269-1295.

Bollen, N., Busse, J., 2004. Short-term persistence in mutual fund performance. Review of Financial

Studies 18, 569–597.

Cai, Z., 2007. Trending time-varying coe�cient time series models with serially correlated errors.

Journal of Econometrics 136, 163–188.

Carhart, M., 1997. On persistence in mutual fund performance. The Journal of Finance 52, 569–597.

Chen, B., Hong, Y., 2012. Testing for smooth structural changes in time series models via nonpara-

metric regression. Econometrica 80, 1157–1183.

Christopherson, J., Ferson, W., Glassman, D., 1998. Conditioning manager alphas on economic

information: Another look at the persistence of performance. Review of Financial Studies 11,

111–142.

Cremers, M., Petajisto, A., 2009, How Active is Your Fund Manager? A new measure that predicts

performance. Review of Financial Studies 22(8), 3329-3365.

Daniel, K., Grinblatt, M., Titman, S., Wermers, R., 1997. Measuring mutual fund performance

with characteristic-based benchmarks. The Journal of Finance 52, 1035–1058.

Doornik, J., 2006. Object-oriented matrix programming using Ox, 3rd Edition. London: Timberlake

Consultants Press and Oxford: www.doornik.com.

Fama, E.F., French, K.R., 1993, Common risk factors in the returns on stocks and bonds. Journal

of Financial Economics 33, 427–465

Ferson, W.E., Schadt, R.W., 1996, Measuring fund strategy and performance in changing economic

conditions. The Journal of Finance 51, 425–461.

38

Garleanu, N., Pedersen, L.H., 2018, E�ciently ine�cient markets for assets and asset management.

The Journal of Finance 73, 1663–1712.

Glode, V., Hollifield, B., Kacperczyk, M., Kogan, S., 2011. Time-varying predictability in mutual

fund returns. Unpublished Manuscript, Wharton School.

Hansen, P., Lunde, A., 2010. Mulcom 2.0, econometric toolkit for multiple comparisons.

Hansen, P., Lunde, A., Nason, J., 2011. The model confidence set. Econometrica 2 (79), 453–497.

Harvey, C.R., Liu, Y., 2018, False (and Missed) Discoveries in financial economics. Unpublished

working paper, Duke.

Harvey, C.R., Liu, Y., 2019, Cross-sectional alpha dispersion and performance evaluation. Journal

of Financial Economics, Forthcoming.

Hoberg, G., Kumar, N., Prabhala, N., 2018. Mutual fund competition, managerial skill, and alpha

persistence, Review of Financial Studies 31, 1896–1929.

Kacperczyk, M., Sialm, C., Zheng, L., 2005, On the industry concentration of actively managed

equity mutual funds. The Journal of Finance 60, 1983-2012.

Kacperczyk, M., Sialm, C., Zheng, L., 2008, Unobserved actions of mutual funds. Review of Finan-

cial Studies 21, 2379-2416.

Kacperczyk, M., van Nieuwerburgh, S., Veldkamp, L., 2014. Time-varying fund manager skill. The

Journal of Finance 69, 1455-1484.

Kacperczyk, M., van Nieuwerburgh, S., Veldkamp, L., 2016, A rational theory of mutual funds’

attention allocation. Econometrica 84(2), 571-626.

Kosowski, R., Timmermann, A., Wermers, R., and White, H., 2006, Can Mutual Fund Stars Really

Pick Stocks? New Evidence from a Bootstrap Analysis. The Journal of Finance 61, 2551–2595.

Mamaysky, H., Spiegel, M., Zhang, H., 2007. Improved forecasting of mutual fund alphas and betas.

Review of Finance 11, 359–400.

Mamaysky, H., Spiegel, M., Zhang, H., 2008. Estimating the dynamics of mutual fund alphas and

betas. Review of Financial Studies 21 (1), 233–264.

Pastor, L., Stambaugh, R.F., Taylor, L.A., 2015, Scale and skill in active management. Journal of

Financial Economics 116, 23-45.

Treynor, J., Black, F., 1973. How to use security analysis to improve portfolio selection. The Journal

of Business 46 (1), 66–86.

39

Wei, K., Wermers, R., Yao, T., 2015, Uncommon value: The investment performance of contrarian

funds. Management Science, October, 2394–2414.

Wermers, R., 1999, Mutual Fund Herding and the Impact on Stock Prices. The Journal of Finance

54, 581–622.

Wermers, R., 2000, Mutual fund performance: An empirical decomposition into stock-picking talent,

style, transactions costs, and expenses. The Journal of Finance 55, 1655-1695.

White, H., 2000. A reality check for data snooping. Econometrica 68 (5), 1097–1126.

40

Table 1: Example of pair-wise comparison

Panel A: alpha (x100)Shearson App. Growth F. of Am. Sogen Int. F. Pioneer II

↵ 0.14 0.46 0.54 0.10Superior X X X X

Panel B: t-statistics of alphaShearson App. Growth F. of Am. Sogen Int. F. Pioneer II

t↵ 2.11 2.98 2.45 0.70Superior X X X �

Panel C: Pair-wise t-statistics (FCS methodology)Step 1 - All

Shearson App. Growth F. of Am. Sogen Int. F. Pioneer IIShearson App. 0Growth F. of Am. 2.03 0Sogen Int. F. 1.67 0.29 0Pioneer II. -0.28 -1.81 -2.04 0

Step 2 - Pioneer II removedShearson App. Growth F. of Am. Sogen Int. F.

Shearson App. 0Growth F. of Am. 2.03 0Sogen Int. F. 1.67 0.29 0

Step 3 - Pioneer II and Shearson App.Growth F. of Am. Sogen Int. F.

Growth F. of Am. 0Sogen Int. F. 0.29 0

Shearson App. Growth F. of Am. Sogen Int. F. Pioneer IISuperior � X X �

The table presents an example of how di↵erent fund selection methodologies identify superior funds appliedto actual data for four funds obtained in November 1990. For each fund we have a time series of estimatedpredictive alpha collected over the previous 60 months. The three di↵erent panels correspond to di↵erentmethods of determining which of the funds are superior. In all panels a checkmark, X, is used to indicatethat a fund has been identified as superior. Panel A presents the average predictive alpha of each fund andlabels a fund as superior if the average is positive. In Panel B the selection is based on a standard significancetest, where the null hypothesis is that the predictive alpha is zero. Funds are labelled superior if the null isrejected at a 5% significance level. Panel C is based on a series of pair-wise tests and divided into three steps.In each step the fund in the row is tested against the fund in the column and the column fund, which isdominated most by a row fund (i.e., generates the highest t-statistic) is eliminated. The methodology labelsfunds as superior, which cannot be eliminated based on a pre-determined level of significance.

Table 2: Cross-section of alpha estimates

Latent skill holdingsalpha SR IR

Mean -0.072 0.309 -0.3495% -0.436 -0.051 -1.91910% -0.322 0.043 -1.37815% -0.180 0.200 -0.80450% -0.065 0.333 -0.30975% 0.037 0.439 0.16690% 0.157 0.535 0.64695% 0.258 0.592 1.006

This table shows the cross-sectional distribution of four-factor alpha estimates (in percent per month), sharperatio (annualized), and information ratio (annualized) obtained from monthly returns data on U.S. equitymutual funds over the period 1986:07-2012:12. Mutual fund returns are net of transaction costs and feesand are calculated in excess of a one-month T-bill rate. The four risk factors are excess returns on a marketportfolio, small-minus-big market cap and high-minus-low book-to-market value Fama-French factors and amomentum risk factor. The table reports results for a latent skill-holdings (LSH) model, which allows fora time-varying alpha and combines returns and holdings data to estimate each fund’s alpha. The extendedKalman filter is used to extract the latent signal underlying the model. The reported estimates of thecross-sectional distribution is based on the individual funds’ average alpha estimates. The cross-sectionaldistribution has been winsorized at 1%.

Table 3: Risk-adjusted performance for alpha-ranked and predictive alpha-ranked portfolios

alpha t-stat SR IR Av. no. alpha t-stat SR IR Av. no.funds funds

Latent skill holdingsAlpha sorted Predictive alpha sorted

Optimally weighted portfoliosPos. Alpha -0.01 -0.50 0.38 -0.11 351 -0.01 -0.50 0.38 -0.11 351Pos. Pred Alpha 0.00 0.09 0.40 0.02 183 0.00 0.09 0.40 0.02 183Top 10% -0.05 -0.54 0.35 -0.13 19 0.12 1.20 0.43 0.27 19Top 5% 0.02 0.20 0.40 0.04 10 0.25 1.95 0.48 0.44 10

Equal weighted portfoliosPos. Alpha 0.01 0.13 0.40 0.03 351 0.01 0.13 0.40 0.03 351Pos. Pred Alpha 0.04 0.83 0.43 0.19 183 0.04 0.83 0.43 0.19 183Top 10% 0.14 1.56 0.45 0.36 19 0.15 1.56 0.43 0.35 19Top 5% 0.17 1.56 0.47 0.34 10 0.29 2.25 0.47 0.50 10

Latent skillAlpha sorted Predictive alpha sorted

Optimally weighted portfoliosPos. Alpha -0.02 -0.15 0.33 -0.03 404 -0.02 -0.15 0.33 -0.03 404Pos. Pred Alpha -0.12 -1.01 0.25 -0.19 209 -0.12 -1.01 0.25 -0.19 209Top 10% -0.03 -0.28 0.34 -0.06 21 0.20 1.51 0.49 0.31 21Top 5% 0.02 0.18 0.37 0.04 11 0.33 2.13 0.53 0.45 11

Equal weighted portfoliosPos. Alpha -0.00 -0.09 0.39 -0.02 404 -0.00 -0.09 0.39 -0.02 404Pos. Pred Alpha 0.04 0.98 0.42 0.22 209 0.04 0.98 0.42 0.22 209Top 10% 0.14 1.60 0.44 0.35 21 0.16 1.62 0.42 0.35 21Top 5% 0.06 0.69 0.42 0.15 11 0.26 1.88 0.43 0.42 11

Constant skillAlpha sorted Predictive alpha sorted

Optimally weighted portfoliosPos. Alpha 0.01 0.39 0.40 0.09 415 0.01 0.39 0.40 0.09 415Pos. Pred Alpha 0.02 0.58 0.41 0.12 223 0.02 0.58 0.41 0.12 223Top 10% 0.16 1.81 0.40 0.39 23 0.19 1.88 0.44 0.43 23Top 5% 0.30 2.12 0.42 0.48 12 0.25 1.90 0.44 0.44 12

Equal weighted portfoliosPos. Alpha 0.01 0.26 0.40 0.06 415 0.01 0.26 0.40 0.06 415Pos. Pred Alpha 0.02 0.51 0.41 0.11 223 0.02 0.51 0.41 0.11 223Top 10% 0.22 1.90 0.40 0.42 23 0.22 1.98 0.44 0.45 23Top 5% 0.35 2.19 0.42 0.50 12 0.26 1.91 0.44 0.44 12

This table reports four-factor alphas (in percent per month) for a set of alpha-ranked and predictive alpha-ranked portfolios. Each month we rank the set of mutual funds with positive expected alpha and positiveaverage predictive alpha according to their expected alpha for the next month ahead and according to theiraverage predictive alphas. We consider two di↵erent sets of portfolio weights. One, where the weight on a fund

i is determined by↵̂i,t+h|t/�̂

2iPn

j=1 ↵̂j,t+h|t/�̂2j, for h = 1 and n funds, which is labeled optimally weighted and one, where

funds are equal weighted. We present results for the portfolio of all funds with positive forecasts of alpha(labelled Pos. Alpha), all funds with positive forecasts and positive average predictive alpha (the candidateset, labelled Pos. Pred. Alpha), and narrow subsets of the candidate set. We present results for a portfolioof the 10% highest ranking funds in the candidate set, as well as the top 5% highest ranking funds. Theranking is repeated each month during the sample 1986:07-2012:12 and so produces a time series of portfolioreturns from which the reported alpha estimates are computed. The table reports results for the model withconstant skill, latent skill, and the latent skill holdings model, which allows for a time-varying alpha andcombines returns and holdings data to estimate each fund’s alpha. Results for the alpha-sorted portfoliosare presented on the left hand side of the table, while results for the predictive alpha-sorted portfolios areon the right hand side of the table. The table reports monthly alpha estimates in percentage terms followedby t-statistics, sharpe ratio (annualized), information ratio (annualized), and the average number of fundsincluded in the portfolio.

Table 4: Risk-adjusted performance for FCS portfolios

Percent alpha t-stat SR IR Av. no. alpha t-stat SR IR Av. no.in top funds funds

Latent skill holdingsSuperior funds Inferior funds

Optimally weighted portfoliosFCS-tight 0.66 3.25 0.61 0.74 29 -0.34 -2.51 0.16 -0.62 89FCS-medium-tight 0.31 1.92 0.49 0.43 47 -0.21 -2.38 0.23 -0.46 137FCS-medium 0.06 0.59 0.40 0.12 76 -0.16 -2.10 0.29 -0.42 201FCS-wide -0.01 -0.21 0.39 -0.05 145 -0.15 -3.61 0.31 -0.81 326

Equal weighted portfoliosFCS-tight 0.67 3.41 0.60 0.77 29 -0.31 -2.40 0.17 -0.58 89FCS-medium-tight 0.33 2.07 0.48 0.46 47 -0.19 -2.31 0.24 -0.43 137FCS-medium 0.10 0.97 0.41 0.21 76 -0.12 -1.70 0.31 -0.33 201FCS-wide 0.04 0.78 0.43 0.18 145 -0.12 -2.88 0.32 -0.64 326

Optimally weighted portfolios (Winsorized)FCS-tight 0.67 3.32 0.62 0.76 29 -0.34 -2.51 0.16 -0.62 89FCS-medium-tight 0.33 2.02 0.50 0.45 47 -0.21 -2.37 0.23 -0.46 137FCS-medium 0.08 0.84 0.42 0.18 76 -0.16 -2.09 0.29 -0.42 201FCS-wide 0.02 0.29 0.42 0.07 145 -0.15 -3.57 0.31 -0.80 326

Latent skillSuperior funds Inferior funds

Optimally weighted portfoliosFCS-tight -0.08 -0.43 0.34 -0.09 54 -0.38 -2.03 0.11 -0.47 104FCS-medium-tight -0.04 -0.23 0.34 -0.05 78 -0.38 -2.48 0.13 -0.54 150FCS-medium -0.04 -0.27 0.30 -0.05 110 -0.28 -1.94 0.17 -0.42 210FCS-wide -0.11 -0.88 0.26 -0.17 171 -0.13 -1.22 0.28 -0.26 323

Equal weighted portfoliosFCS-tight 0.20 1.32 0.47 0.29 54 -0.42 -2.52 0.10 -0.63 104FCS-medium-tight 0.17 1.42 0.44 0.32 78 -0.34 -2.61 0.16 -0.61 150FCS-medium 0.06 0.72 0.40 0.15 110 -0.25 -2.22 0.20 -0.51 210FCS-wide 0.02 0.43 0.40 0.09 171 -0.12 -2.77 0.32 -0.63 323

Optimally weighted portfolios (Winsorized)FCS-tight 0.15 1.01 0.46 0.23 54 -0.38 -2.02 0.11 -0.47 104FCS-medium-tight 0.14 1.15 0.45 0.26 78 -0.38 -2.46 0.13 -0.54 150FCS-medium 0.05 0.68 0.42 0.14 110 -0.28 -1.95 0.17 -0.42 210FCS-wide 0.02 0.31 0.42 0.07 171 -0.13 -1.22 0.28 -0.26 323

Constant skillSuperior funds Inferior funds

Optimally weighted portfoliosFCS-tight 0.32 1.88 0.49 0.40 42 -0.23 -2.90 0.24 -0.53 118FCS-medium-tight 0.28 1.97 0.49 0.41 64 -0.21 -3.52 0.25 -0.75 163FCS-medium 0.09 0.98 0.42 0.20 98 -0.20 -3.96 0.26 -0.89 218FCS-wide 0.03 0.64 0.42 0.14 180 -0.15 -3.74 0.31 -0.89 327

Equal weighted portfoliosFCS-tight 0.34 1.97 0.50 0.42 42 -0.21 -2.49 0.25 -0.47 118FCS-medium-tight 0.27 1.83 0.47 0.40 64 -0.18 -2.99 0.27 -0.65 163FCS-medium 0.10 1.02 0.41 0.21 98 -0.17 -3.27 0.28 -0.76 218FCS-wide 0.03 0.50 0.41 0.11 180 -0.13 -2.97 0.32 -0.73 327

Optimally weighted portfolios (Winsorized)FCS-tight 0.32 1.87 0.49 0.40 42 -0.23 -2.89 0.24 -0.53 118FCS-medium-tight 0.28 1.95 0.48 0.41 64 -0.21 -3.50 0.25 -0.75 163FCS-medium 0.09 1.03 0.42 0.21 98 -0.20 -3.93 0.27 -0.88 218FCS-wide 0.03 0.52 0.42 0.11 180 -0.15 -3.72 0.31 -0.89 327

Caption on next page

Caption for Table 4. This table reports four-factor alphas for a set of portfolios of funds identified bythe fund confidence set (FCS) approach. Alpha estimates are in percent per month and presented withcorresponding t-statistics. The table also presents sharpe ratio (annual), information ratio (annual), and theaverage number of funds included in the portfolios. Each month we apply the FCS approach to all fundswith positive (negative) predictive alpha one month ahead to identify the set of superior (inferior) funds. Wethen form a portfolio of these funds and record its return during the following month. We consider three

di↵erent sets of portfolio weights. One where the portfolio weight on fund i is given by↵̂i,t+1|t/�̂

2iPn

j=1 ↵̂j,t+1|t/�̂2j, which

is labeled optimally weighted, one, where funds are equal weighted, and one, where the portfolio is optimallyweighted, but the weights are winsorized to limit the influence of the 10 percent highest information ratios.This procedure is repeated each month during the sample 1986:07-2012:12 and so produces a time series ofportfolio returns from which the reported four-factor alpha estimates are computed. The left panel presentsresults for the set of superior funds, while the right panel presents results for the set of inferior funds. In eachpanel the four rows report results for four di↵erent values of the tightness parameter (�) used to determinehow strict to be when eliminating funds from the FCS. The top row uses a tight choice (� = 0.90), resultingin a narrower set of funds being included, while the second, third, and fourth rows give rise to medium-tight(� = 0.75), medium (� = 0.50) and wide (� = 0.10) fund confidence sets. The table presents results for amodel assuming constant skill, the latent skill model, and the latent skill-holdings (LSH) model, which allowsfor a time-varying alpha and combines returns and holdings data to estimate each fund’s alpha.

Table 5: Risk-adjusted performance for alternative portfolios

alpha t-stat SR IR Av. no. alpha t-stat SR IR Av. no.funds funds

Panel A: Funds with positive forecastsOptimally weighted Equal weighted

Positive forecast -0.01 -0.50 0.38 -0.11 351 0.01 0.13 0.40 0.03 351

Panel B: FCS with iterative portfolio approachOptimally weighted Equal weighted

FCS-tight 0.44 3.04 0.55 0.67 31 0.50 3.58 0.56 0.79 31FCS-medium-tight 0.22 1.88 0.47 0.39 48 0.23 2.00 0.45 0.44 48FCS-medium 0.07 0.93 0.42 0.19 77 0.10 1.20 0.42 0.25 77FCS-wide -0.01 -0.11 0.39 -0.02 145 0.04 0.79 0.43 0.19 145

Panel C: FCS with minimum five fundsOptimally weighted Equal weighted

FCS-tight 0.33 2.48 0.50 0.54 31 0.31 2.58 0.47 0.56 31FCS-medium-tight 0.12 1.02 0.41 0.22 48 0.15 1.38 0.41 0.30 48FCS-medium 0.05 0.72 0.41 0.14 76 0.07 0.95 0.40 0.19 76FCS-wide -0.01 -0.21 0.39 -0.05 145 0.04 0.78 0.43 0.18 145

Panel D: FCS with minimum ten fundsOptimally weighted Equal weighted

FCS-tight 0.20 1.95 0.43 0.41 33 0.20 2.01 0.42 0.44 33FCS-medium-tight 0.09 1.03 0.39 0.21 49 0.11 1.27 0.38 0.27 49FCS-medium 0.03 0.38 0.39 0.08 77 0.06 0.86 0.40 0.18 77FCS-wide -0.01 -0.21 0.39 -0.05 145 0.04 0.78 0.43 0.18 145

Panel E: Quantiles of performance distribution for FCS with cap on maximum number of fundsOptimally weighted Equal weighted

Maximum one fund Maximum one fund5% 0.48 2.11 0.47 0.46 0.48 2.11 0.47 0.4610% 0.52 2.24 0.49 0.49 0.52 2.24 0.49 0.4925% 0.59 2.55 0.53 0.56 0.59 2.55 0.53 0.5650% 0.67 2.93 0.57 0.64 0.67 2.93 0.57 0.6475% 0.75 3.28 0.61 0.71 0.75 3.28 0.61 0.7190% 0.81 3.59 0.65 0.78 0.81 3.59 0.65 0.7895% 0.85 3.78 0.67 0.82 0.85 3.78 0.67 0.82

Maximum three funds Maximum three funds5% 0.57 2.69 0.55 0.60 0.59 2.84 0.54 0.6310% 0.59 2.81 0.56 0.63 0.61 2.95 0.55 0.6625% 0.63 2.97 0.58 0.67 0.64 3.10 0.57 0.6950% 0.67 3.19 0.61 0.72 0.67 3.30 0.59 0.7475% 0.71 3.39 0.63 0.76 0.71 3.48 0.61 0.7890% 0.75 3.59 0.65 0.81 0.75 3.64 0.63 0.8195% 0.78 3.72 0.66 0.83 0.77 3.77 0.64 0.84

Maximum five funds Maximum five funds5% 0.59 2.83 0.57 0.64 0.61 2.99 0.56 0.6810% 0.61 2.91 0.58 0.66 0.62 3.09 0.57 0.7025% 0.63 3.05 0.59 0.69 0.65 3.21 0.58 0.7250% 0.66 3.21 0.61 0.73 0.67 3.35 0.59 0.7575% 0.70 3.37 0.62 0.76 0.70 3.49 0.61 0.7890% 0.72 3.50 0.64 0.79 0.73 3.62 0.62 0.8195% 0.74 3.60 0.65 0.81 0.74 3.69 0.63 0.83

Caption on next page

Caption for Table 5. The table presents risk-adjusted performance for di↵erent portfolios of funds. PanelA presents results for a portfolio of funds chosen each month to consist of all funds with a positive alphaforecast for the next month. For each month we estimate the FCS of superior funds and construct a portfolioof the funds identified to be superior. Panel B presents results for a iterative approach, where, at each month,we include the last fund to be eliminated in the portfolio and adjust the portfolio weights accordingly. If theextra fund improves the information ratio of the portfolio more than a pre-specified threshold we keep thefund in the portfolio and include yet another fund. We continue until the information ratio of the portfoliodoes not increase more than the threshold. Results are tabulated for a threshold of one percent. In panel Cand D we present results for a constrained version of the FCS where the methodology each month selects aminimum of five (Panel C) or ten (Panel D) funds respectively. Panel E presents results from imposing a capon the maximum number of funds included. When too many funds are included in the FCS we chose fundsfrom the set at random until we reach the cap. We construct 1.000 of such portfolios and this panel presentsselected quantiles of the performance distributions from imposing di↵erent caps.

Table 6: Dispersion and risk-adjusted performance sorted by volatility

Panel A: Dispersion in Industry Concentration and CS MeasureIndustry concentration CS measure

Aggregate risk Aggregate riskAll funds All funds

Low risk 24.943 [0.000] 2.573 [0.000]

Med. risk 25.202 [0.000] 4.669 [0.000]

High risk 25.168 [0.000] 9.022 [0.000]

High-Low 0.226 [0.268] 6.449 [0.000]

Panel B1: Dispersion of performance for superior funds (12 months)Aggregate risk Idiosyncratic risk

FCS Top 5% FCS Top 5%Low risk 0.165 [0.031] -0.125 [0.004] 0.307 [0.001] -0.074 [0.121]

Med. risk 0.261 [0.000] 0.017 [0.736] 0.251 [0.000] -0.093 [0.047]

High risk 0.880 [0.000] 0.035 [0.564] 0.749 [0.000] 0.094 [0.122]

High-Low 0.715 [0.000] 0.160 [0.032] 0.442 [0.002] 0.168 [0.030]

Panel B2: Dispersion of performance for superior funds (36 months)Aggregate risk Idiosyncratic risk

FCS Top 5% FCS Top 5%Low risk 0.093 [0.004] -0.077 [0.000] 0.145 [0.001] -0.002 [0.930]

Med. risk 0.363 [0.000] 0.018 [0.500] 0.244 [0.000] -0.095 [0.000]

High risk 1.047 [0.000] 0.236 [0.000] 1.115 [0.000] 0.273 [0.000]

High-Low 0.954 [0.000] 0.313 [0.000] 0.970 [0.000] 0.275 [0.000]

Panel C: Breadth of fund confidence set of superior funds across volatility statesAggregate risk Idiosyncratic risk

12 months 36 months 12 months 36 monthsAll 0.035 0.035 0.035 0.035Low risk 0.035 0.041 0.042 0.050Med. risk 0.049 0.046 0.040 0.044High risk. 0.023 0.024 0.025 0.016High-Low -0.013 -0.017 -0.018 -0.034p-value [0.062] [0.025] [0.016] [0.000]

Panel A of this table reports dispersion in industry concentrations and CS measure across all funds sortedinto groups according to volatility. We define the aggregate risk in period t as |�t�mt|, where �t is theaverage market beta across funds and �mt is the realized volatility of the market based on daily returns. Theidiosyncratic risk is calculated in a similar fashion. The risk measures are based on a rolling window witha length of 36 monthly observations. Dispersion in industry concentration is calculated as 1

48

P48c=1(w

ci,t �

wcavg,t)

2, where wci,t is fund i’s weight in industry c at time t, and wc

avg,t is the weight of the average fundin industry c at time t. The dispersion in the CS measure is calculated as the average squared deviationfrom a fund’s CS measure to the average CS measure across funds. Panel B1 and B2 report average alphaperformance of portfolios of superior funds identified by the fund confidence set (FCS) and the top five percentfunds from the benchmark sorting approach sorted according to the rolling 12-month and 36-month volatilityestimates, respectively. Average alpha estimates are reported in percent per month and corresponding p-values are presented in brackets. Panel C presents means of the percentage of funds identified by the tight FCSapproach as being superior across di↵erent volatility states. The percentage of funds selected are presentedfor all periods, for periods with high volatility only, periods for medium levels of volatility only, and forperiods with low volatility only. The row labelled High-Low presents the di↵erence between the breath of theset in high and low volatility period and the row labelled p-value refers to the test that equal percentages offunds are included in high and low volatility periods. Each month we apply the FCS approach to all fundswith postive expected alpha one and three months ahead and a positive average predictive alpha in orderto identify the set of superior funds. We then form a portfolio of these funds, where the weight on fund i

is given by↵̂i,t+1|t/�̂

2iPn

j=1 ↵̂j,t+1|t/�̂2j, and record its return during the following month. This procedure is repeated

each month during the sample 1986:07-2012:12 and so produces a time series of portfolio returns from whichfour-factor alpha estimates are computed based on the same 12- or 36-month rolling window used to calculatethe volatility measures.

Table A.1: Alternative specifications of predictive alpha

alpha t-stat SR IR Av.no.

alpha t-stat SR IR Av.no.

funds funds

Panel A: Pi,t = P(1)i,t Panel B: Pi,t = P

(2)i,t

FCS-tight -0.12 -0.97 0.25 -0.19 1 0.17 1.13 0.37 0.24 59FCS-medium-tight -0.13 -1.09 0.26 -0.21 2 0.12 1.00 0.39 0.22 80FCS-medium -0.13 -1.19 0.24 -0.23 2 0.09 0.97 0.40 0.22 105FCS-wide -0.09 -0.85 0.28 -0.17 3 0.03 0.53 0.40 0.12 160

Panel C: Pi,t = P(3)i,t Panel D: Pi,t = P

(4)i,t

FCS-tight 0.24 1.55 0.47 0.34 18 0.30 2.32 0.56 0.53 26FCS-medium-tight 0.15 1.15 0.45 0.27 34 0.23 2.45 0.54 0.53 42FCS-medium 0.11 1.12 0.45 0.25 55 0.09 1.30 0.46 0.28 65FCS-wide 0.04 0.56 0.42 0.14 115 0.04 0.81 0.43 0.19 126

Panel E: Pi,t = P(5)i,t Panel F: Pi,t = P

(6)i,t

� = 10 � = 2FCS-tight 0.59 2.86 0.56 0.65 26 0.71 3.58 0.61 0.81 29FCS-medium-tight 0.37 2.26 0.49 0.51 43 0.35 2.13 0.48 0.48 47FCS-medium 0.22 1.69 0.46 0.36 70 0.07 0.72 0.39 0.15 77FCS-wide 0.04 0.64 0.43 0.15 141 0.04 0.76 0.43 0.18 145

� = 5 � = 1FCS-tight 0.65 3.26 0.61 0.73 23 0.70 3.53 0.61 0.80 29FCS-medium-tight 0.40 2.35 0.51 0.53 40 0.34 2.17 0.48 0.48 47FCS-medium 0.16 1.40 0.43 0.29 67 0.06 0.63 0.39 0.14 76FCS-wide 0.04 0.74 0.43 0.18 137 0.04 0.78 0.43 0.18 145

� = 1 � = 0.5FCS-tight 0.51 2.65 0.52 0.59 15 0.68 3.47 0.60 0.79 29FCS-medium-tight 0.54 3.24 0.60 0.71 29 0.33 2.07 0.48 0.46 47FCS-medium 0.21 1.91 0.46 0.41 53 0.10 0.96 0.41 0.21 76FCS-wide 0.04 0.54 0.42 0.13 113 0.04 0.78 0.43 0.19 145

Panel G: Pi,t = P(7)i,t Panel H: Pi,t = P

(8)i,t

FCS-tight 0.60 2.94 0.55 0.66 27 0.47 2.40 0.53 0.53 14FCS-medium-tight 0.39 2.38 0.50 0.54 44 0.51 3.20 0.59 0.73 28FCS-medium 0.25 1.97 0.47 0.42 72 0.22 1.99 0.50 0.42 52FCS-wide 0.04 0.74 0.43 0.17 142 0.06 0.86 0.44 0.20 111

The table presents risk-adjusted performance for equal weighted portfolios based on eight alternative spec-ifications of the predictive alpha. Panel A presents results for a specification, where the predictive alphais simply the forecast of alpha. In Panel B, the predictive alpha is specified as the realized return for afund, controlled for common risk factors. Panel C and Panel D present results for a specification, where theforecast of alpha is multiplied by 1 or -1 depending on, whether the realized return is positive or negative,respectively. The two panel deal with outliers in di↵erent ways. Panel E-H present di↵erent alternatives toour main specifiction presented in (2). Each month we estimate the FCS based on a particular specificationof predictive alpha. We form a portfolio of the funds identified as superior and track the performance overthe following month.

Superior Funds

−0.5 0.0 0.5 1.0 1.5

0

5

10

Figure 1: Predictive alpha for top-ranked funds. The figure presents distributions of predictive alphas forfunds included in various portfolios at a single month in our sample (November 1994). The figure presentsdistributions of average predicted alphas for the top-ranked funds. The gray bars represents a portfolioconsisting of all funds in existence in December 1994, which fulfil the requirements to be included in ouranalysis. The green bars show the distribution for funds with positive alpha forecasts. The red bars showthe distribution for funds with positive alpha forecasts and positive average predictive alpha. The blue barsshow the distribution of funds included in the superior FCS assuming a narrow set (� = 0.90) and using thetime-varying latent skill and holdings performance model.

−0.5

0.0

0.5

1.0

1.5

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013

Figure 2: Time variation in alpha estimates for superior funds. This figure shows nonparametric estimates oflocal time-variation in four-factor alpha estimates (in percent per month) for a variety of portfolios consisting

of top-ranked funds. In each portfolio the weight on fund i is given by↵̂i,t+1|t/�̂

2iPn

j=1 ↵̂j,t+1|t/�̂2j. The blue line tracks the

performance of the tight FCS portfolio (� = 0.90) of superior funds based on the latent skill holdings model.The green line tracks the performance of a portfolio consisting of all funds with positive forecasts of alphawhile the red line tracks the performance of a portfolio consisting of the funds with positive alpha forecastsand positive average predictive alpha. The purple line tracks the performance of a portfolio consisting of thetop 5% of predictive alpha-ranked funds with positive alpha forecasts and positive average predictive alphas.For comparison the black line tracks the variation in the alpha of the average fund. The sample period is1986:07-2012:12.

−0.6

−0.4

−0.2

0.0

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013

Figure 3: Time variation in alpha estimates for inferior funds. This figure shows nonparametric estimates oflocal time-variation in four-factor alpha estimates (in percent per month) for a variety of portfolios consisting

of top-ranked funds. In each portfolio the weight on fund i is given by↵̂i,t+1|t/�̂

2iPn

j=1 ↵̂j,t+1|t/�̂2j. The blue line tracks the

performance of the tight FCS portfolio (� = 0.90) of inferior funds based on the latent skill holdings model.The green line tracks the performance of a portfolio consisting of all funds with negative forecasts of alphawhile the red line tracks the performance of a portfolio consisting of the funds with negative alpha forecastsand positive average predictive alpha. The purple line tracks the performance of a portfolio consisting of thebottom 5% of predictive alpha-ranked funds with negative alpha forecasts and positive average predictivealphas. For comparison the black line tracks the variation in the alpha of the average fund. The sampleperiod is 1986:07-2012:12.

Percentage of Superior Funds Included in FCS

Number of Superior Funds Included in FCS

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013

0

100

200

300

400

0

10

20

30

Figure 4: Evolution in the set of funds identified as being superior by the FCS approach. The top panelshows the evolution in the number of funds included in the tight, medium and wide fund confidence sets ofsuperior funds. The bottom panel shows the corresponding evolution in the percentage of funds identifiedas being superior by the FCS approach. Funds are selected from the set of funds with significantly positivepredictive alpha using the latent skill-holdings model with a time-varying alpha to compute each fund’s alphaestimate. Dark blue areas correspond to � = 0.90 (tight set), while lighter areas correspond to � = 0.75(medium-tight set), � = 0.50 (medium set), and � = 0.10 (wide set).

xx xxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xx xx xxxxxx xxxxxxxx x x xx xxxxxxx x xxx xxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx x xxxx xx xx xxxxx xx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxx xxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xx xxxxxxxxxxxxxxxxx x xx xxxxxxxxxx x x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxx xxxxx xxxxxxxxxxxx xxxxxxxx xxxxxxxxxxx xx xxxx xxxxx xxxxxxxxxxxxxxxxxxxx xxx xx xx xxx x xxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxx xx xxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x x xx xxxxxxxxxxxxx xxxxxxxxxx xxx xx xx xx xxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxxx xxx xxx xx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xx xx x xxxx xxxxx x xx xx xx xxxxxxxxxx xxx xxx xxxxxx xxx x xxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxx xx xxxxxxxxxx xxx xxxxxxx xxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xx xxxxxx xxxxxx x x x xxxxxxxxxxxxxxxxxxx

x

xxxxxx xxx xxxxxxxxxxxx xxxxxxxxxxxx xxx xx xx xxxxxxxxxx xxxxxxxxxxxxxxxx xxx xxxxx xxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxx x xxxxxxxx xxxxxxxxxxxxxxx x xxxxxxxxxxx xxx xxxx x x x xxxxxxxxxxxxxxxxxxxx xxxxx xx xxxxx x xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xx xx xxxx x xxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxx x xxx xxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxx xx x xxxxx xxxxxxxxxxxxxxxxx xxxx xx x x x xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxx xxxxxx xxxxxxxxxxxxxxxxxxx xxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxx x xx xxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxx xx xx x x xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxx x xxxxxxxxxx x xxxx xxx xxxxxxxxxxxxxxxxxxxxxx xxxx x xxxx xxxxxx xxx xxxx xxxxxxxxxxxxxxxxxxx x x x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxx x xx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx x xx xxxxx x xxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx x xx xxxx x xx xxx x xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxx xxx xxxx xxxxxxxxxxxxxxxxxxx xx xxxx xxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xx x xxxxxxx x xxxxxx xxx xxx xx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxx xxxx xx xxx xxx x xx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xx xx x xx xxx x xxxxxxxxxxxxxxxx xxxxxx x xxx xx xxxxxxxxxxxxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xx x xxx x xxxxx xxxxxxxxxx xxxx x xxxxxxxxxx xxxxx xxxxxxxxx xxxxxxxxxxxxx xxx xx xx xxxxxxxxx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxx xxxx xxxxxxxxxxxx xxx x xxx x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxx xxxxxxxxxxxx xxx xx x xxxx x x xxxx x xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxx xxxx xxx xxxxxxxxxxxxx xxx xx xxx x xxxxx x xxxxxxx xxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxx x xxxxx xxx x xxx xxx x x x xxxxxxxxxxxxxxxxxxxxxx

xx xx x x xxxxxxxxxxxxxxxxxxxx

xx xx xx xxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxx xxx xx xxxxxx xxxxxxxx xxxxx xxxx xxxxxxxxxx xxx xxxx x xx xxx xxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxx xxx x x x xxxxxxxxx xxxxxx xxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxx x xxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xx xxxxxxxxxxxxx xxx xxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxx xx x xx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxx x x x xxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxx xxxxxxxxxxx xx xxxx xxx xxxx xxx xx xx xxxxx xxxxxxxxxxxxxxxxxxx

x

x x xxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxx xxx xx xxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxx xxx xx xxxx x x xxxxxxx xxxxxxxxxxxxxxxx xxxxxxx xx xxxxxx x xxxxx xxxxxxx x x x xx x xxxxxxxxxxxx xxxxxx xxxx xxxxxx xxxxx x xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxx x xxx x xxxxxxxxxxxxxxxxxxxxx

x x xxxxxxxxxxxxx

x

xx x xxx x x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx

x x xxxxx xxxxxxxxxxx xxxxxxxxxxxxxxx xxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx x x xx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxx xxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxx x x x xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxx xx xxxxxxxxxxxxxxxxx

xxxxxxxx xxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxx xxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx

x

xxxxx xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxx xxxxxxxxx x xxxxxxxxxxxxxxxxxxx

x

xxx x x xxxxxxxxxxxxxxx xxxxxxxx xxxxxxxx xxxxx xxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxx

x

xxx x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xx x x xxx xx xxxxxxx xxxxxxxxx xxxx xxxxxxxxxxxx xxx x xxxxxxxx xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xx xx xxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxx xxx xxxx x x xxxxxxxxx x xxxxxxxx xxxxxxx xxx xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx xxx x x xxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxx xx xxxx x xxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxx

x

xx xxx xxxxx xxxxxxx xx xxxx xxxxx xxx xx xxxxxxxxxxxxxxxxxxxxx xxxxxx xx xx xxxxx xx xx xxxxxxxxx

xxx x xxxxxxxxx xxxxxxxxxxxxxx xxx xxxx x xxx xxxx xxxxxxxxxxx xxx xxxxxx x x xxxx xxxx xxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxx xxxxxx x x x xx xxxxxxxxxxxxxxxxxxxx

x

xxx x x xxxx xxxx x xx x x xxxxxxxxxx xxxxxx xxxx x xxxxxxxxxxx xxxxx xxxxxxxx xxxxxxxxxxx xxxxxxxx xxxxxxxxxxxxxxxx xxxxx xxxxxxxx xxxxxxxxxx xxxxx xxxxxxxx x xxxxx x xxxxxxxxxxxxxxxxxxxxxxx x xx xxxx x x xx xxxx xxxxxxxxxxxxxxxxx xx xxxxxxxxx x xxxx

xxxx x xx xxx xxxxxxx x xxxxxxxxxx x x xx xxxxxxxx x xxxxxxxxxxxxxxxxxxxx x x xxxx xxx x xxx xxxxx x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxx xxxxxxxxxxxxxx x xxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxx xx xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxx xx xx xxxx xxxxx xxxxxxxxxxxxxxxx xx xxx xxxxxxxxx x xxxxxxxxxxx x xxxxxxxx xx xx xxxxxxxxxxxx x xxxxxxxx xx x xx xxxxxx x x xx

xx x xxxxx xx x xx x x xxx xx x xx x x xx xxxxxxxxx xxxxxxx xxxxxx xxxxxxxxx xxxxxxxxxxxxx xxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx x xxxx x x xxxxxxxxxxxxxxxxxxx xxx xxxx x x x xx

xxxxxxxxx x xxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx x xxxxxxxx xxxxxxxxx x xxxxx x xxxx x xxxxxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxxxxxxxx xxxx x xxxxxxxxxxxxxxxxxx x xxxxxxxx x x x xxxxxxxxx xxxxx x xxxx xxxx xxxxxxxxxxxxxx x xx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xx x xx xxxx x x xxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxx xx

xxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxx

xxx xxxxxxxxxxxxxx xxxxxxxxxxx xxx xxxx xxxx xxx xxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxx x xxxxxxxxxxxxxxxxxxxx xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxx xxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx x x xxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x x xxxxx xxxx xxxx xxxxxxxxxxxxxxxxxxxxx xxx xxxxx x xxxx xxx x xxxxxxxxxxxxx xxxxxxxxxx xxxxxxxx xxxx xxxxxxxx x xxxxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxx

xxxxxxx x xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx x x xxxxxxxxxxxxxxxxxxx xxxxxxxxxx xxx xx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxx

x

xxxxxxx xx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x x x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxx xxxx x xxxxxxxxxx xxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxx xxxxxxxxxxxx x xxxxxxxxx xx xxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxx x xxx xxx xxxxxxx xxxxxxx xxxx

x

x x xx xxxxxx

x

xxxxxxxxxx x xxxx x xxxxxxxxxxxxxxxxxxxxxx

xxxxx xxxxxxxxxxx x xx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxx x

x

xxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxx xxx xxxxx xxxx xxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xx xxxxx xxx xxxxxxxxxxxxxxxx xxx xxx xxx xxxxxxxxxxx x x xxx xxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxx x xxxxxxxxxxx xxxx xx x xxxxxxxxxxxxxxxxxxx x xx xxx xxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxx xx x

x

xxxxx x xxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx

x

xxxxxxxx xxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxx x xxxx xx xxxxxxxxxxxxxxx xx x xxxxxxxxxx

x

xxx x x xxxxxxx xxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxx x xxxxxxxxxxxxxx xxxxxx xxx x xxxx xxxxxxxxxxxxxxxxx

x

xxx xx xxxx xxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxx x xxxxxxxxxx xxxx x xxxxxx xx xxxxxx xxx x xxxxxxxx xxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x

x

x xxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxx xxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xx

x

xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx

x

xxxxxxxxxxx xxxxxxxxx x

x

xxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxx

x

xxx xxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxx xxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xx xxxxxxxxxxx xxx xxx xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxx xxxxxx xxxxx xxxxx x xxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxxxxxxxxxxx

xx xxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxx xxxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxx xxxxx

x

xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

x x xxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxx x xxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx

x

xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxx xxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxx xxxxxxxxxxxxx x

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxx x

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxx x xx

xxx xxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

xxxxxx xxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxx xxxx xxx xxxxxxx xxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxx xxxx xxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxx xxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxx xxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxx

x

xxxxxxx xxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

x xx xxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx

x

x xxx x

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxx xxxxxxx xxxxx xx xxxx xx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxx xxxxxxxx

x

xxxxxxxxxxxxxxxxxx

xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx xxxxxxx xxxxxx xxxxxxxx

xxxxxxxxxx xxxxx xxxxx

xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxx xxxxx

x

xxxx xxxxxxxxxxxxxxxxxx xxx

x

xxxxxxx xxxxxxx

x

xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx

x

x

x

xxxxxxxxxxxxxxxx

xxx xxx xxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxx xxxxxxx

x

xxxxxxxxxxxx xxxx xxxxxx xxxxxx

x

xxxxxxxxxxxxxx xxx xx xx

xxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxx

x

xxx xxxxxxxxxxx

x

xxxx xx

xxxxxxxxxx

x

xxxx

x

xxx xxxx

x

x

x

x

x

x

x

x

xxx

xxxxxxxxxxxxxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx x x xxxxxxxxxxxxxxxxxxxx x xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxx xxxx x x x xxxxxxxxxxxxxxxxxxxx

x

xxx xxxx x xxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxx xxxxxxx xx xx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx x xx xxxx x x x xxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxx xxx x x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxxxxxxxxxxx

x

xxxx x x xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxx xxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxx

x

xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxx xxxxxxxxxxxxx xx xxxxxxxxxxxxx x xxxxx x x xxxx x xxxxxxxxxx xxxxxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxx xxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx x xxxxxx xxxx xx xxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxx x x x xxxx xxx xxxxxxxxxxxxx xxxx x xxxx xxxx x xxxxxxxxxxxxxxxxxxx xxxx xxxxxxxx x x x xxxxxxxxxx xxxx

xxxxxxxxxxxx xxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x xxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxx xx xx xxxx xxxxxxxxxxxxxx xxxxx xxxxxxx x xxx x xxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxx x x xxxx xxx x x xxxxxxxxxxx xxxxxx xxxxxxxx xxxx x xxxxxxxxx xxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxx xx xxxxxxxxxxxxx xxxx x x xxxxx xxxxxxx x xx xx xxxxxxx xxxxx xx xxx x xxxxxxxxxxx xxxxxxxxxxx x xxxxxxxxxxxxxxxx xxxxxxxxxxx xxxxxx x xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxx xx x xxxxxxxx xxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxx xxxx x xxxxx xx xx x xxxxxxxxxxxxxxxx x xxxx x xxxxxxxx x xx xx x x xx x xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xx xxxxx xx x x x xx xxxxx xx x x xxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxx xx x xxxxxx xxxx xxxxxxxxxxx x xxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx xxxx xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx x xxx xxxxx xxxxxxxxxxxxxx xx x xx xxxxxxxx xxxxxx xxxxxxxxx xxxxxxxxxxxxxx xx xxxxx x x xxxx xxxxxxx x x xxxx xxxxxxxxxxxxx xxxxxxxxxxxxx x xxxxx xxxx xx xxxx xxx xxx xxxxxx xxxxx x xxxxxxxxxxxxxxxxxxx xxx xxxxxxxx xxxxxx xxxxxxx xxxx xxxxxxxxxxxxx xx xxxxx xxxxxxxxxxx xx xxxxxx xxxxxxxxx xxxxxxxxxxxxxxx

x x xxxx xxxx x xx x xx xx xxxxx xxxxxxx x xxxxxxxxxxxxxxx xxxxxxx xxx xxxxxxxxxxxxxxx xxxxx xxxxx xxx xxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxx

x xxxx xx xxxxxx xxxxxxx x xxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x xxxxxxxxxxxxxxxxxxxxx xxx xxxx xxxxxxxx x xxxxxxxxxx xxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxx

xxx

xxxxx x x x xxxxx x xxxxxxxxxxxxxxxxxxxx

x

xxxxxxx x xxx xxxxx xxxxx xxxxx x x xxxx xxx x xxx xxxxxxxxxxxxxx xxxx xx xxxxxxxxxxxxx x xxxxxxxxxxx x xxxxxxxx xxxxxxxxxxx xxx xxxxxxxxxxxxxxxx x xxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxx x xxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxxx xxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxx

x

xxxxxxx xxxxxx x xxxxxxxx x x xxxx xxx xx x xx xxxx xxxxxxx x x x xxxx xxxxxxxx xxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxx xxxx x x xxxxx x xxxx xxxx xxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxx x xxxx xxx xxxxxxxxxxxxxxxxx x xxxx xxxxxxx x xxxxxxxxxx xxx x xx xxxxxxxxx xxxxxxxxxxx x xxxxx xxxxxxx x x xxxxxx xxxx xxxxxxxxxxxxx x xxxxx

x xxxxxxxxx x xxxxxx xxxx xx xx x xxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxx xxxx xxxxxxxxx xx xx xxxxx xxxxx xxx xxxx xxx xxxxxxxx xx

x xx xxx xxxxxxxxxxxxxxxx xxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxx xxxx xxxxxxxxx xxxxxx xxxx xxxxx xxxxxxxx x x xxxxxxxxxxxx xxxxxx xxxxx x xxx xxxxxxx x x xxxxxxxxxxxxxxxxxxxx

xxxx xxxxxxxxxxxxxxxxxx

xxxx x x xxxx xxxxxxxxxxx xx xxxx xxxxxxxxx

x

xxx xxx xxxxxxx xxx x xxxxx xxxxxxxxxxxxxxxxxxxxxx x xxxxxx x xxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xx xxxx xxxxxxxxxxx

x

xx xxxxx x xxx xxxx xxxxx xxxx

x xxxxxxxx xxxxxxxxxxxxx xxx xxx xx

xxxxx xxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

x xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxx xxxxxxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxxx x xxxx xxxxxxx xxxx

x

x xxxxxxxxxxxxxxxxxxxx

x

xxxx xx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxx xxxxx xxxxxxxx xxxxxxxxxxxxxxxxx xx xxxxxxx xxxxxxxxxxxxxxxxxx

x

x x

x

xx xxx xxxxxxxx xxxxxxxx xxx xxxxxxxxxx

x

x x xx x x xxxxxxxxxxxx x

x

x xxxxxxxxxxxx x xxxx xxxx xx xx xxxxxxxx xxxxxxxx xx xx xxx xxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxx xxxxxxxxxx xxxxxxx x

x

xxxxxxxxxx xxx x x

x

x xxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxxxxxxxx

x

xx xx xxxxxxxxxxxx

x

xx xxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxx xxx xxxxxxxxxxxxxxx xxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxx

x

xxxxx xxxxxxxxxxxxxxxxxxxxx x xxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxx xxxxxxxxxxxxxxxxxxxxx

xxxxxxxx x xxxxxxxxxxxxxxxxx

x

x xxxxx xxxxxxxxxxxxxxxxxxxxx

xxxx xxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxx xx xxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

x xx x xx xxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxx xxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxxx xxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxx xx x

x

xxxxxxxxxxxxxxxxxxxxxxxxx

x

xxx xxxxxx x

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxx xxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxx xxx xxx

x

xxxxxx xxxxxx

x

xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxx xxxxxxxxxxxxxxxxxx x

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xx xx xxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

x

xxx xxx xxxxx x

x

x xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxx xxx xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxx xxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxx xxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx

x

xxxxxxxxxxxxx xx

x

xxxxxxxxxxxxxxxxx

x

xxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxxx

x

xx xxxxxxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xx xx xxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxx x xxxx

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxx

x

xx xxxx

x

xx xxxxxxxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xx xx xxx

x

xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx

xxxxx xxxxxxxxxxxx xxx xxxx

x

xx xxxxxxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxx xxxxxxxx

x

xx xxxxxxxxxxxx x xxxxx xxxxxxxxxxxx

x

xxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxx xx

x

xxxxxx xxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx

x

x xxxxxxxx x

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx

x

xxx xxxxxxxxxxx xxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx

x

xxxxxxxxxxx xxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxx xxxxxxxx xxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxx xxxx

xxxxxxxxxxxxxxxxx

xxxxxxxx xxxxxxx xxxxxxxxxxxx xxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx

x

xxxxxxxxxxxxxxxxx

xxxxx xx xxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxx xxxxxx

x

x xxxxxxxx

x

xx xxxxxxxxxxxx xxxxxxxxxxxxx xxxxx

x

xxxx xxxx

x

xxxxxx xxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x xxxxxxxxxxxxxxxxx

xx xxxxxx xxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxx

x

xxxxxxxxx xxxxx

x

xxxxxxxxxxxxxxx xxx

x

xx xxxxxxxxxxxxxxxxxxx xxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x x xxxxxxxxxxxxxxxxxxx xxxxx xx

x

x x xxxx

x

xxxxxxxxxxx xx xx

x xxxxxxx

xx xxxxxxxxxxxxxxxxxx

x

xx xxxxx

x

xxxxxxxxxx

x

xxx xxxxx xxxxxxxxxxxxxxxxx xx

xxxx

x

xxxx

x

x xxxxx

x

x

x

x

x

xx

x

x

x

Tight FCS

Medium−tight FCS

1990 1995 2000 2005 2010

0

250

500

750

0

250

500

750

Figure 5: Identification of individual funds with superior skill by the FCS approach. The plot illustratesthe evolution in the composition of individual funds with superior skills as identified by the FCS approach.Each fund that is included in the FCS at least once during the sample is assigned a unique number on they-axis based on the date of the first inclusion and a cross shows when this fund is included. The FCS isbased on the latent skill holdings model with time-varying alpha, considers funds with significantly positivepredictive alpha as candidate funds and assumes � = 0.75 in the top panel and � = 0.90 in the bottom panel.

Percentage of Superior Funds Included in FCS

Number of Inferior Funds Included in FCS

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013

0

200

400

600

0

10

20

30

40

50

Figure 6: Evolution in the set of funds identified as being inferior by the FCS approach. The top panelshows the evolution in the number of funds included in the tight, medium and wide fund confidence sets ofinferior funds. The bottom panel shows the corresponding evolution in the percentage of funds identifiedas being inferior by the FCS approach. Funds are selected from the set of funds with significantly negativealpha using the latent skill-holdings model with a time-varying alpha to compute each fund’s alpha estimate.Dark blue areas correspond to � = 0.90 (tight set), while lighter areas correspond to � = 0.75 (medium-tightset), � = 0.50 (medium set), and � = 0.10 (wide set).

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xxxxx xxxx xxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxx xxxxxxxxxxxxx xx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxx xxxxxxxxx x xxx xxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxx x xxxxxxxxxxx xx xxxxxx x x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx x xxx

x

xxxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xx xxxxxxxxxxxxxxxx xxxxx xxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xx xxxxx xx xxxx x xxx xxxxxxxxxxxxx x x x x xxxxxxx xx xxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxx xx x xxxxxxxxxxxxxx xxxxxx xxxx xx xxxxxxxxxx xxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx x xx xxxxxxx x xx xxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xx xxxxx xxxxxxxxxxxxx xxxx xxxxxx xxxx xxx xxx xxxxxxx xxxxxxxx xxxxxxxxxxx xxx xxxxxxxxxxx x x xxx xx xxx xxxxxx x x xxxxxxxx xx xx x xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xx xx xxxx xxx x xxx x x xxxx x xxx x xxx x xxxxxxxxxxxxxxxxxxx x x xxxxxxxxxx xxxx x xxxxxxxx

x

xxxxxxxxxxxx xx x xxxxxxxxxxxxxxx xxxxxxx xx x xx xx xxx xx xxxxx xxx x x x xxxxxx xxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx

x

xxxxxx xxxx xxxx xxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxx xx xxxxxxx xxx x x x x x xxx xxxxxx xxxxx xxxxx xxx xxx xx xxxx x xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxxxxxx xxx xxx xx xx x xx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxx xxxxxx xx xxxxxx

x

xxxx xxxx x xxxxxxx xx xxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxx x x xxxxxxxxxxxxxxxxxxxx x xxxxxx x xxxx xxx xxxx xxxxxxx xx xxxxx xxx x xxxxxxxxxxxxxxx xx xxxx xx xx xxxxxxxx xxxx xxx xxxx xx xxx xxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xx xx xxxxxxxx xxx x x xxxxxxxxxxxxxxxx xxxxxxx x xxxxxxxxxxxxx xxxxxx xxxx xxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxx xxx xxx xxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxx xxxxxxxxxx xxxxxxx xxxxx xx xxxxxxxxxxxxx xxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxx xxxxxxxxxxx xxxxxxx x xx xxx xxxx

x

xxxxxxxxxx x xxxx x xxxxxxxxxx xxxxx xxxxxxxxxxxxxx xxxxxxxxxx x x xxxx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xx xx xxxxxx xx xxxxxx xxx xx xx x x xxxx xxxx xxxxxx x x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx x x xxxx x xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx x xxxxx xxxxxxxxxxxxxxxxxxxxxx xx xx x xxxxxxxxx xx xxxx xx x x x xxxxx x x xxxxx xxxxxxx xxx xx x xxxxxxxxxxx xxxxxxx xxxxxx xx xxxxxxxxxxxxx xx xxxxxx xxxx xxxx xxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxx xxxxxx x x xxxxxxxxx xx x xxxxxxxx xxx xxxxx xxx xx xx xxx x x xxxx x xxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxx xxxx xxxxxxx x x xxx xxxx xxxxxx xxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x x xxxxxxxxxxxxxxx x xxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xx x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxx xxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xx xxxxxxxx x x xxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xx xxxxxxxxxxxxx xxxxxxxx xxxxxxxx xx x xxxxxx xxx xxxx x xxx xxxxxx x xxxxxxxxxxxxxx x xxxxxxxxxx xxxxx xxxxxxx x x x xxxxxxxxxxxx x x xxxxxxx xxxxx xxxx xxxxxxxxxxxxxxxxxxxxx xxxxx xx xxxxx x xxxxx xxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxx xx xx xxxxxx xx xx xxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxx xx x xxxxxxxxxxxxxx xxxx xxx x xxxxxxxxxxxxxxx x xxxxxxx xxxxx xxxxxxxx xxxxxxxxxxxxxxxx xxxxxxx xxxxxxx xxxxxxxxx x x x xxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxx xxxxxxxxxxxxxxxxxxxx x xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxx xxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxx xx x x xxxxxxxxx x xx xxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxx xxxxxxxxx xxxxxxxxxxxxxxxxx xxxxx xxxxxx xxxxxxxxxxx

x

xx xxxxxxx xxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxx xxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxx xx xx x x x x xxxxxxx xx xxxxxxxxxxxx x x xx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxx xx x x x xxxxxxxxxxx x x xxxxxxxxxx xxxx x xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxx xx xxxxx xxxxxxx xxxxxxxxxxxx xxxxxx xx xxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxx x xxxxxxxx xxxxxxxx x xxxxxxxxxxxxxxxxxxxx x xxxxxxx xxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxx xxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxx xxxxxxx xxx xx x xxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxx x x xxxxxx xxxxxxx xx x x x xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xx xxx x xxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx x xx x xxxxxxxx x xxxxxxxxx xxxxxxxxxxxxxx x xxxx xxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxx xx x x xxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xx x xxxxxxxxxxxxxxxxxxxxx x xx xxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxx

x

xxx xxxxxxxx x xxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx xx x xx xx xxxxxxxxx xxxxx x xxxxxxxxxx x x x xxxxxxxxxxxxxx x xxxxxxxx x xxxxxxxxxxxxxxxx xxxxxx xxxxxxxx x xxxx x xxxxxxx x xxxxxxxxxxxxxxxxx xxx x xxx x xxxxx xx x xxxxx xxxxxxxx x x x x xxxxxxxxxxxxxxxxxxxxxxxxxxx xxx

x

xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxx xx x xxx xxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxx xxxxxxx xxxxxxxxxxx xxxxxxxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxx xxxxxxxxxxxxxxx xxxx x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxx x x x xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx x xxxx x xxxxxx xxx xxx

xx xxxxxxx xxxxxxxxxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxx x xxxxxxx xx x xx xxx xxxxxxx xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x x xxxxxxxxxxxx xxxxxxx x xxxxx xxxxxx xxxxxxx xxxxxxxx xxxxxxxxx xxxxxxxxxx xxx x x xx xxxxxxxxx xxxx xxxxxx x xxxxxx xxxxxxxx x xxxxxxxxxxxxx xxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxx x xxxxxx xx xxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxx xxxxxx x xxxxxxxxxxxxx xxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxx xxxxxxxxxx xxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx x xxxxxxxx xxxx x xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx

xxx xx x xxx x xxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxx xx xxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxx xx xxxxxxxxxxxx xx

x

xxxxxxxxxxxxx xxxxx xxxxxxxx

x

x xxxx x xxxxxxxxxx

xxx x xx xxxxxxxxxxx xxxxx xx x xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x x xx xxxxxx

x

xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xx xxx xxxxxxxx xxxxxx xxxxxxxxxxxxxx xxxxxxxxxx xx x xxxxxx x x xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxx xxxx xxxxxxxxxxxxxxxx xxxxxxx x xxxxxx xx xxxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxx x xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxx x xxxxxxxxxx xxxxxxxxx xx x xxxxxx x x x xxx xxxx x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxx xxxxx x xxxxxx x xxxxxxxxx x xxxxxxxxx xxxx x xxxxxxxx xxxx xxx xx xxxxxxxxxxx x x xxx xxxxxxxxxxxxxxxxxx xxxxxxxx xx xxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxx x xxxxxxxxxxxxxx xxxxx xxxxxxxxxxx xxxxxxxxx

xxx xxxxxx x xxx xxx xxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxx xxxxxxxxxx xxxxxxx xxxxxxx x xxxxx xxxxxxxxxxxx xxxxxxx xxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxxxxxxxxx x xx xxxx xxxx xx

xx x xxxxxxxxxxxx xxxxxx x xx xxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxx xxxxxxx xxxxx x xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxx xxxxxxxxxxxx xxxxxxx xxxxxxx xx xxxxxxxxxxxxx xxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxx xxxxxxx xxx xxxxx xxxxxxxxxxxxxxxxx x xxx xxxxxxxx xxxxxxxxxxxxxxxxx xxxxxx x x x xxxxxxxxxxxxx xx xxxxxxxx x x xxxxx xxxxxxxxxxxxxxxxxxx xxxxx xxx xx x x xxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxx xxxxxxxxxxx xxxxxxxxxxx xxxx x x xxxxxxxxxxxxx xxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxx xxxxx xxx xx xxxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxx xx xxxxx xxxxxx xx xxxxxxx xxxxxxxxxxxxx xxxxxxxxxxx xxxxxxx xx x x x xxxxxxxx x xxxxxxxxxx xxx x x x xxxxxxxxxxx xxxx x xxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxx xxx xxxxxxxxx xxxxxxx xxxxxxxxxxxxxx x x x xxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxx x xxxxxxxxx x xxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxxxx xx xx x xxxxxxxxxxxxxxx xxxxxxx x x xxxxxxxxxxxxxx x xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxx

x

xxx xx xx xxxxx xxxxxxxxxxxxx xxxxxxxx xx x x xxxxxxx xxxxxxxxx xx xxxxxxxxxxxxxx

x

xxxxxxxxxx xxxxxxx xx xxxxxxxx x xxxxxxxxxxx xxxxxxx xx xx x x xxx x xxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx x xxxxxxx xxxx x xxxxxxxxxxxxxxxx xxx x xxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxx xxx xxxxxxx x xxxxxxxxxxxx xxxxxxxxxxxxx x xxxx xxxxx xxxxxx xxxxxxxxxxxxxx xxxxxxx x xxxxxx xx xxxxxxxxxxxxxx xxxxxxxx xxxxxxx xx xxxx xxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx x xxxxxxx xx x x xxxxxxxxxxx xx xxxxxxxxxxx xxxxxxx xxxxx xxx xxxxxxxxxxxxx xx xxxxxxxxxxxx xxx xxxxxxxxxx xxxxxxx xxxxxxxx xxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx x xxxxxxx x

x

xxxxxxxx xxxxxxx xxxxxxxxx xxxxxxxx xxx x x xxxxxxxxxxxxx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx x xxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxx x x x x xxx xxxxxxxxx xx

x

x xxxxxxxxx xxxx x xxxx x xxxxxxx x xxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxx

x

xxxx xxxxx xxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxx xx xxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxx x xxxxxxx xxxxxxxx xxx x xx xxxxxxxxxxxxxxx xxxxxxx xxxx x x xxxxxxx xxxxxxxx xx xxxx xxxxxxxx xxxxxx xxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx x xxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxx xx xxxxxxx xxxx xxxxxxxxxxxx xxxxxxxx xxxx x xxxxx xxxxxxxxxxxxx xxxx x x x x xxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxx xxxx xxx xxxxxx xxxxxxxxxxxx xxxxxxxxxxxxx xxx xxxxx xxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxx xxxxx xxxxxxxxxxxx xxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxx xxxx xxxxxx xx xxxx x xxxxxxx xxxxxxxxxxxxxxxxxxx x x xxxxx x xxxxxxxxxxxxxxx xxxx xx xxxxxxxxxxxxx xxxxx x xxxxxxxxxxxx x x x xxxxxxxx xx xxxxxxxxxxxx xxxxxxxxxxxxx xxxxx x xxxxx x xxxxxxxxxxxxxx xx xxxxxxxxxxx

x

xxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxx xxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxx xxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxx xxxxx xxxxxxx x xxxxxxxxxxx xx xxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxx xxxxxxxxxxxxx xxxxxx xx x x xxxxxxxxxxxxx xxxxx x xx x xxxxxxxxxxxxxxxxx xxx x xx xxxxxxxxxxxxxxxxxxxxxxxx xx

x

xxxxx xxxxx x x xxxxxxxxxxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxx x x xxxxxx xxxxxxxxxxxx xxx xxxxxxxxx xx xx x xxxxxx x xxxxxxxx xxxxxxxxxx xxx x x xxxxxxxxxxx xxxxxxx xxxxxxxx

x

xx x x xx xxxxxxxxx xxxxxx xx x xxx xxxxxxx x xx xxxx x xx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxx x xxxxxxxx xx xxxxxx xx xxxxx xxxxxx xx xx x xxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx x xx x xxxxxx xxxxx xxx xxxxxxxxxxxxxxxxxxxxxxx xxx x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx

x

xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxx xxxxxxxx xxxx xx xxxxx x xx x xx xxxxxxx x xx xxxxx

xxx xxxxxxxxxxxx xxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxx x x xxxxx xx xxxxxxx x x xxxxx xxxxxx xxxxxxxxxxxx xxxxx xx xxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxx x xxxxxxxxxxxxxxxxx xxxxxxx xx x xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x xxxxxxxxx x xxxxxxxxxx x xx xxx xxx xx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxx xxx xxx xxxxxxxxxxxxx xxxxxxxx xxxxx x xxx xx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxx xxxxxxxx xx xx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xx x xxx xxx xxxxxxxxxxxxxxxxxxxxxx xxx

xx xxxxxxxxxxxx xxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxx xxxxxxx xx xxxxxxxxxxxxx xx x xxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x x xxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxx x x xx xx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxx xxxxx x xxxxxx

x

x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxx x

x

xxxxxxxxxxxx xxx xx xxxxxxx xxxxxxx x xxxxx xxxxx x xxxxxxxx

x

xxxxxxxxx xxx x xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxx xxx

x

xxxxxxx x xxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxx xxxxxxxxx xx x x xxxx xx x xxxxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxxx xxxxxxxxx x x xxxxxxxxxxxxxx xxxxx xxxxxx x xxxxxxxx xx xx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxx xxxxxx x x x xxxxxxxxxxxx xx xxxxxxx xx xxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x x xxx x xxxxxxxxxxxxx x xxx xx x xxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxx

x

xxxxx xx xxxxxxxxxxxxx x x xxxxxxxxxxxxxxxx xx xxxxxxxxxxxxx xx xx xxxxxxxxx x x x xxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxx x xxx xxx xxxxxxx xxxxxxxxx xxxx xxxxx xxx

x

xxxxxx xxxxxxxxx x xxxxxxxxxx x x xxxxxxx xx xxxxxxxxx xxxxxxxxx x x xx x xxxxxx xx x xxxxxxxxx xxxxxxxxxx x xx xxxxxx xxxxxxxxx xxxxxxxxxx xxxxx

x

xxxx x xxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxx x xxxxx xxxx xxxxxxxx xxxxx xxxxxxxxxxxxx xxxxxxxxxxxxx x xx x xxxxxxx xxx

x

xx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxx xxx

x

xxx x xxxxxxx x xxxxxxxxxxxxxxx xx x x xx xxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxx xxxx x xxxxxxxxxxxxx x x xxxxxxxxxxxx xxxxxxx xxxxxxxxxxx xx xxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxx x xxxxx xxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxx xxxx x xxxxxxxxxxxxxxxxxxxxx x xxxxxxx x xxxxxxx xxxxxxxx xx xx xxxxxxxx xx xx xxxx xxxxxxxxxx xxxx

xxxxxxx xxxxxxxxxxxxx xx xx xxxxxxxxxxxx xxx x x x xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxx xxx xxxxx xxxxx xxxxx x x xxxxxxxxx xxxxxxxxxxxxxx xxxxx xxxxxx x xxx xxxx xxxxxxxxxxxxxxxxx x x xxxxx

xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxx x xxx xxxxx x x xxxxx xx xx xxxxxxxxx x xxxxxxxxxx xxxx xxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxx x xx xx xxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxx xxxxx xxxxxxxx xxxx

x

xxxx xxxxxxxxxxxx xxxxx xxxxxxxxxxx xx x x xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxx xxxx xxxx x xxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxx x xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxx xxxxxxxxxxxxx x xx xxxxxx xxxxxxxxxxxxxxxxxx xxx

x xxx xxx xxxxxxx xxxxxxxxx xxx xxx xxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxx

xx xxxxxxxxxx xxxxxxxxxxxxxx xxxx xxx x xxxxxxx xxxxxxxxxxxx x xx xxxxxxxxxxxxxxxx xxxxx

x

x x x xxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xx xxx xxxxxxxxxxx xxx xx xxxxxxxxxxxxxxxxxxx xx xxxxxxx xxxx xxxxxxxxxxxx x x xxxx xxxxxxxxxxxxx xxxxxxx xxxxxxxx xx xxxxxxxxx x xxxxx xxxxxxxxxx xxxxx xxx x xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxx x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxxxx xx xxx x xxxxxxxxxxxxxx xxxxxxxxxxxxx

x

xxxxxxxxx xx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxx x xxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxx xxxxxxxxxxxxxx xxx

x

xxx x xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x xxxx xx xxx xx x xxxxxxxxxxxxx

x

xxxxxxxx x xxxxxxxxxxxxxx x xx x xxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxxxx xxxxxxxxx xxxxx xxx xxx xxxxxx xxxxxxxxxxxxxxxxxx xxxxx xxxxxxx x xxxxxxxxxxxx xxxxxxxx

x

xxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x x xxxxxxxxx x x xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx x xxxxxxx xxx xxxxxxxxx xxxxxxxxxxx x xxxxxxxxx xxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxx xxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxx xxxxxxx xxxx x xxxx

xxxxxxx xxx x xxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xx x xxxxxxxx

x

xxxxxxxxxxxxxx xx xxxxxx xxxxx x xx x x xxxxxxxxxxxxxxxxxx xxx

xxxxx xx xx x xxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxx xx x x x x xxxxxxxxx xxxxxxxxxxxx xxxxx

x

xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxx xx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxx x x x xxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxx xx x xx xxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx x xxx x xxx xxxxxxxxxxxxxxxx xxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xx x xx x x x xxxxxxxxxxxxxxxxxxxx xxxxx xxxx xxxxxxxxxxxxx

xxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxxxxxxxxxxx xxxx xxxxxxxxxxx xxxxxxxxxxxxx x x x xxxxxxx xxxxx xxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxx x x

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxx x xx xx x x xxx xxx xxxx x xx xxx xxxxxxx x x xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxx x xxxxxxxxxx xxx x xxxxxxxxxxxxxxxxxx x x xxxxxxxxx xx xxxxxxxx xxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxx x xxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx xx x xxx xx x xxxxxx x xxxxxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxxx x x xxxxxxxxx xx xx xxxxxxxxxxxxxx xx xxxxxxx x xxxxxxxxxxxx x xxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxxxx x xxxxx xxx xx

x

xx xxxxxxx xxxxx x x x xxxxxxxxx xxx xxxxxx x xxx xxxxxxxxx

xxxxxxxxx xxx xxxxxxxxxxx xxxx x xxxxxxxxxxx x xx xxxxxx xxxxxxxxxxxxxxxxxxx xx xxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxx x x x xxxxxx xxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxx xxxxx xx xxxxxx xxxxxxxxxxxx x xxxxxxxxxxxxxxxx xxxxxxx xxx xxxxxxxxxxx x x xxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx x x x xxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x x xxxxxxxxxxxxxx xxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx x x x xxxxxxxxxxxxxxx x xxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xx x x xx x xxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxx xxxx x xxxxxxxxx xxxxxxx xxxxx x xxxxxxxxxxxx xxxxxxxxxxxxxxxx xx x x x x xxxxxxxxx xx xxxxxxxxxxxxxxxxx xxxxxxxx

x

xxxxxxxxxxx xxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxx x xx xx xxxxx

xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxx x x xxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x xxxxx x xxxxxxx xxxxxx xxxxxxx xx x x xxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxx x x xxxxxxxxxx xx x xxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xx xx xxxxxxxxxxxx

x

xxxxxxx xxxxx x xxxxxxxxxxx x x xx xxxx x x xxxxx xxxxx xxx xxxxxxxxxxx x xxx x x xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx x xx xxxxxxxxxxxxxx xxx xx xxxx x xxx x xxxxxxxx x xxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxx x x xxxx x xxxxxxxxxxxxxxxxxx x xxxxxx x xxxx xx xxxxxxxxx xxxxx x xx xxx xxxxxx xx xx x xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx x x xxxxxx x xx x xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx x xxx x xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxx xxxx xx xxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxx xxx xxxxxxxxxxxxx x xxx xxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x xxxxxxxxxxxxxxxxx xxxxxxxxx xxxxxx xx xx xxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxx xxxxxxx xxx xxx xxxxxxx xx xxxxxxxxx xxx xxxxxxx xxxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxx x xx xxxxxxxxxxxx x x x xxxxxxxx xxxxxxxxx xxxxx x xxxxxxxxxxxxxxxx x x xxxxxxxxxxx xx x x xxx xxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxx xxxxxx xxxxxxxxxx x xx xxx xxxxxxxx x xxxxxxxxxxxx

x

xxxxx x xxx x xxx xx

x

x xxxxxxxxxxxx xxxxxx xxxxxx xxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxx x

x

x xxxxx xx xxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x x xxxxxxxxxxxxxxx xxxxxxxxxxx xxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxx xx xxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxx xxxxx xxx xx x xxxxxxxxx x x xxxxx xxxxxxxxx xxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxx x x x xxx

x

x xxxx xxxxxxxxxxxxxxx xxxxxx x xxxxx xxxxxxx xxxxxxx x xxxxx xx x x xxx

x

xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxx x x xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxx xxxxxxx

xxx x xx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x x xxxx x xxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxx xxx x xxx x xxxxxxxx

x

xx x x x xxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxxx xx xxxx xxxxxxxxxxxxxxxxxxxxx x x xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxx x x x xx xxxx xxxxx xx xxxxxxx x xxx x x xx xxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxx

x

x xxxx x xxx xx x xx xxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx x xxxxxx xx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x x x xxx xx xxxxx xxxxxxxxxxxxxxxxx xxxxxx xxxxxxxx

x

xxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx x xxx x x x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxx x xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xx xxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxx

xx x xxxxxx xxxxxxxxxxxx x xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxx xxxxxxxx xx

x xxxxxxxxx xxxxxxxxxxxx

x

xxxxxxxxxxxxxxx x x xxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx x xxxxx xx xxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx x x x x xxxxxxxxxxxxx x x x xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxx xxx xx xxxxxxxxxx

x

xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xx xx x xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxx xxxxxxx xxxx x xxxxxxxxxx xxx xx xx xxxxxxxxxxxxxxxxxxx x xxxx xx xxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xx x xxx xxxxxxxxxxxxxxxxx x xx xxxx xxx xxxxxxx x xxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx x

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x xxxxxxxxxxxxxxxxx xxxxxxx xx xxxxxxxxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxx xxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxx xx

xxxxxxxxxxxx x x xx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx x x xxxxxx

x

xxxxxxxxxxxx x xx xx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxx xx xxxxxx x xxxxxxxxxxxxxxxxxxxxx x x xxx xxxxxxxxxx xx xxx xxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxx x xxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx

x

xxxx xx x xxxxxxxx x xx xxxxxxxxx xxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxx xxxxxx x x xxx x x xxxxxx xx xxxxxxxxxxxxxxxxxxxx x x xxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxx xxxxxxxxxxxxx x xxxxxxxxxx x xx xx xxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx x xxxxxxxxxxxxx xx xxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxx xxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx x xxxxx xxxxxx x xxxxxxxxxx xxxxxxxxxxx x xxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxx x xxxxxxxxx x xxxxxxxxxxxxxxxxxxxx x x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxx

x

x x xxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxx xx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx x xx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxx xx x x xx x xxxxxx xxxxxxx xxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxx x x xxxxxxxxxx xx x xx xxxx x x xxxxxxxxxxxxx xxx x x xxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxx x x xxx xxxx xxxxxxx xxxxxxxxxxx

x

x x xxxxxx xxxx x xxxxxxxxxxxxx xx xxxxx x x xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxx x xx xxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxx x x xx xxxx x x xxxxxxx xx xxxx xxxxxxxx xxxxxxx xxxxx x xxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx x x xxxxxx xxxxxxxx xx x xxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxx xxx xxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x x xxxxxxxxxxxxxxxx xxxxxxxxxxxxxx x xxxxxxx xxxxxxxxxxxxxx xxx xxxxxxxxxxxxx xxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x xx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxx x xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxx xxxxxxxxxxx xx xxx xxxxxx xxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxx

x

xx x xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x xxxxx

x

x xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxx x xxx xxx x x xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx

x

x xx xxxx xxxxxxxxxxxx xx xxxxx xxxxxxxxxxxx x x xxx x xxxxxxxxxx

x

x x xxxxxxx xxx xxxxxxx

x xx xxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx

x

xxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxx xx xxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxx xx x xxx xx xxxxxxxxxxx xxxxxxxxxxxx x xxxxxxx x xxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xx xxxxx x xxxxxxxx xxxxxxxxxxxxx xxxxx xxxxxxxx xxxx xxxx x xx xx xxx xxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx x xxxxx

x

x xx xxxx xxx xxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xx x xxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxx xxxxxx xxx xxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xx xxxxxxxxxxxxx xxxxxxx xxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxx xx x xxxxxxxxxx xxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxx x xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxx x xxxxxxxxxxx

x xxxxxxxx xxxxxxx x xxxxx xxxxxxxxxxxxxxxx xx xxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxxxx x x xxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxx x x x xxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx x x xx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx x x x xx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx x xxx x x xxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxx xxxxxxxx

x

x x x xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxxxxxxxx xxxx xx xxxxx x

x

xxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxx xxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xx x xxxx xxxx

x xxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx

x

xxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxx xxxxxxxx xxxxxx xxx xx xx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxx xx xx xxxxxxxxx xxxxxxx xxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx x x xxxxxxxxx

x xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx xx xxxxxxx xxxx xxxxxxxxxx xxxxxxx x xxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxx x x xxxxxxx

xxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxx xx xxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xx xxxxxxxxxxx xxxxx x xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x xxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxx x x xxxxxx xxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxx x xx xxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxxx

xxxxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxx x xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxx x xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxx xxxx x xxxxxx

x

xxxxxxxxxxxxxxxxx xxxxxxxxx x xxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx x x x xxxxx xxxxxxxxxxxxxxxx x x xxxx xxxx xxxx x xxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxx x xxxx xxxx xxxxxxxxxx xxxxxxxxx

xx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxx x xx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxx

x

xx xx xxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxx xxx xx x x x xxxxxxxx xxxxxxxxxxxxxxx

x x xxxxx x

x

xxxxxxxxxxxxxxxx xxx xxxxxxx xxx x xx xxxxxxxxxxxx xxx xxx xxxxxx x xxxxx x xx xxxxxxxxx xxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxx xxxxx xxxxxxx xxx xx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x x xxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxx xxx x xxxxxxxx

x

x xx xxxx xxxx

x

xxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x xx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx x xxxxxxxxx x xx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x xxxxxxx x xxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x x xxxxx x x

x

xxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxx xxx xxxx x x xxxxxxxx xxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxx xx x xx xxx x xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxx xx xxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xx xx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxx xxx xxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x x xxxxxxxxxxxxxxxxxx x xx xxx xx xxxxx xxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx x xx xxxxxxxx xx xx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx

x

xxxxx xxxxxxxxxxxx x x xxxx x x xxxx xxxx xx

x

xxxxxxxx xx xxxxxxxxxxxxx xx xxx xxxxxxxx xxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxx x xxxxxxxx xxx xxxxxxxxx xx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx x xx xxxxx xxx x xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxx xxxxxx xxxxxxxxxxxxx x xxxxxxxxxxx x xxxxxxxxxx x xxxx

xxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxx xxxxxxxxxxxxxxxx xx x xxx x xx xx xx xx xxxx

x

xxxxxxxx xx x xxxxxxx xxx xxxxxxxx xxxxx x xxxxxxxxxxxxxxxxx x x x xxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxx x x xxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxx xxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx x xxxxxx x xx xxxxxx x x xxxxx x x xx x x

x

xxxxxxxxxxxxxxxx x x xxxxxxxx x xxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxx xxxxxxxxxx xx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxx x x xxx xxxxxx xxx xxxxxxx x xxxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxx x x xxxxxxxxx xxxxxxxx xxxx xxxxxxx x x xxx xx xxxxxxxxxxxxxxxx x x x xxxxxx xx

xxxxx xxx xxxxxxxxxx

x

xxxxxxxx xxxxxxxxxxxx x xxxxxxxxxxxxxxx xxx

x

x xxxxxxxx x xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxx xx x xxx xxxx xxxxxxxxxxxxx xxxxx xxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx x xx xxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxx x x xxxxxxx x xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx x xx xxxxxxxxxxxxxxxxxxx xxxxx xxx xx

x xxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxx xxx xxxxxxx x xxxxxxxxx x x xxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxxxx xxxxxx xxxx xxx xxxxxx

xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxx x x xxxx xxx xxxxxx xxx xxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxx x xxxxx xxx xxxx x x xxxx xxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxx x xx xxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxx x x xxxxxx xxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxx xxxx xxxx xx x xxxxxxxxx

x

xxxxxxxx xxxxxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxx x x x xxxxxxx xxxxxxxxxxxxx x xxxxxxxxxxxxxx xxxx x xxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxx x x

x

xxxx xxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxx x xxxxxxxxx xxxxxxxxxx xxxx

x

xxxx xxxx xxxx xxxxx xx x

x

xxxxxxxxxxxxxxxxxxxxxxx xx xxxxxx x xxxxxxxxxxx x xxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxx xx xx xxxxxx x xx xxxxxxxxxxxxxxxxxx xxxxxxxx

x

x xxxxxxxxxxxxxxx xx xxxxxxxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxx x x xxxxxxxxxxxxxx xxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xx

xxxxxxxxxxxxxxxxxxxxxxx xxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxx xxxxxx x x xxxxxxxxxx xx x xxxxxxxxxxxxxxxx x x

x

x xxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxx xx

xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxx

x

xxx x xxxx xxx xxx x xxxxxxxxxx

x

x x xxxxx xxxxxxxxxxxxxxx x x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxx x xxxxxxx xxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxx xxx xxxxx x xx xxxxxx xxxxxxxx x xx xxx x xx xxxxxxxxxxx

xxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxx x xxxxx xxxxx x xx xxxxxxx xxxxxxxx x xxxxx xxxxxxxxxx xxxxxx x xxxxxxxxxxxxxxxxxxxxx x x xxxxxxx xxx x xxxxxx

x

x x xxxxxxxx xxxxxx xxxxxxxx xx xxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxx xxxxxx x xxx xxx xxxxxxxxxxxxx xxxxxxxxxx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxx x x xx x xxxxxxxxxxxx xxxxxxxxxx x xx xxxxx xxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxx xxxxxxx x

x

xxxxxxxxxxxxx xxxxxxx xxxxxxxxxxxxxxx xxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxx x xxxxx xx xxxxxxxxxx xxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxxxxx xxxxxxxxxx xxxxxxxxxxxxxxxx x x xxx xxxxxxxx

x

xxxxxxxxxxxx xxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx

x

xxxxxx xxxxxxxxxxxxxxxx xxxxxx xx x xxxxxxx x xxxxxxxxxxxx xxxxxxxx x xxxxxxxxxxxxxxx x xxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxx xxxxxx xxxxx xxxxx x xxxxxxxxxxxxxxxx x x xx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxx xxxx xxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxx xxxxxxxxxxxxxx x x xxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxx x xxxxxxxxxxx x xxxxxx xxxxxxx xxxxxx x x xxx xxxxx x xxx xxxxxxxxxxxx xx x xxxxxxxxxxxxxx x x xx xxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxx xxxxxxxxxx x xxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxxxxx xxxxxxxxxxxxxxx xxx

x

xxxx xx xxxxx xxxxxxx xxxx x xx xxxxxxxxxxxxxxxxxx x xxxxxxxxxx xxx x x xxxx xxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxx x x xxxxxxxxxxxxxxx xxx x xx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxx x xxx x x x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxx xx xxxxx xxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx x xxxxxx xxxx x xxxx x x xxx xxxxxx xxxxxxxxxxxxxxxxxxxx x xxxxxxx xxxxxxx x xx xxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxx

x

x x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxx x x xxx xxxxxx xxxxxxxxxx

x

xxxx x x x xxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxx xxxxx xxx x xxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxxx x xxxxxx x xx xxxxx x xxx x x xxxxxxx x x xxx xxxxxxxxxxx x xxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xx xx x xxx x x xxxxxxxxxxxx xxxxxx

xxxx xxx x xxxx xxxxxxxxx

xxxxx xxxxxxxxxxxxxxx x xxx xxxxxxx

x

xxxx xx xxxx xxxxxx xxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x x xx xx xxxxxxxx xxx xxxxxxx x x xxxxx xx xxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxx x x xxxxxxxxxx x xx

x x xxx xxx xxx x xx xxx x xxx xxxxxxxxxxxxxxxxxx xxxx xx xxxxxxxx xxx xxxxxxxxxxxxxxxxxxxx xxxxx xxxx x xx x x xxxxxxxx xxxxxxxx xxxx x

x

x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxx x xxx xxxxxxxxxxx x x xxx xxxxxx x xxx xxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxx xxxx x xxxxxxxxxxxxxxxx xxxxxxx xx x xxx xxxxxxxxxxxxxxxxx xx x xxxxxx xxx x x xxx xxxxxx

x

x x xxxxxx xxxxx xxxxxxxxxx xxxxxxxxxxx xxx

x

xx x xx xxxxxxxxxxxxxxx xxxx x x xxxx xxxxxxxxxxx

x xx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxx x xx xx xxxxx xxx xxxxxxxxxxxxxxxxxxxx xxxx x xx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxx xxx

x xxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxx xxxxx xxxxxxxx

x

xxx xxxxxxxxxxxxxxxxx xxx x x xxxxx

x

xxx xxxxxxxxxxxxxxxx xx xx xxx xxxxxxx

xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxx xxxxxxxxxxxxxx x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxx xxxxxxxx x x xxxxxxxx

x

x xxx xx xxx xx xxxx x xxxxxxxxxxxxxxxx x xx xxxxxxxxx xxxxx xxxx xxxxxx

x

x xxxxxxxxxxxxxxxxxxx xxxx x xxxxx xxxx xxx

x xx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx

x xxxxxxxxxxxxxxx xxxxxxx xxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx x x

x

xxxx x xxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxx

x xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxx x xxxx x xxxxxx

x

xxxxxxx xxxxxx x x xxxxx xx

x

xxx xxx xxxx xxxxxxxxxxxx xx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x x xxxxxxxxxxxxxxxxxx xxx xxx x xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx

x

x x xxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x

x

xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xx xxx

x

xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxx x xxxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxx xxxx x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx

xxxxxx xxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xx xxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx

xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxxxxxxxxxxxxx xxxx x xxxx

x

xxxxxxxxxxxxxxxxxxx x x xxxxxxxxx

x

xxx x x xxxxxxxxxxx

xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxx xxxxxxxxxxxxx xxx xx

x

xxxxx x xxx xxxx

x

xxxx xxxxxxxxxxxxxxxxxxxxxxxx

xxxxxx xxxxxxxxxx

x

xxxxxxxx xxxxxxxxxxxxxxxxxxx xxxx xxxx xxxxx xxxxxxxx x xx

x

x xxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x

x

xxxxxxxx x xxxxxxx x x xxxxxxxxxx

x

xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxx x xxxxxxxxx x xxxx xxxxxxxxxxxxxxxxx xxxxxxxxxx xxxxxxxxx

xx xx xxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxx

xxxxxxxx x xxxxxxx xxxxxxx xxxxxxxxxx

x

x xxxxxxxxx

x xxxxxx

x

xxx xxxxxxxxxxxxxxxxxxx

x xxxxx xxxxx

xx xxxxxxxxxxxx x xxxxxx

x

xxxx xxx x

x

xx xxxxxxxx x

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxx xxxxxxxxxx

x x

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxx

xxxxxxxx xxxxxxxxxxxxxxxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx

x

xxxxxxxxxxxxxxxx

x

xxxxxxxxxxxx xxx xxxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxx xx xxxxxxxxxxxxx

xxxxxxxxxxxx xxx xxxx

x

xxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxx

x

xxxxx xxxxxx x xxxxxxxxxxxxx

x

xxxxxxxxx xxxxxxxxx

x

xxxxxxxxxxxxxxxxx

x

xxxxxxxx

x

xxxxxx xxxxxxxxxxxxxx

x

xxxxxx

x

xxxxxxxxxxxxx

x

x xx

x

xxxxxx

x

xxxx

x

xxxx

x

xxxx

x

xxxxxxxxxx

x

xxxx

x

xxxxx

x

xxx

x

x

x

x

x

x

xxx xxxxxxxxx xxxxxxxxxxx x x xxx xxx xxxxxxxxxxxx xxxxx xxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxx x xxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxx xxxxx xxxxxxxxx x xxxxx xxxxxxx x xxx xxx xxxxxxxxxxxxxx xx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxx xxxxxx x xxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxx xxxxx xxxxxxxxxxxxxxxx xxxxx xxxxxxx xxxxxxxxxxx xx x xxxxx x xxxxxxxxxxxxxxxx x xxxxxx x xx xxxxxxxxxxxxxxxxxx x xxxx x

x

xx xx x x x xxxxxxx xxx xxxx xxxxxxxxxx xx xxxxxxxxx xxxxxx x xxxxx xxx x xx xxxxxxxxxx xxx xxx xxxxxxx xxxxxx x xxxxx x xx xxx xx x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxx x xxxx x xxxxx xxxxxxxxxxxx x xxxxx xx x xxx x xxx x xxxxxx xxxx xxxxxxxxxxxxxxx xx xxxxxxxxx x xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx x xxx xxxx

x

xxx x xx xxxxxxx xxxxxxxxxx x x xxxxxxxxxx xxxxx xxxxxxxx x x x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx x xx

x

xx xxx xxx x x xxxxxx xxxxxx x xxxx xx xxx xxxxx x xx xx xxxx xxxxxxxxxxxxxxxxxxxx xx xx xxxxxx x x xxxx xxxxxxx xxxx xxxxxxxxxx xx xxxx xxxxxxxxxxxxxxxxx x xxxx xx x xxx xxxx xx x x xx x xxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xx xxxxx xxxxxxxx xx xxxx xxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxx x x xx x xxxx xx xxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x x x xxxxxxxxxxx x x xxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xx xxxx xxx x xxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxx xxx xxxx xx xx xxx xxxx xxxxxxxx xxxx xx xx xxxxxxxxxxxx xxxxxxxx xxx xxxx xxxxxxxxxxxxxxxxxxxxx x xxxxxx x xx x xx xxxxxxxxxxxxxxxxxxxxx xxxxxx xx xxx xxxxxxxxxxxxxxxxx xx xxx xxxxxx x xx xxxxxxxxxxxxxxxxxxxxx xxxxxx x xxxxxxxxxxxxxx xxx xxxx xxxxx xxx xxx x xxxxxxxxx xxx xxxxxxxxxxxxxxxxxxx xxx xxx xxxx xxxx x xxx x xxx xx x xxxx xxxxxxx x xxxxxxxxxx x xxxx xxxxxxxxxxxxxxxxxx

x

x x xx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxx xx xx x xxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxx xxxxxxx xx xxx xxxxxxxxxxxxxxx x xxxxx xxx xxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxxxxx xxxxx xxxxxxx x xxxxxx xxxxxxxxxxxxxx xxxxx xxxxxx xxxxxxxx

x

xx x xxxxxx xxxxxxxxxxxxxxxxxxxxxx x x xx x x xxx xxx xx xxx xx xxxxxx xx xx x xxxxx xx xxxx xxxx xxxxxxxxxx xxxx x xxxxxx xxxxxxxxxxxxxxxxxxxx xx xx xxxxxxxxxxxxxxxxxxxxxxx x xxxx x xxxxxxxxxxx xx xxxxxxxxxxxxxxxxxx xxx xxx x xxx xxxx xxxxx x xxxxxxxx xx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx x xxxxxx x x x xxxxxxxxxxxxxxxxxx xxx xxx xx x xxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxx x xxxxxx xx xxxx xxxxxxxx x xxxx xxxxxxx x xx xxxxxx xxx xx xxxxxxxx xxxxx x xxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxx x xxxxxxx xxxxxxxxxxxxxx x xxxxx xxxxxx xxxxxx x xxxxx xxxxxxx x xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x xxxxxxxxxxxxx

xx xxxxx x xxxxx xxxxxx x xx xx xxx xxxxxx xx xx xxx xxxxxxxxxxxx xxxxx xxxxx xxxxxxxxxx xxxxxxx xxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxx xxxxxxxxx xxx xxx xxxxxxxxxxxxxxxxx xx xx xxxxxxxxxxx xxxxxxxx x x xxxxxxxxxxxxxxxxxx xxxxx xxxxxxxx x xxxxxxxxx xxxxxxxx xx xxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxx xxxxxxx

xxxxxxxxxxxx xx xxxxxx xxxxxxx xxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxx xxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x x

x

xxxxxx x xxxxxx x xxxxxxxxxxxxx xxxxxxxxx xxxxxxx xxxxxxxxxx xxxxx xxx xx x

x

xxx xxx xxxxxxx xxx xxxxxxxxxxxxxx xx xx xxxxx xxx xxxxxx xx xxxxxxx x xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxx xxx xxxxxxxxx xx x xx xx x xxx x xxxxxxx xxxxxxxxxx xxxxxxx xxxxxxxx x xxxxx xxxxxxx x xxxxxxx xxx xxxxx xxxxxxxxxxx xxxxxxxxx

x xxxxxxxx xx xxxxxxx xxxxxxxxxx xxxx xx xx xxxxxxxx x xxxxx xx xxxxxxxxxxxxxx xxxxxxx xxxxxx x x xxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxx

x xxxxxxxxxxx x x xx xxxx xxxx xx

x xxxxxx x xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x xxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxxxxx xx xxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx xxxx xx xxxx x x xxxxxx x xx xxxxxxxxx x x xxxx xxxxxxxxxx x xx x x xxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxx x x xxxxxxxxxxxxxxx x xx x x xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx x xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxx xxx xxxxxxxxxxxxxxxxxx x xx xxxxx x x x xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxx xxxxxx x xxxx xx xxxxxx xxxx xxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxx xxxx xxxxxx x xxxxxx xx xxxxxxxx x xxxxxxx xxxxxx x x xxxxxxx x xxxxxxx xxxxx xxxxxxxxx xxx xxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxx x xxxxxxx xx xxxxxxxxx x xx xxxx x x xxxxxxx xxxxxxxxx xx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx

x

xxxxx x xxxxxxx x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxx xxxxxxx xxxx xxxx x xxxxxxxxxxxxxx

x

xxxxxxx xxxxxx xx xxxx xxxxxx xx xx xxx xxx xxxxxxx xxx x x xxxxxxxxxxxxxxxxxxx xxxx xxxxxxxx

x

x x xxxxxxxxx xxxxxxx xxx x xx x x x xxxxxxxxxxxxxxx xxxxxx xxxxxx x x x xx xx xxx xxxxxxxxxxxxxxxxxxx xxx xxxxxxx xxxxxxxxx x xxxx xxxxxxx x xxxxx xx xxxxx xxxxxxx x x xxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x xxxx xx xx xx xxxxxxxxxxxx xx xxxxxxx xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x

x

xxxxxx xxxxxxxxxxxxx xxxxxxxx xxxxxxx x xxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxx x xxxxxxx

x

xx x xxxxxxx xxxxxxxxxxxxxxx xxxxx xxxxxxx xxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxx xx

x

xxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxx xxxxxx xxxxxxx x xxx xxxx xxxxxxxxx x xxxx xxxxxx xxxxxx x x xxx xxxxxxx x xxxxxxxxx x xxxx xxxxxxxxxx x xxxxxxxx xxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxx xxxxx xx xxx x x xxxxxxxxxx xxxxxxxxxxxxxxx xxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxx xxx xxxxxxx x xxxx xxxxxx xxxxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxx xxxxxxxxx x xx x x xxxx xxxxxxxxxx

x

xxxxxx xxx xxxx xxxxxxx xxxxxxxxxxxxx xxx x xxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxx xx xxxxxxxxx xxxxx xxx x xxxx xxx xx xxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxx x xxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxx x xxxxxxxxxxxx xxxxx xxxxxxx x xxxxxx xx xx xx xxxx xxxxxxx xxxxxxxx x xxxxx xxxxxxx x x x xxx xx x xxxxxxxxxxx

x

x x xx xx xxxxxx xxxxxxxxx x x xx xxxxxxx xx xx x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxxxxx xxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx x xx x x xxxxxxxxxxxxxxxxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x

x

xxxxxxxxxxxxxxxxxx xxxxx xxxxxxx x xxxxxxxx xxxxxxxxxxxxxxxxxxx x xx xx x x x xxxxxxxxxxxxxxxxx xx xxxx x xxxxx xxx x x x x xx x xxx xxxxxxxx x xx xxxxxx xxxx x xxxx xxxxxxx xxxxxxxxxxx

xxxxxxxxxxx x xxxxxxx x xxxxxxxxxxx xxxxxxxxx xxxxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxx x x xxx xxx xxxxxxxxxxxxxxxxxxxxxx xxx

xxxxxxx xxxxxxxxxxxxx xxxx x xx x x x xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxx xxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxx xxxx xxxxxxxxx xxxxxxx x xx x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxx xxxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxx x xx xxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxx

x

xxxxxx xxxx xx xx x xxxxxxxxxxxxxx xxx x xxxx xxxxxxxxxxx xxxxxxxx xxx xxxxx xxxxx xx

x

xx xxxx xxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxx xx xxx xxx xxxxxxx

x

xxxxx xx xxxxxxx x xxxx xx xxx xxxx x xx xxx xxxxxxxxxxxxxxxxxxx xxx xxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxx x x

x

xxxxxxxx xxxxx xxxxxxx x xxxxxxxxx xxxxxxxxxx xxxxxx x x xxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxx xxx xxxxxxx x xx xxxxxxxxxxx xxxx xxxxxxxxx xxxx xxxxxx xx xxxxxx x x xxxxxxxxxxxxxxxx xxxx x x xxxxxxxxx xxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxxx x xxx xx x xxxxxxxxxxxxxxx xxxxxx xxxxx x xxxx

xxxx x x xxx xxx xxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxx

x

xxxxxxxxx xxxx xxxxxxx xxxxx xxx

x

xx xxxxx xx xx xxxx xx xxxxxxxxx xxx x xxx xxx xxxxxx x xxxx xxxxxxx x xxxxxxxx xxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxxxxx x xxxxxxxxxxxx x xxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxx xx xx xxx

xxxx xxxx xx xx x xxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx

x x xxxx xx xx x x x xxxx xxxx xxxxxxx xxxx xx xxxxxxxxxx xxxxx xxxxxxx x x xxx xxxxxxxxxxxxxxxx x xx xx xxx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxx x xxxx x xxx xxxx xx xx xxxxxx xxxxxxxxxxxxxxxxxx

x

xxxx xxxxx xxxxxxx x xxxxxxx xxx xxxxxxx x x x xxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxx xxx x xxxxxxxxxxxxx xxx x xxxx xxxxx xxxx xxxxxxxxxxxx

x

xx xxxx xxxxxxx x xxxxx xxxx xxxx xx xxx x xx xxxx xxxxx xx x xxxx x xx xxxxx xxx xxxx xxxxx x xx xxx x xxxxxxxxxxxxxx

x x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx x xxxxxx

xxxxx xxxxxxx xxxxxxx x

x

x xx x x x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x xx xxxxx xxxxxx

xxxxx xxxxxxx xx xxx x x xxxxxxxxxxxxxxx xx xxxxxxx x x xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx x xx x xx xxxxxxxxxxxxxxxx xxxxxxx xxxxxxxx xxx xxxxxxxxxx xx xxxxxxxxxxxxxxxx xxxxxxx xxxxxx xxxxxxx xx x xxxxxxxxxx xxxxxx xxxxxx xxx xxxx x xxxxxxxxxxxxxxxxx xxx xxxxxx xxxxxxxx xxxxxxx x xxxx xxxxxxxxxxxxxxxxx xxxxxxx x x xxxxxxxxxxxxxxxxxx xxxxxxx x xxxxx x x x xxxxxxxxxxxxxx xxxxxxxxxxxxx

x

xxxxx xxxxxxx x xxxxxxxx xxxxxxxxxxxxxxxx xxxx xxxx xxxxx x xxx xxxxxx xxxxxxxxxxxx xxxxxxx xx xxxxxxxx xxxxxxx x x xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxx xxxxxxx xxxxx xxxxxxxxxx xxxx x xxxxxxxxxxxxxxx xx xxxxxx xxxxxxx xxx x xxxxxxxxxx xxxxxxxxxxxxxxxxx x x xxxxx xxxxxxxx xx xxxxx xxxxxx x x xxxxxxxx xxxxxxxxxxxxxxxxxx xxxxx xxxxxx xx xxxxx xxxxxxxx x xxxxxxxxx xxxxxxxxxxx xxxx xxxxxxx xxx x x xxxxx

x

xxxxx x xxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxx

xxxx xx xxxx x xxxxx xxxxxxx x x xxx xxxxxxxxxx x x xxxxxxxxxxxxxx x

x

xxxx x xx x x xx xxxxx xxxxxxxxx xxxxxxx xx xxxxxx

x

xxx xxxxxx xxxxxxx xxxxxxx xxxxxxx xxxx xxxxxxx xxxxxx xxxxxxxxx xxx x xxx xxxxx x xxxxxxx x xxx xxxx xxxxxxxxxx

x

xxxx xxxxxxx x x xx xxxxxxxxxxxx xxxx x xx xxxxxx xxxxx xxxx x

x

xx xx xxxxxxxxxx xxxxxxxxxx

x

xxxx x xx xxxxx xxxxxxx xxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxx xx xxx x xxxx xxxxxxx x xxxxx xxx x xxxxxxxx xx xxxxxxxxxxxx xxxxxxxxxx xxxxxxxxxx xxxx xxxxxxx xxxxx xxxx xxxxx x xx xxxxx xxxxxx xxxx xxxxxxxx xxx

x

xx xx xxxxxxx xxxxxxx x x x xxxxxxxxxxxxxx xxx xxxxxxxxx

xx xxxxxxxxxxxxx x xxxxxx x xxxxxxxxxxxxxxx xxxxxxxx xxxxx x x xxx xxxxxxx x xxx xx xxxxxxxxxxxxxxxxx xxxx xxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxx x xxxxxxxxx xxxxxxxxxxxx xxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x x xxxxxxxxxxxxxxxxxx xxx xx xxx xxx xxxxxxx x x xx xx xxxxxxx xxxx xxxxxxx xxxxxx xx xx xxxxxx

x

x x xxx x xxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxx x xx x xxx x xx xxxxxxx x x xxxxxxxxx xxx xxxxx xx xx xxxxxxx x x xxxxxxx x xxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxx

xxxxxxxxxx xxxxxxxxx xxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx x xxxxxxx x xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xx xxxxxx xxxxxxxxxxxxx xxxxxxxxxxxx x xxxxxxxxxxx x x xxxxxxxxxxxxxxx x xxxx x xx x xxxxxxxxxxx xxxx xx xxxxxxxxxxxxxxx x xxxxxxxxxxxxx x xxxxxxxx xxxxxxxx x x xxxxxx xxxxxxx x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxx x xx x xxx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx

x

x xxxx x xx xx xxxx xxxxxxxxxxxxxxx x xxx x xxxx x xxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxx xxxxx xxx xx x xxxxxxx x x x xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxx x xx

xxxxxx x xx x xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxx x x xxxxxxxxxxxx xxxx xx xxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x x xxxx xxxxxxxxxxxxxxxxxxx xxxx x xxxxxxxxxxxx

x

xx x x xxxxxxxxxxxxx xxxxxx x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x xxxxxxxxx x xxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxx x xxxxx x xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxx

x

xxxxx x x x xxxxxxxxxxxxxxxxx xxxxxxxxxxx xx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx x xxxxx x xx

x

x xxxxxxxxx xxxx xx

x

xx x xxxxx x xxxxxxxxx xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x xxxxxxxxx xxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxx xxxxxx xxx xxxxxxx xxx x xx xxxxxxxxxxxxxxx xxxxxxxxx x x xx x x xxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx x xxxxxxxxxxxx xx xxxx xxxxxxxxxxxxx xx xxxxxxxxxxx x xxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx x x xx xxxxx x x xxx xxxxx x xx xx xxxxxxxxx x x xxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx x x xxxxx xx xxxxxxxxxx xxxxxxxxxx x xxxxxxxxx xxxxxxxxx xx x x x x xx xxxx xx xxx xxx xxxxxxx

x

xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxx xxxx

x

xxxxxxxxxxx xxxxx xxxxxxxxxxxxx xxxxxxx x x xxxxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx x xxxxxxxxxx xxxxxxx x xxxxxx xx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxx xxx xxxxxxxxxx x xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxx xxx xxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxx xx xxx xxxxxxx x xxxxxxxxxxxxxxxx xxxxxxxxxxxxxx x

x

x xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxx xxxxxxxxxxxxxxxxxxx xx xxxx xxxxxxx xx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx x x xxxxxxxx xxxxxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxx xx xxx

x

x xxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxx xxxxxxxxx x xxxxxxxxxxxxx xx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xx x x xxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxx xxxxxxxxx xxxxxxx xxxxxxx x xx xxxxxxxxxxxxxxxxxx x xxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx x x xxxxx xxx xxxxx xx x xxxxxxxxxx xx x

x

xxxx x xxxxxxxxxxxxxxxxxxx x x xxxxxx xxx xx x x xxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxx x xxxxxx xx x x xxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xx xx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x x xxxxxxxxxxxxxxxxxx xxxx x x xxxxxxxxxxxxxx xxxxx xx xxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxx x xxxxxxxxxxxx x xxxxxxxxxxxxxx xxxx xxx xxx x x xxxxxxx x x x xxxxxxxxxxxxx xxxxxx x xxxxxxx xxxxx x xx xxxxxx xx xxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxx

x

xxx x x xx x xxx xxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x x xx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxx x x x x xx xxxxxx xxxxx xxxxxxxxxx

x

x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxx xx xx xxxxxx x xxxxxxx xxx xxxxxxx xx xxxxxxxx

x

x xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xx xx xx x xx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxx xx xx

x x xxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxx x xxxx xxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxx x xxxxxxxxxxx

x x x xxxxxxxxxxxxxxxxxxxx xx xxxxxxx xxxx xx xxxxxxxxxxxxxxxxxx xxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxx xxxxxx xxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx x xxx xx xx xxxxxxx xxxx x xxxxxxxxxx

x

xxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxx xxxxx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxx

x

x xxxxxxxx x xx xxxxx x xxxxxxxxx xx xxxxx xxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxx x xxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxx x xxxxxx xxxxx x xxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxx x xxxxxxxxxxxxxxxxxxxx x xxxxx x xxx xx xx x xxxxxxxxxxxx xxx x xxxxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxx xx x xxxxx xxxxx xx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxx xxxxxxxxx x xxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xx xxxx xx x xxxxxxxxxxxxxxxxx xxxxxxxxxx xx xxxxx xx xxxxx xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxx xxxxxxxxxx xxxxxxxxx xx

x

x x xxxxxxxxxxx x xx xxxxxxxxxxxxx xxx xx xx xx

x

x xx xxxxxxxxxxxx x x xxxxxx xxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxx xxxxxxxxxxxx xxxxxxxx

x

x xxxxxxxxxxxx xx xxxxx xxxxxxxxx xx xx xx x xxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxx xx xx xxx x xxxxxxxxxx

x

xxxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx x xxxxx

x

xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxx x xx xxxxx xx xxxxxx

x

x xxxxxxxxxx xxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxxxx x xxxxx xx xxxxxxxxx xx x xxxxxxxx xx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxxxxx xx xxxx

x

x xxxxxxx xxxxxxx xxxx xxxxxxxxxxxxxx x x x x xxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxx x xx xxx xx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxx xx xxx xxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x xxx xxxxxxxxxxxx xxxxxxx xxxxxxxx

x

xxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxx xx xx

x xxxxxxxxxxxxxx xx xxxxxxxxxxx x xxx xxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxx

x

x xxx xx x xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxx xxxx xxx xxx xxxxxxxxxxxxxxx xxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxx xxxxxxxxx x xxx x x xxxxxxxxxx x x xx xx xxx xxxxxx

x

xxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxx x xxxxxxxx

x

x xx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xx xxxx xxxx

xxxxxxxxxxxx xxxxxxx xxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxx

x xxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxx x xxx x xx xxxxxxxxxxxxxxxx x xxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xx xxxxxxxxxxxxxxxxxx x xxx xxxxxxxxxxxxxxxxx x x xx x xxxxxxxxxxxxx x xx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxx xxxxxxxxxxxxx xxxxx xxxxxxxxxxxxx x xx xxxx x x x xxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxxxxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxx x xx xxxxxxx xxxxxxx xxxxxxxxxx

x

xxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx x xxxxx xxxxxxxxx xxxxxxx xxxxxxxxxx

x

xxxxxx xxxxx x xx xxxxxxxxxxxxxxxx xx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xx xxxxxx xxxxx x xxxx xxxxxxxxxxxxxxxxxxxxxx x x xxxx x xxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxx x xxxxxxxxxxxxxxxxx x xxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxx xxxxx xxxxxxxxxx x xxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxxxxx xxxx xxxxxx xxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxx xxxxxx xxxxxxxxxxxx xxxx xxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxx xxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxx xx x xxxxxxx

xxxxxxxx x xxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxx xx xxxxx

x

xxxx xxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx x xxxx xx xxx xxxxx x xxxxxxxxxx

x

x xxxxxxxxx xx xxxxxxxxxxxxxxxxxxx x xxxxx x xx

x

xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxxxxxxxxxx xx xx xxxx xxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxx x x xx xxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx x xx xxxxxxxxxxxxxxxx xxx xx xxxxxxx xxxxxxxxxxxxxxxx x xxxxxxxxxxx xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x x xxxxxxxxxxxxxxxxx xxx xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxx xxxxx xxx xx xxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxxxxx xxxxxxxxxxx

x xxxxxxxx x xxx xxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx

x

xx x xxxxxxxxxxxxxx xxxxxx xxxx xxxxx xxxxxxxxx xx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxx x xxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxx xxxxxx xxx xxxxxxxxxxxx x xxxxx x xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxx x xx xx xxx xxx xxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxx x xxxxx x x xxxxxxxxxxxxxxxxxxx x xxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xx x xx xxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxx xxxxxxxxx xxxxx xxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxx xxxxxx xx xxxxxxxxxxxxxxxxxxx x x xxxxxx xxxxxxxxx xxxxxxx xx xx xxxxxxxxxxxxx x xxxxx xxxxx x xxxxxxxxx

x

xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x x xxxx xxxxxx xxxxxxxxx xxxxxxxxx xxxxx xxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxx x x x xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx x

x

xxxxxxxxxxxxxxxxxxxxxxxx xxxxxx

x

xx xxxxxxxxxxxxxxxxx xxxxxxxxxxx x xxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx xx xxxxxxxxxxxxx xx xxx xxxxxxxx xxxxxxxxxxxxx x xxxxxxx xx xx xxxxx xxxx xx xxxxx xxxxxxxxxxx xxxxxxxxxxxx

x

xxx xxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxx xxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxx xxxxxxxxxx xxxx x x xxx x x x xxxxx x x x x x

x

xxxx xxxxxxxxxxxxxxx xxx xxxx xxxxxxxxxxx x xxxxxx x xxxxxxxxxxxxxxxxx x x xxxxxxxxxx xxxxxxxxxxxx xxxxxxxx xxxxxxxxx x xxxxxxx xxx xxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxx xxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxx xxx xxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xx x xxxxxxxxx xxx x x xxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxx x xxxxxxx xx xxxxxxxxxxx xx x x

x

xx xx xxxxxxxxxx xxxxxxxxxxxxxx xxxxxx x xxxxxxxxx xx x xxxxx x x xxxxxxxxxxxxx xxxx x

x

xxxxxxx xxxxx xxx xxxxx x xx xx xx x xxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxx xxx xxxx xxxxxxxxxxxxxxxxxxx x xxxxx xxx xx xxxxx xx xxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x xx xxxx

x xxx xxxxxxx xxxx x xxxxxxxxxx

x

x xxxxxxxxxxxx xxxx xxx xxxxx xxxxxxxx xxxxxxxx x xxxxxxxxx xx x xxxxxxx xx xxxx xxxxxxxx x xxx xxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxx xxxxxxxx x xxxxx xxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxx xxx x xxxxxxxxxxxx xxxxxxxxx x xxxxxxxxxxxxx xxxxxxxxx x xx xxx x x xxxxxxx

xxxxxxxxx x xxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xx x x

x

xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx x xxxxxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxx x xxxxx x

x

xxx xxxx xxxxxxxx xxxx xxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxx xx x xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxx x xxxx xxxxxxxxxxxxx x xxxxx xxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xxx

x

xxxxxxxxxxxxxxxxxxxx xxxx xxxx xx

xx xxxxxxx x xxxxxxxxx xxxxxxxx xxxxxxxxxxxxx xxxxx x xx x x xxxxxxxxxxxxxxxxxx xxxxx xx xxxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxx x xxxxxx x xx x xxxxxxx

x

xxxxxxxxxx xxxxx xx xxxx x xxxx xxxxxxxxxxx xxxxxxxxx

xxxxxxx xx xx xxxxxxxxxxxxxxxxxxxxxxx x xxxxxxx xxxxxxx xxx x xxxxxxxxx xxx xxx x xx xxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxx xxxx x xx xxx xxxxx xxxx xxxx xxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxx xxxxxx x xxxxxxxxxxxxxxxxx x xxxxxx x x xxxxxxxxxx x xxxxxxxx x xxxxxx xxxxx x xxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxx xx xxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxxx xxxxxx x x xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxx xxxxxxx xxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx x xxxxx xxxxxxxxxxxxxxxxxxxxxx x xxxxxxx

x

xxxxxxxxxxxxxx x xxxxxxxxxxxxxxxx xxxxx xxxx

x

xxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xx x xxxxxxxx xxxxx xxx xxxxxxxxxx

x

xxxxxx xxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxxxxxx xx x x xxxxxx

x

xxx xxxxx x xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxx xx xxxxxxxxxxxxxx

x

xxxxxxx xxxxxx xxxxxxxxxx xxxxx

x

xxxxxxxx xxxxxx xxxxxxxxx xxxxxxxxxxxxxx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxx x xxx xx xxxxxxxxxx xxx xxxxxxxxxxxxxxx xxxxx xx xxxxxxxxxxxxxxxx x xxxxxxxxxxxxxxxxxx xxx x xxxxxxxxxxxxxxxxx xxxxxxx xxxxx xxx xxx xxx xx x xxx xxxxxxxxxxx

xxxxxx xxxxxx xxxxxxxx x xxxxxxxx xxx xxxxx xxxxxxxxxxxxx xxx

x

xxxxxxxxxxxxxxxx x x xxxx xx xxxx

x

xx x xx xxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxx

x

xxxxxx x xxxxxxxxxxxxxxxx xxxxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x xx xxx xxxxxxxx x x xxx xx xxx xxxxxxxxx x xx xxx xx xxxxxx xxxxxxx x xx xxx xx x xx x x x x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxx x xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxx xxxx xxx xxxxxx

x

xxxx x x xxxxxxxxxxxxxxxx xxxx xxxxxxx

x

x xxxxxxxxxxxxxxxx xx xxxxx

x

xxxx x xx xxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx xxxxx x xxxxxxxxxxxx xxxx

x

xx xx xx xxxx xxxxxxxxxxxxxxxxxxxxxxxx x xxxxxxxxxxx

xxx xxxxxxxxxxx x xxx x xxxxxxxxxx x xxxxx xxxxxxxxxxxxxxxxxxx x x xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx xx xxx xx x xx xx xxxxxxxxxxxxxxxxxxx xxxxxx x x xxxxxxxxxxxxxx xxxxxxx

x xxxxx xxxxxxx

xx xx xxx xx xx xxx xx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx xxxxxxxx xx x xxxxxxx xx xxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xx xxxx xx xxxxxxx xx xxx x xxxx xx x xx x xx xx xxxxxxxxxxxxxxxxxx xx xxxx xxxx x xxx xxxxxxxxxxxxxxx xxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxx

x xxxxxxxx xxxxx xxxxxxxx

x

xx x xx xxxxxxxxxxxxx xx x xxx xxxxxx

xx xxxxx xxxxx xxxxx xxxxxxxxxxxxx x

x

xxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxx x xxxxxxxxxxx xxxx xx x x x

x

xx xxxx xxxxxx xxx xxxxx xxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxx xxxxxxxxxxxxx xxxx xx xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxx xxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxxx

xxxxxxxxxxxxxxxx xxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxx xxxxxxxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxx

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxx

x

xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

x xxxxx x x xxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxx x xxxxxxx xx

x

xxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxx xxx xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x

x

xx x xxx x xxxx xxxxxx xxxxxxxxxxxxxxxxxxxx xxxxxxxxx x x x xxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxx xxx xx

xxx xxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxx xx xxxxxx xxxx x xxxxxx xxxxxxxxxxx xxxxx xxxxxxxxxxxxxx xxxxxxxxxxxxxxxx x xxxxxxxxx

xxxxxxxxxxxxxxxxxxxx xxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxx xxx xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xx xxxxxxxxx x x xxxxxx xxxxxxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxx

xxxx x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxxxxxx xx xxxxx

x

xxxxxxxx xxxxxxxxxx xxxxx x xxxxxxxxx

xxxxxxxxxxxxx xxxxxxxxx

xxxxxxxxxxxxxxxxx xxxx x xxxxx

x

x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxx x xxxx xx xxx x xx xxx xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx xx xxxxxxxxxxxxxxxxxxxx

xxxxxxx xxxxxxx x xxxxxx

x

xxxxxxxxxxxxxxxxxxxx x

x

xxxxx xxxxxxxxxxxxxxxxx

x

xxxxx x xxxxx xxx xxxxxxxxxx xxxxxxxxx

x

xxxx x xxxxxxxxx x xxxx x xxxxx xxxxxxx xxxxxxxxxxxxxx xxxxxxxxxxx xxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxx x xxxx

x xxxxxxxx

x

xxx xxxxxxxx xxxxxxx

x

xxxxxxxxxxxxxxxxxxx xxxxxx xx xxxxx xx xxx xxxxx xx

xxxxxxx xxxxxxxxxxxxxxx x xxxxxxxxxx

x

x xxxxxx xxxxxxx xxxxx xxx xxxxxxxxx x xxxxxxxx

x

xxx xxxxxxxxxxxxxxxxxxx

x xxxxxxxxxxx

x

xx xxxx xx

x

xx xxx xxxxxxxxxxxx

x

xx xxxxxx

xx xxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx x xxx

xxxxxxxx xx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxx

x

xxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx

x

x xxxxx

x

xx xxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxx xxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxxxxxx

x xx xxxxxxxxxxx

xxxxxxxxxxxxx

x

xx x xxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxxxxxxxxxxxxx

x

xxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxx

x

xxxxxx

x

xxxxxx

x

xxxxxxxxx xxxxxxx

x

xxxxxxxxxx

x

xxxxxxxxx

x

xxxxxxxxxx

x

xxxxxxxxxx

x

xxxx

x

xxx

x

xxx

x

xxxxxxx

x

xx

x

xx

x

x

x

x

x

x

x

xx

x

x

xx

Tight FCS

Medium−tight FCS

1990 1995 2000 2005 2010

0

500

1000

1500

0

500

1000

1500

Figure 7: Identification of individual funds with inferior skill by the FCS approach. The plot illustrates theevolution in the composition of individual funds with inferior skills as identified by the FCS approach. Eachfund that is included in the FCS at least once during the sample is assigned a unique number on the y-axisbased on the date of the first inclusion and a cross shows when this fund is included. The FCS is based onthe latent skill holdings model with time-varying alpha, considers funds with significantly negative alpha ascandidate funds and assumes � = 0.75 in the top panel and � = 0.90 in the bottom panel.

120 Observations

60 Observations

2.5 5.0 7.5 10.0

0.00

0.25

0.50

0.75

1.00

0.00

0.25

0.50

0.75

1.00

Figure B.1: The figure presents simulation results for the overall level of two selection methods. The redline represents the level of the FCS procedure, while the blue line represents the alternative specificationbased on the maximum t-statistic. The black line represents the nominal level of the tests. The level ispresented as a function of the percentage of truly superior funds in the simulated sample of 100 funds. Thelevels are calculated as average rejection rates over 100 simulations. The top panel presents results for asample size of 60 observations and the bottom panel presents results for a sample size of 120 observations.