Beta is not Sharpe Enough….

September 2010Steven P. Greiner, Ph.D. sgreiner@factset.com 0101.312.566.5109

Sharpe-r Risk Measures Agenda• Tracking Error Measures• FactSet’s Balanced Risk Module in PA• Tracking Error Forecasts• Introducing the “g-Factor”, a robust Volatility

Measure• Value-at-Risk• Stress Testing: Time & Event• Stress Testing: Black Swan Event• VAR Extreme Event Stress Testing• Fat-Tail VAR

Raising the IQ of the Intelligent Investor

Sharpe-r Risk Measures…

Ben Graham said: In a Barron’s article, he said that what bothered him is that

authorities equate beta with the concept of risk. Price variability yes, risk no

Excerpt from Barron’s, Sept 23, 1974, Dow Jones and Company

Real risk he wrote, is measured not by price fluctuations but by a loss of quality and earnings power through economic or management changes

As for variance or standard deviation of return being a useful risk measure, in the same Barron’s article he says that the idea of measuring investment risks by price fluctuations is repugnant to him, because it confuses what the stock market says with what actually happens to the owner’s stake in the business

Tracking Error: What it isn’t!• Usually, TE is reported as meaning that the portfolio’s return is

“bounded” by being within +/- TE of the Benchmark 67% of the time. Is this True?

σ = sqrt[Σ{(x-μ)/(n-1)}^2]

Avg(x) = μ = 2.0

Tracking Error: What it isn’t!• Using the math from the previous slide, substitute “P-BM” for “x” and re-

plot the graph…

• This then implies TE is the stdev about the average value of the XS return, not the BM return..

σ’ = sqrt[Σ{((P-BM)-μ’)/(n-1)}^2] = TE

Avg(P-BM) = XS Ret = μ’ = 1.4

Tracking Error… What it is!!+ Consider the impact this has on interpretation

+ There can be considerable asymmetry around bench returns

using Port = XS + Bench….

Annualized long term numbers.. so 68% of time XS is: Port's Abs Ret Bounds Portfolio about BenchPort Bench XS TE XS-TE XS+TE Lwr Bnd Upr Bnd Lwr Bnd Upr Bnd

4.0 3.0 1.0 4.0 -3.0 5.0 0.0 8.0 -3.0 5.04.0 5.0 -1.0 4.0 -5.0 3.0 0.0 8.0 -5.0 3.0

6.0 5.0 1.0 6.0 -5.0 7.0 0.0 12.0 -5.0 7.06.0 7.0 -1.0 6.0 -7.0 5.0 0.0 12.0 -7.0 5.0

8.0 7.0 1.0 9.0 -8.0 10.0 -1.0 17.0 -8.0 10.08.0 9.0 -1.0 9.0 -10.0 8.0 -1.0 17.0 -10.0 8.0

Empirical Data for:S&P, 2 SPDR’s, Exxon, ISRG, LCV, Magellan, Nikkei & 2 Hypothetical's

• Weekly returns downloaded from FactSet from December 31st, 2006 to August 31st, 2010

Empirical FactSet Data for:S&P, 2 SPDR’s, Exxon, ISRG, LCV, Magellan, Nikkei & 2 Hypothetical's

Data is Weekly Returns From 12/31/2006 to 8/31/2010…

S&P500 XLK XLF XO M ISRG LCV Magellan Nikkei Normal t-Dist-12

TE=> 1.42 3.92 2.61 6.65 1.03 1.29 2.67 5.46 5.95XS=> 0.09 -0.21 0.02 0.93 -0.11 -0.05 -0.17 0.06 0.06

Mean Ret -0.07 0.04 -0.34 -0.00 1.11 -0.19 -0.11 -0.24 -0.15 -0.18Stdev Ret 2.85 2.89 5.59 3.15 7.53 3.20 3.40 3.43 4.44 4.61

% of time XS return is found within it's average value and +/- TE76.0% 82.3% 77.1% 81.8% 87.5% 81.8% 68.8% 68.8% 81.8%

% of time Portfolio Return is found between S&P500 Ret and +/-TE39.1% 64.1% 60.9% 74.5% 29.2% 32.3% 62.0% 78.6% 88.5%

True Defn =>

Usual Defn =>

Empirical Data for:S&P, 2 SPDR’s, Exxon, ISRG, LCV, Magellan, Nikkei & 2 Hypothetical's

+ For smaller TE, the effect is more pronounced!

Tracking Error Measures….

+ If the TE is large and the abs(XS) return is small, you can stick to the old paradigm

+ If in 2008 one lowered TE hoping to lower relative risk while under-performing, one actually increased the likelihood of continued under-performance, hence risk actually increased.

+ This is because as TE goes down for a given XS return, one draws a narrower range around (P-BM) where the portfolio spends the majority of time in. If (P-BM) is negative, you lose the opportunity to out-perform as TE decreases.

+ If you have negative XS return, increase your TE to lower risk. E.g. XS Ret = -200 bps & TE = 4%; -6% < Port Ret < 2% (67% of the time) XS Ret = -200 bps & TE = 6%; -8% < Port Ret < 4% (67% of the time)

+ If you have positive XS return, decrease your TE to lower risk. XS Ret = 200 bps & TE = 6%; -4% < Port Ret < 8% (67% of the time) XS Ret = 200 bps & TE = 4%; -2% < Port Ret < 6% (67% of the time).

FactSet’s Balanced Risk Module…..

+ Components Uniting Equities, Fixed Income and Currencies.. Monte Carlo Value-At-Risk Stress Testing 1: Time & Event Weighting (Equity Only) Stress Testing 2: Extreme Event (Equity Only) MC Extreme Event Risk Global Equities, Corp, Hi-Yld, Agencies, Tips, U.S.Treas, Sovereign, U.S. MBS, Exc-Trad Options

+ Four Equity Vendor Risk Models, Plus Factset’s Own.. SUNGUARD – APT (Country, Regional, & Global, MT & ST, Equity only) Axioma (Global, EMG, Euro, U.S., Canada & Japan, Equity only) MSCI-Barra (Country, Regional and Global, Equity only) Northfield Inf. Services (Country, Regional, Global, MT and ST, Equity only) MAC-ST (Included in Balanced Risk Product & Required for FIIncluded in Balanced Risk Product & Required for FI)

+ Fast Re-Pricing Algorithm for FI.. Yield Curve (Int. Rate) Risk Specific to Underlying Currency of Security

17 KR Dur specified by 4 PCA of 6 Libor & Govt Curves (U.S., Can, Aus, EUR, Jap, UK)

Each Major Asset Class Has its Own Spread Model 3 Base Currency (USD, EURO, GBP) Reporting Options w/ Exp. to 13 Currencies Available

+ Fully Integrated with Portfolio Attribution..

Example of Global Equity Portfolio…

+ Construct Global Portfolio and Compare VAR and TE computed through FactSet Balanced Risk Module

Percent of Total HoldingsGLOB_EQUITY vs. MSCI EAFEMAC Global Multi-Asset Class Model (USD)U.S. Dollar

12/31/2008

MC % MC % MC %MC % Marginal Standalone Relative

Port. Bench. Value at Risk Value at Risk Value at RiskTracking Error (StDev)Asset Class Weight Weight Difference 22 Day, 95% 22 Day, 95% 22 Day, 95% 22 Day

Total 100.00 100.00 -- 12.26 12.26 3.55

Equity 96.26 100.00 -3.74 12.18 0.13 12.65 --United States 26.14 -- 26.14 2.85 0.11 16.71 --Japan 15.57 25.25 -9.68 1.09 0.07 17.75 --France 11.82 10.50 1.33 1.95 0.17 18.90 --Germany 8.66 8.74 -0.09 1.06 0.12 19.84 --Netherlands 6.02 2.52 3.50 0.89 0.15 18.04 --Sw itzerland 4.59 8.41 -3.82 0.51 0.11 15.77 --Australia 4.12 5.94 -1.82 0.61 0.15 21.84 --Hong Kong 3.95 2.01 1.93 0.54 0.14 22.03 --

China Mobile Ltd. 3.73 -- 3.73 0.51 0.14 22.31 --Hutchison Whampoa Ltd. 0.20 0.14 0.06 0.02 0.10 21.55 --Lenovo Group Ltd. 0.02 -- 0.02 0.00 0.05 35.61 --

United Kingdom 2.86 19.88 -17.01 0.38 0.13 18.13 --Canada 2.45 -- 2.45 0.67 0.27 36.72 --Sw eden 2.07 1.97 0.10 0.37 0.18 23.70 --Spain 1.72 4.53 -2.82 0.26 0.15 19.61 --Finland 1.46 1.39 0.07 0.23 0.15 20.66 --Denmark 1.26 0.84 0.42 0.21 0.17 23.59 --Brazil 1.01 -- 1.01 0.11 0.10 40.18 --Portugal 0.77 0.33 0.44 0.10 0.14 21.61 --Israel 0.59 -- 0.59 0.10 0.17 35.90 --Peru 0.55 -- 0.55 0.13 0.24 46.63 --Italy 0.51 3.62 -3.11 0.10 0.19 30.37 --Singapore 0.14 1.06 -0.92 0.02 0.11 20.29 --

Singapore Telecommunications Ltd.0.14 0.18 -0.04 0.02 0.11 20.29 --[Cash] 3.74 -- 3.74 0.10 0.03 3.77 --

Euro 1.32 -- 1.32 0.05 0.04 6.01 --British Pounds 1.17 -- 1.17 0.04 0.04 6.23 --U.S. Dollar 1.14 -- 1.14 -0.00 -0.00 -0.00 --Japanese Yen 0.10 -- 0.10 -0.00 -0.02 5.95 --

Tracking Error Forecasts….+ Computed TE using VAR and Historical (black) for Global Portfolio Measured

with various risk models………Which is right?

Tracking Error Forecasts with CI’s….+ Which is right? Most are, whence you compute the 95% Confidence Interval

on the Historical….Note Asymmetry…

Tracking Error… Bias+ A cross-section of the TE at a point in time has the following form..

bootstrap : test : var

v ar1.1

Den

sity

1 2 3

0.0

0.2

0.4

0.6

0.8

1.0

Observ edMean

Using Betas for measures of Volatility…+ What is the impact of the

correlation on one’s interpretation of how volatile a stock or portfolio is?

+ Beta’s ~ XLK: 0.9, ISRG: 1.2 XOM: 0.7

Using Betas for measures of Volatility…+ So a portfolio that has

next to no correlation with it’s bench then, has essentially no volatility?

+ Beta’s ~ Norm: 0.08 & t-Dist-12: 0.01

The Way to a Better Volatility Measure…g-Factor A question we might ask is, what’s the amount of time the bench & portfolio spend in a constant vicinity of their mean return?

Stdev of Bench = SD

+ Form the distribution of returns for a time period

+ Measure the area under curve between Mean +/- SD for both Bench and Portfolio….. Use the Bench’s SD for each…

+ Ratio of Bench area to Portfolio area is g-Factor

The “g-Factor”…+ The g-Factor is independent of the correlation and just compares the amount

of time the benchmark and portfolio “spend” within an identical distance of their mean values

g-Factor: (% of time Bench within +/- SD) / (% of time Port within +/-SD)

SP50 XLK XLF XOM ISRG LCV Magellan Nikkei Normal t-Dist-12

Variance 11.752 11.455 42.698 12.160 62.615 14.132 16.049 14.653 20.003 24.018Covariance 11.752 10.535 19.429 8.515 14.982 12.342 12.999 9.582 0.974 0.164

% of Time Ret is Spent

within +/- SD of its Mean 76.6% 76.0% 58.9% 69.8% 50.0% 74.5% 71.4% 72.4% 56.3% 80.7%g-Factor 1.000 1.007 1.301 1.097 1.531 1.028 1.073 1.058 1.361 0.948

Beta 1.000 0.896 1.653 0.725 1.275 1.050 1.106 0.815 0.083 0.014R^2 on Beta 0.83 0.76 0.51 0.31 0.93 0.91 0.54 0.00 0.00

Issues for Value-at-Risk..

+ Trading or portfolio positions change over time, thus the longer horizon VAR calculated, the less realistic it’s going to be, which is why we use daily VAR

+ VAR techniques are subject to model risk. In particular, the parametric model used for the drawing in Monte Carlo influences the value of the VAR calculated, hence there’s no “correct” VAR, it’s just an estimate

+ VAR isn’t effective when macro-risks, extreme events (Black Swans or ELE) are occurring. The returns distribution obtained from either a covariance based method or a copula, predicated on modeling the past years dependencies, isn’t representative of how the returns will behave in extreme events.

Even in a copula fitting of the factor returns with an attempt to garner non-linear dependencies in the tail, VAR will not show how the dependency really behaves during a Black Swan event

Existing VAR models reflect risks that are not useful during transition periods or when “broken” correlation structures occurs across assets

+ For a given covariance matrix, there are many, many datasets whose variance or covariance will satisfy it. There is no unique set of factor returns for a given covariance matrix (or copula)

Value-at-Risk Example_1

Stress Testing One: Time & Event Weighting..+ Pick a “shock”, any risk model factor or exogenous factor that has a time-

series (obviously, cause & effect economic variables, not weather forecasts)

+ Determine covariance/correlation of this “shock” to all risk model factors

+ Compute “Beta” between shocked factor “K” and all risk model factors from the covariance measurements

+ New Factor Return = Beta * Shock

Table 1.1 EXAMPLE OF STRESS TEST

Bet

a

Ear

ning

s/P

rice

Boo

k/P

rice

Tra

ding

Act

ivit

y

Log

of M

arke

t Cap

Ear

ning

s V

aria

bili

ty

EP

S G

row

th R

ate

Rev

enue

/Pri

ce

Deb

t/E

quit

y

Indu

stry

Current Factor Exposures 0.103 0.658 0.085 0.587 0.720 0.711 0.022 0.132 -0.158 0.049Current Factor Returns 0.802 0.848 0.851 1.153 0.557 1.033 1.066 0.822 0.687 1.390

Return Forecast 2.62 0.082 0.558 0.072 0.677 0.401 0.734 0.024 0.108 -0.109 0.069Factor Contribution to Return Forecast 3.2% 21.3% 2.8% 25.9% 15.3% 28.1% 0.9% 4.1% -4.2% 2.6%

Oil Shock Magnitude -30%Beta between Oil Shock and Factor Return 0.185 0.139 -0.038 -0.015 0.208 0.032 0.014 0.000 0.106 -0.037New Factor Return w/Oil Shock -0.056 -0.042 0.011 0.005 -0.062 -0.010 -0.004 0.000 -0.032 0.011

Shock Return Forecast -0.08 -0.006 -0.027 0.001 0.003 -0.045 -0.007 0.000 0.000 0.005 0.001Factor Contribution to Shock Return Forecast 7.5% 36.3% -1.3% -3.5% 59.3% 8.9% 0.1% 0.0% -6.6% -0.7%

Stress Testing One: Time vs. Event Weighting..

Test Name: S&P 500 30% DeclineReport Date: 8/23/2010Report Currency: U.S. DollarRisk Model: NIS US Fundamental ModelTime Decay: 0.98Event Decay: 0.94Factor: Shock % -30.00%

Date Factor Chg (%) Time Weight (%) # Date Factor Chg (%) Event Weight (%)7/30/2010 7.01 2.01 1 10/31/2008 -16.79 6.006/30/2010 -5.24 1.97 2 8/31/1998 -14.46 5.645/28/2010 -7.98 1.93 3 9/30/2002 -10.87 5.304/30/2010 1.58 1.89 4 2/27/2009 -10.65 4.983/31/2010 6.03 1.85 5 2/28/2001 -9.12 4.682/26/2010 3.10 1.82 6 8/31/1990 -9.11 4.401/29/2010 -3.60 1.78 7 9/30/2008 -8.91 4.14

12/31/2009 1.93 1.75 8 6/30/2008 -8.43 3.8911/30/2009 6.00 1.71 9 1/30/2009 -8.43 3.6610/30/2009 -1.86 1.68 10 9/28/2001 -8.08 3.44

" " " " " " " " " " " " " "" " " " " " " " " " " " " "" " " " " " " " " " " " " "" " " " " " " " " " " " " "

7/31/2006 0.62 0.76 49 1/31/2005 -2.44 0.316/30/2006 0.14 0.75 50 6/29/2001 -2.43 0.295/31/2006 -2.88 0.73 51 4/30/1993 -2.42 0.274/28/2006 1.34 0.72 52 5/28/1999 -2.36 0.263/31/2006 1.25 0.70 53 5/31/2000 -2.05 0.242/28/2006 0.27 0.69 54 8/31/1992 -2.05 0.231/31/2006 2.65 0.68 55 12/31/1996 -1.98 0.21

12/30/2005 0.04 0.66 56 2/28/2007 -1.96 0.2011/30/2005 3.78 0.65 57 3/31/1992 -1.95 0.1910/31/2005 -1.67 0.64 58 2/28/2002 -1.93 0.189/30/2005 0.81 0.62 59 4/29/2005 -1.90 0.178/31/2005 -0.91 0.61 60 2/29/2000 -1.89 0.16

Stress Testing One: Example

Percent of Total Holdings50 notsonifty and 50 sp100 eq.wgt vs. Russell 10009/07/2010R-Squared Daily Global Equity Model (USD) USD/EUR FX Rate 30% Decline

U.S. DollarPercent Percent Benchmark Benchmark

Percent Standalone Percent Standalone Percent PercentPort. Bench. Return Return Return Return Return Return

Economic Sector Weight Weight Difference (Time Wght) (Time Wght) (Event Wght) (Event Wght) (Time Wght) (Event Wght)

Total 100.00 100.00 -- -21.19 -21.19 -18.62 -18.62 -19.17 -16.34

Materials 6.19 4.07 2.12 -1.29 -20.80 -1.00 -16.20 -0.85 -0.67Consumer Staples 5.99 10.42 -4.43 -0.61 -10.22 -0.48 -8.06 -1.12 -1.00Industrials 13.03 10.96 2.08 -2.97 -22.80 -2.64 -20.22 -2.66 -2.42Energy 10.27 10.55 -0.28 -2.60 -25.33 -2.00 -19.48 -2.40 -1.93Information Technology 14.37 18.01 -3.64 -3.22 -22.38 -2.97 -20.69 -3.38 -2.84Utilities 4.75 3.93 0.82 -0.76 -15.99 -0.61 -12.88 -0.53 -0.46Health Care 8.93 11.66 -2.74 -1.25 -13.96 -0.89 -9.98 -1.68 -1.24Telecommunication Services 1.86 3.09 -1.22 -0.03 -1.50 -0.11 -6.14 -0.39 -0.36Consumer Discretionary 19.54 10.95 8.59 -4.32 -22.12 -4.00 -20.48 -2.30 -2.08Financials 15.07 16.36 -1.29 -4.15 -27.53 -3.91 -25.95 -3.85 -3.32

Holdings Data As Of 50 notsonifty and 50 sp100 eq.wgt 12/31/2008 Russell 1000 9/07/2010Risk Model As Of R-Squared Daily Global Equity Model (USD) 9/06/2010Market Portfolio: Russell 1000

08 09 10

1.20

1.25

1.30

1.35

1.40

1.45

1.50

1.55

1.60

00

Volume in Thousands (max/avg)

FX Rate - US$ per Euro (!XREUR)Daily from 31-Aug-2007 to 23-Aug-2010 High: 1.60U.S. Dollar (Split / Spinoff - Adjusted) Low: 1.19

Last: 1.27

Data Source: IDC / Exshare

Stress Testing One: Example …same data, but perspective has changed…

Total Mtrls CnStpls Indus EnergyInfoTech Utes H-Care Telecm CnDisc Finance7/31/2007 -2.42 0.06 0.00 -0.02 -0.05 -0.14 -0.17 -0.17 -0.31 -0.65 -0.958/31/2007 -0.91 0.09 -0.07 0.01 -0.15 -0.45 0.16 0.06 -0.15 0.44 -0.869/28/2007 -2.23 0.08 -0.15 0.13 -0.06 -0.41 -0.12 0.05 -0.31 0.00 -1.4410/31/2007 -2.98 0.16 -0.51 0.03 -0.12 0.06 -0.24 -0.30 -0.07 -1.03 -0.9411/30/2007 -2.34 0.14 0.20 0.08 -0.36 -0.70 -0.08 -0.07 -0.60 -0.35 -0.5812/31/2007 0.73 0.00 -0.12 0.07 0.09 -0.29 0.05 -0.12 -0.30 1.00 0.331/31/2008 -3.12 -0.03 -0.05 0.05 -0.15 0.20 0.12 -0.05 -0.52 -0.73 -1.972/29/2008 -3.13 -0.05 -0.28 -0.24 0.26 -0.31 0.10 0.30 -0.24 -0.62 -2.043/31/2008 1.08 0.21 0.29 0.69 -0.23 -0.19 0.11 0.25 0.23 0.81 -1.094/30/2008 -4.05 -0.10 0.05 0.13 0.03 0.07 0.12 0.01 0.23 -1.25 -3.335/30/2008 -4.40 0.14 -0.12 -0.02 -0.34 -1.06 -0.07 0.03 0.33 -0.92 -2.386/30/2008 -2.16 0.22 -0.37 0.07 0.55 -1.24 -0.45 -0.40 -0.24 0.11 -0.427/31/2008 -3.02 -0.06 -0.12 -0.03 0.01 -0.69 -0.18 0.01 0.09 -0.22 -1.838/29/2008 -9.67 -0.15 -0.59 -0.06 -0.20 -0.52 -0.32 -0.06 -0.42 0.41 -7.789/30/2008 -3.55 -0.01 -0.28 0.51 -0.57 -0.27 0.18 0.04 -0.94 -1.69 -0.5210/31/2008 -2.13 -0.40 -0.23 0.04 -0.64 -0.51 -0.50 0.40 -0.45 0.35 -0.1811/28/2008 -4.16 -0.63 0.22 0.12 -0.24 -0.35 -0.26 -0.57 -0.52 -1.08 -0.9012/31/2008 1.81 0.21 0.25 0.51 -0.16 0.51 0.37 -0.24 0.44 -0.38 0.311/30/2009 -0.18 0.34 -0.25 0.16 0.01 -0.73 -0.18 0.27 0.41 0.24 -0.442/27/2009 0.66 0.21 -0.12 -0.90 0.17 0.80 -0.24 -0.18 0.08 -0.07 0.903/31/2009 5.41 0.32 0.80 -0.14 0.57 0.62 0.05 -0.11 0.50 2.09 0.724/30/2009 -1.23 -0.34 -0.40 0.32 0.38 -0.30 -0.20 -0.15 0.52 -1.22 0.185/29/2009 0.04 -0.20 0.08 0.18 -0.14 -0.31 0.15 0.07 -0.19 0.14 0.266/30/2009 0.88 0.26 0.03 -0.31 0.22 0.22 -0.16 -0.13 -0.51 1.25 0.017/31/2009 1.25 -0.10 0.28 -0.02 0.02 0.76 0.06 -0.13 -0.03 0.08 0.338/31/2009 0.97 0.04 0.07 -0.22 0.30 0.41 0.17 0.20 0.06 0.05 -0.109/30/2009 -2.49 -0.07 -0.09 0.06 0.08 -1.70 -0.17 -0.01 -0.34 -0.12 -0.1510/30/2009 -0.21 0.02 -0.09 0.09 -0.21 0.11 -0.09 -0.24 0.23 0.05 -0.0811/30/2009 3.01 0.00 0.17 -0.01 0.11 1.51 0.05 0.08 -0.14 0.72 0.5112/31/2009 0.80 0.16 -0.08 0.16 0.15 -0.03 -0.01 -0.19 0.04 0.94 -0.341/29/2010 0.51 -0.19 -0.14 0.06 0.17 0.11 -0.13 0.50 0.09 0.06 0.002/26/2010 0.77 -0.32 0.08 -0.15 -0.15 0.80 -0.17 0.20 0.13 -0.14 0.513/31/2010 0.96 -0.05 0.19 0.00 0.07 -0.08 -0.04 0.12 0.20 0.22 0.324/30/2010 -0.35 -0.31 -0.14 0.07 -0.28 0.21 -0.11 0.06 0.36 0.01 -0.215/28/2010 -2.10 -0.13 -0.31 0.17 0.27 -0.63 -0.04 0.05 -0.38 -0.54 -0.556/30/2010 0.31 0.51 -0.11 -0.16 -0.01 -1.00 0.01 0.02 -0.06 0.43 0.697/30/2010 -0.89 0.16 -0.10 0.17 -0.27 -0.44 0.24 0.25 -0.31 -0.51 -0.07

USD/EURO Time -2.02 -0.43 0.51 -0.31 -0.20 0.16 -0.23 0.43 0.36 -2.02 -0.29USD/EURO Event -2.29 -0.33 0.52 -0.21 -0.07 -0.13 -0.15 0.35 0.25 -1.92 -0.59

-10.0

-9.0

-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7/31

/200

7

9/28

/200

7

11/3

0/20

07

1/31

/200

8

3/31

/200

8

5/30

/200

8

7/31

/200

8

9/30

/200

8

11/2

8/20

08

1/30

/200

9

3/31

/200

9

5/29

/200

9

7/31

/200

9

9/30

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9

11/3

0/20

09

1/29

/201

0

3/31

/201

0

5/28

/201

0

7/30

/201

0

Even

t

Excess Monthly Return

Stress Testing Two: Extreme Event Stress..

+ Extreme Event Stress let’s us go back in time and measure the current portfolio’s response to factor returns garnered from the past

+ It’s like using the cross-security relationships, the dependence structure from the past, because the factor returns used from a chosen historical stressed market environment, were those used to construct the covariance matrix at that time

+ In this module, we use past factor returns, multiplied by current exposures to allow us to examine how a portfolio today might behave should history “almost” repeat itself

Stress Testing Two: Example

+ What’s the Internet Bubble’s impact on Global Equity Portfolio, “Today”?

+ Borrow factor returns from April 2000

97 98 99 00 01 02 03 04 05 06 07 08 09

1500

2000

2500

3000

3500

4000

Russell 1000 (R.1000)Daily from 31-Dec-1996 to 31-Dec-2009 High: 3850.86Total Return Low: 1487.29

Last: 2909.18

Data Source: Russell

Percent of Total HoldingsGLOB_EQUITY vs. MSCI EAFE9/23/2010 Internet Bubble (4/2000)NIS Global ModelU.S. Dollar Percent Benchmark Port vs Bench

Percent Standalone Percent PercentPort. Bench. Return Return Return Difference

Asset Class Weight Weight Difference (Event) (Event) (Event) (Event)

Total 100.00 100.00 -- -6.71 -6.71 -7.03 0.32

Equity 97.06 100.00 -2.94 -6.64 -6.84 -7.03 0.39United States 25.36 -- 25.36 -1.38 -5.42 -- -1.38Japan 12.51 21.62 -9.11 -1.23 -9.87 -2.04 0.81France 11.80 9.52 2.28 -0.74 -6.31 -0.66 -0.09Netherlands 6.29 2.75 3.54 -0.42 -6.60 -0.21 -0.21Germany 6.25 7.75 -1.50 -0.35 -5.64 -0.65 0.29Switzerland 5.40 7.85 -2.45 -0.32 -5.86 -0.35 0.03Australia 4.54 8.59 -4.05 -0.11 -2.44 -0.39 0.27United Kingdom 4.51 21.72 -17.22 -0.24 -5.42 -0.89 0.64Sweden 3.59 3.02 0.57 -0.31 -8.62 -0.23 -0.08Canada 3.46 -- 3.46 -0.21 -5.97 -- -0.21Hong Kong 3.24 2.66 0.58 -0.36 -11.11 -0.27 -0.09Denmark 1.84 1.00 0.84 -0.27 -14.70 -0.08 -0.19Spain 1.80 3.72 -1.91 -0.19 -10.38 -0.39 0.21Finland 1.78 1.08 0.70 -0.14 -7.95 -0.10 -0.04Israel 0.94 0.84 0.10 -0.07 -7.73 -0.04 -0.03Italy 0.91 2.70 -1.79 -0.08 -8.45 -0.22 0.15Portugal 0.91 0.27 0.63 -0.05 -5.78 -0.02 -0.03Peru 0.89 -- 0.89 -0.11 -12.55 -- -0.11Brazil 0.89 -- 0.89 -0.05 -5.26 -- -0.05Singapore 0.14 1.64 -1.49 -0.01 -5.81 -0.15 0.14

[Cash] 2.94 -- 2.94 -0.07 -2.37 -- -0.07British Pounds 0.99 -- 0.99 -0.02 -1.91 -- -0.02

Euro 0.98 -- 0.98 -0.05 -4.74 -- -0.05

U.S. Dollar 0.88 -- 0.88 0.00 0.01 -- 0.00

Japanese Yen 0.08 -- 0.08 -0.00 -5.09 -- -0.00

Global Equity EAFE1 -18.224 -55.5912 -14.397 -50.7773 -13.050 -38.9374 -11.580 -32.9615 -11.116 -31.2396 -9.936 -27.7227 -9.670 -27.1328 -9.208 -26.8129 -9.182 -24.273

10 -8.498 -22.71811 -8.424 -20.16312 -8.381 -17.74613 -7.570 -16.54114 -7.340 -14.75815 -7.329 -14.715

16 -6.708 -14.467

17 -6.470 -13.90018 -6.364 -13.75019 -5.572 -13.07720 -4.903 -11.25521 -4.153 -11.17922 -4.128 -10.88323 -3.902 -10.37024 -3.798 -10.23525 -3.630 -9.74926 -3.497 -9.66327 -3.207 -9.49428 -3.189 -9.38229 -3.162 -9.19930 -3.150 -8.09331 -3.107 -7.492

32 -2.957 -7.03033 -2.909 -5.31534 -2.636 -5.28135 -2.602 -4.397

-60.0

-55.0

-50.0

-45.0

-40.0

-35.0

-30.0

-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101

106

111

116

121

126

131

136

141

146

151

156

161

Monthly Returns: 3/1997 to 8/2010

Global Equity

EAFE

Stress Testing Two: Example+ Internet Bubble’s impact on Global Equity Portfolio is…

+ Wouldn’t be the worst since 1997!!

Monte-Carlo Extreme Event Risk..+ Monte-Carlo Extreme Event Risk is enabling and is a unique combination of

FactSet’s stress testing platform combined with Value-at-Risk methodologies

+ Go back in time and literally take the covariance matrix from the past, decompose it via “Cholesky”, while separately and simultaneously, Monte Carlo-generated scenarios are made, and multiplied by this historically fashioned Cholesky matrix to compute “factor returns”

+ The Monte Carlo VaR is computed by multiplying each set of Monte-Carlo generated factor returns by the current exposure matrix

In this way, we use the dependence structure from a “Black Swan” event and past co-variances to see what a current portfolio’s VaR would look like under that past stressed situation

Monte-Carlo Extreme Event Risk Example..+ LTCM occurred August of 1998

+ Retns ~ -10% to -20%

Percent of Total Holdings50 notsonifty and 50 sp100 eq.wgt vs. Russell 10009/07/2010 Current Sim LTCM (8/1998) - SimNIS US Fundamental ModelU.S. Dollar MC % MC % ST % ST %

MC % Expected Standalone ST % Expected StandalonePort. Bench. Value at Risk Tail Loss Value at Risk Value at Risk Tail Loss Value at Risk

Economic Sector Weight Weight Difference 1 Day, 95% 1 Day, 95% 1 Day, 95% 1 Day, 95% 1 Day, 95% 1 Day, 95%

Total 100.00 100.00 -- 2.65 3.27 2.65 1.95 2.45 1.95Consumer Discretionary 19.51 10.94 8.57 0.58 -- 3.08 0.44 -- 2.34Consumer Staples 5.99 10.43 -4.43 0.08 -- 1.59 0.06 -- 1.41Energy 10.26 10.53 -0.27 0.25 -- 2.57 0.16 -- 2.21Financials 15.02 16.32 -1.31 0.51 -- 3.47 0.36 -- 2.58Health Care 8.94 11.69 -2.75 0.11 -- 1.62 0.08 -- 1.42Industrials 13.05 10.97 2.08 0.29 -- 2.31 0.22 -- 1.80Information Technology 14.40 18.03 -3.63 0.49 -- 3.81 0.39 -- 3.14Materials 6.19 4.07 2.12 0.18 -- 3.27 0.13 -- 2.52Telecommunication Services 1.88 3.09 -1.21 0.07 -- 4.95 0.04 -- 4.30Utilities 4.76 3.93 0.83 0.09 -- 2.30 0.07 -- 1.81

Holdings Data As Of 50 notsonifty and 50 sp100 eq.w gt 12/31/2008 Russell 1000 9/07/2010Risk Model As Of NIS US Fundamental Model 8/31/2010Market Portfolio: Russell 1000

Monte-Carlo Extreme Event Example..

+ When LTCM happened, the covariance matrix defined more lepokurtic return distributions

+ Whereas now, it shows a much broader distribution of returns

+ So today’s VAR is greater than that of this past extreme event

Monte-Carlo Extreme Event Risk Example Two + Credit Crisis of November 2008

Percent of Total HoldingsGLOB_BAL_MAND vs. MSCI EAFE

9/23/2010U.S. Dollar Report

Port. Bench.Asset Class Weight Weight Difference

Total 100.00 100.00 --Equity 73.60 100.00 -26.40

United States 25.15 -- 25.15Japan 13.10 21.62 -8.52France 9.34 9.52 -0.18

Germany 7.34 7.75 -0.41Australia 4.38 8.59 -4.21Canada 3.48 -- 3.48United Kingdom 2.81 21.72 -18.91Sweden 1.60 3.02 -1.42Hong Kong 1.59 2.66 -1.07

Hutchison Whampoa Ltd. 0.48 0.18 0.31Sun Hung Kai Properties Ltd. 0.31 0.22 0.09Hang Seng Bank Ltd. 0.28 0.11 0.17Swire Pacific Ltd. 0.26 0.10 0.16China Mobile Ltd. 0.20 -- 0.20Lenovo Group Ltd. 0.06 -- 0.06

Netherlands 1.32 2.75 -1.43Finland 0.95 1.08 -0.14Switzerland 0.84 7.85 -7.01Italy 0.73 2.70 -1.97Singapore 0.38 1.64 -1.26

United Overseas Bank Ltd. 0.26 0.16 0.10Singapore Telecommunications Ltd. 0.11 0.18 -0.07

Ireland 0.32 0.23 0.09Israel 0.28 0.84 -0.56

Fixed Income 20.69 -- 20.69Corporate 14.05 -- 14.05

Canada 4.60 -- 4.60South Korea 2.18 -- 2.18Australia 2.12 -- 2.12France 2.01 -- 2.01United States 1.95 -- 1.95United Kingdom 1.04 -- 1.04Italy 0.12 -- 0.12Spain 0.02 -- 0.02Hungary 0.02 -- 0.02Japan 0.02 -- 0.02

Honda Bank Gmbh 0.0% 12-oct-2010 0.01 -- 0.01Toyota Motor Credit Corp. 0.0% 04-jan-2011 0.01 -- 0.01Toyota Finance Australia Ltd. 4.12% 31-jul-2017 0.01 -- 0.01Toyota Capital Malaysia Sdn. Bhd. 4.2% 02-jul-2014 0.01 -- 0.01

Government Related 5.08 -- 5.08United States 1.07 -- 1.07

Sovereign 0.48 -- 0.48United States 0.48 -- 0.48

Derivatives 5.39 -- 5.39Metlife Inc Call DEC10 36 1.71 -- 1.71Factset Research S Call DEC10 80 1.57 -- 1.57State Street Corp Put JAN11 32 1.02 -- 1.02Bank Of Ny Mellon Put DEC10 22.5 0.40 -- 0.40Costco Whsl Corp N Put JAN11 65 0.25 -- 0.25Kraft Foods Inc Put DEC10 28 0.25 -- 0.25Bristol-Myers Squi Put DEC10 23 0.15 -- 0.15Astrazeneca Plc Put OCT10 28 0.02 -- 0.02Standard Chartered Plc Put OCT10 14 0.01 -- 0.01

[Cash] 0.32 -- 0.32U.S. Dollar 0.10 -- 0.10British Pounds 0.09 -- 0.09Euro 0.08 -- 0.08Japanese Yen 0.06 -- 0.06

Holdings Data As Of

GLOB_BAL_MAND 12/31/2009

MSCI EAFE 9/23/2010

Hidden: Benchmark Only Securities and Groups

Monte-Carlo Extreme Event Risk Example Two..

+ Using Global Portfolio of Equities, FI, Options and Currencies (Balanced..)

+ Examine impact of Credit Crisis (11/30/2008) on VaR

Monte-Carlo Extreme Event Risk Example Two..+ It’s clear that if the crisis of 2008 were to occur again, the addition of

derivatives in the portfolio would offer a strong hedge against losses

Percent of Total HoldingsGLOB_BAL_MAND vs. MSCI EAFE9/23/2010Factset/R-Squared Daily Global Multi-Asset Class Model (USD)U.S. Dollar Credit Crisis

ST % MC % MC %ST % Standalone MC % Marginal Standalone

Port. Bench. Value at Risk Value at Risk Value at Risk Value at Risk Value at RiskAsset Class Weight Weight Difference 22 Day, 95% 22 Day, 95% 22 Day, 95% 22 Day, 95% 22 Day, 95%

Total 100.00 100.00 -- 8.78 8.78 6.88 6.88

Equity 73.60 100.00 -26.40 8.78 14.05 5.89 0.07 8.76Fixed Income 20.69 -- 20.69 0.63 7.29 0.23 0.02 3.35

Derivatives 5.39 -- 5.39 -0.62 42.31 0.73 0.12 48.48[Cash] 0.32 -- 0.32 0.01 2.59 0.00 0.01 2.11

U.S. Dollar 0.10 -- 0.10 -0.00 -0.01 -0.00 -0.00 -0.01British Pounds 0.09 -- 0.09 0.00 6.04 0.00 0.02 3.94Euro 0.08 -- 0.08 0.00 5.38 0.00 0.03 4.25Japanese Yen 0.06 -- 0.06 -0.00 5.91 -0.00 -0.00 4.32

Exchange Traded Options+ Barone-Adesi & Whaley (JOF Vol42, No.2, June 1987)

1. Analytical approximation of American option pricing starting with European formula

2. Many times faster than most other methods

3. Loses accuracy for long dated options unfortunately (e.g. LEAPS) but acceptable accuracy for short to mid-maturity options

“They” used a normal approximation for the implied volatility, but that was written in 1987 before the 19 Oct 1987 “Black Monday” event inaugurated the volatility “smile”

Therefore FactSet uses an implied vol that’s fit to “f(strike/price, time to maturity)” from stock’s option chain, incorporating the observation that implied vols vary as the stock’s price varies from the option strike (volatility smile effects). This is a very smart methodology

1. The option pricing first involves solving iteratively for a critical stock price (Eq. 19 in their paper), below which the option’s call value is given by the Black-Scholes equation and above which the option’s call value is given by its exercisable proceeds (Price-Strike)

2. The critical price solution is placed into an analytical expression involving the addition of a early exercise premium to the Black-Scholes equation (Eq. 20 of their paper)

3. The next step, given option strike, vols, risk-free rate, time to maturity and stock price from the MC generating process, is simply to “plug-and-chug” to compute the option’s price

Ramifications for Fixed Income..+ Due to liquidity issues, seldom have real FI security returns to regress

against factor exposures to compute Betas

+ Hence we used previously calculated “sensitivities” (dur, convex..)

+ Monte-Carlo generated Interest Rate (yield curve) moves, spread and currency changes

+ Fast Re-Pricing (Taylor Series expansion) schema utilizes these changes to price “FI” instruments along with time decay

1. All securities of same currency have same yield curve exposure to the same set of 17 key rate risk factors (6 Libor & Govt Curves: U.S., Can, Aus, EUR, Japan, UK)

2. Different types of instruments have differing spread models, currently configured for:

Corporates Sovereigns (that we have yield curves for) High Yield U.S. MBS Agency Treasury Inflation-Protected Securities U.S. Treasuries Exchange Traded Derivatives

Rotund Posteriors, Hefty Backsides & Pudgy Extremities..+ Fat-Tails should be considered when skewness &/or kurtosis are prevalent

0.0%

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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Magellan

normal

Frechet

Rotund Posteriors, Hefty Backsides & Pudgy Extremities..

+ Q-Q Plots of 12 randomly selected small cap stocks

+ Most stocks are non-normal, the evidence is overwhelming..

Quantiles of S tandard NormalO

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GAM

VAR techniques are subject to model risk so the parametric model used for drawing in Monte Carlo influences the value of the VAR calculated..

95% VAR - 95% VAR EmpiricalFat-Tails->

Normal 1 2 3YEN/GBP -0.017 -0.070 -0.135 -0.108GBP/USD 0.039 -0.057 -0.094 -0.052S&P 500 0.113 -0.075 -0.076 -0.065DAX 30 0.115 -0.059 -0.057 -0.056CAC 40 0.124 -0.063 -0.085 -0.085NIKKEI 225 0.073 -0.125 -0.190 -0.016DJI 0.208 -0.035 -0.072 -0.055

..mean.. 0.094 -0.069 -0.101 -0.062

99% VAR - 99% VAR EmpiricalFat-Tails->

Normal 1 2 3YEN/GBP -0.451 0.268 0.133 0.515GBP/USD -0.248 0.447 0.426 0.894S&P 500 -0.162 0.266 -0.093 0.691DAX 30 -0.258 -0.100 -0.189 0.182CAC 40 -0.308 0.127 -0.049 0.076NIKKEI 225 -0.691 1.408 0.414 2.585DJI -0.249 0.393 0.232 0.550

..mean.. -0.338 0.401 0.125 0.785

Fat-Tailed & Skewed Asset Return Distributions; Frank Fabozzi Series; Wiley Finance 2005, pg 237

+ Normal is acceptable at 95% VAR

+ Fat-Tails underestimate 95% VAR, but are closer to it than normal method

+ Normal approximation leads to overly optimistic forecasts at 99% VAR

+ Fat-Tails generally result in conservative and accurate 99% VAR

VAR techniques are subject to model risk so the parametric model used for drawing in Monte Carlo influences the value of the VAR calculated..

+ Our own work suggests that normal method under-estimates the VAR compared to Fat-Tailed methods, even at 95% confidence level

Fat-Tail Value-at-Risk

+No “magic bullet” as it doesn’t capture correlation structural changes which occur in real “Black Swan” events (not modeling the volatility of volatility)

Currently @ FactSet+Internal discussions on methodology+Robustness tests, ease of use, computation time+On-going development continuing..