Study Session 2 – Quantitative Analysis · Web viewThey could have a financial advisor saying something like, “the stock isn’t expected to move much, so let’s put together

2004 CFA L 3 – S tudy T ips

Schweser CFA Level 3 Study Tips 2004

Test Format As you no doubt are aware, your Level 3 examination will be 50 percent essay and 50 percent multiple choice

(item set), with the essay portion in the morning and the multiple choice in the afternoon. Since AIMR®

doesn’t release old multiple choice questions, it’s very difficult to predict what you’ll see in the afternoon

session. However, we have provided many old AIMR® essay questions, as well as new ones we’ve written,

to help you prepare. You’ll find these questions in our study notes.

Your 2004 Level 3 Study Guide states that 10 percent of the exam will be Ethics and Professional Standards,

0 to 10 percent will be quantitative analysis, 30 to 40 percent asset valuation (Equity, Debt, and Derivatives),

and 40 to 60 percent Portfolio Management. Remember that AIMR reserves the right to test material in either

essay or multiple choice format. For example, the new material on behavioral investing is quite suitable as a

portion of an essay or multiple choice question. Even Ethics, which is an odds-on favorite for item set format,

could show up as part of an essay.

ContentThere is a lot of new material this year, much of it in derivatives. If I were making my CFA®-season study

plan (I’ve included a sample 18-week plan in book one of our study notes), I would definitely plan extra time

at the end to go back and re-study that material. Also, the behavioral/psychological investing material isn’t

particularly difficult, but I would read it thoroughly and be familiar with it. Study Session 18 (global investing) is

new this year, but it doesn’t really add much to the curriculum. Much of it was already covered in material that

was removed from other study sessions for 2004.

StrategyDO NOT take Level 3 lightly! I strongly recommend that you make a study plan and follow it throughout the

season. And don’t deviate from your plan assuming you can “make it up” in the coming weeks. I realize this is

very tempting, but I speak from experience in saying it’s very difficult to make up for lost time!

If at all possible, maintain a steady exercise program. Try to eat right and get plenty of sleep, especially in the

6 – 8 weeks before the exam. Keeping yourself in good shape will help keep your mind and body sharp under

the stress of the exam.

Quantitative Methods: Study Session 3 Quantitative methods is always a sure thing for the exam. Look for a regression output that you will have to

utilize/analyze. You will probably be asked to forecast the value of a dependent variable using the

coefficients, as well as evaluate the significance of the individual coefficients and the overall model. I strongly

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feel that you will be asked to “fill in the blanks” in an ANOVA output. Here is a sample regression output

including the ANOVA output with the relationships of the various cells, so you can get a start on feeling

comfortable with the process:

(The model is trying to estimate a home building company’s annual sales as a function of GDP and changing

interest rates.)

df = degrees of freedom; SS = sum of squares; MSS = mean sum of squares; n = total observations;

k = number of independent variables

Estimated model: annual sales = 6.0 + 0.004(GDP) – 20.5(Change I)

Fcritical at the 5% level of significance with dfnumerator = 2 and dfdenominator = 19 is 3.52.

Tcritical at the 5% percent level of significance (two-tailed t-values with df = 19) = 2.093

Conclusions:

F is highly significant, meaning at least one of the independent variables is statistically significant.

The r-square is marginal; the model explains 67% of the company’s annual sales.

The adjusted r-square adjusts for the number of independent variables, because as the number of

independent variables increases, the r-square will increase whether or not the model is better.

In this model only change in interest rates is significant in explaining the company’s sales (t = –

5.758). However, for the exam remember that even though GDP is not found to be significant (t =

1.327 < 2.093), you would use all the model’s coefficients in forecasting the company’s future sales

(the dependent variable).

Quantitative methods will most likely be tested in item set format during the afternoon session of the exam,

and can be extremely challenging. Look for quant concepts overlapping other sections (e.g., factor models,

portfolio theory).

Important topics in quantitative methods include:

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Multiple Regression

Understanding how to read an ANOVA table and how to interpret the economic meaning of results

from a multiple regression analysis are your keys to success in this Study Session. You should be

able to calculate t-statistics for regression coefficients, calculate confidence intervals for slope

coefficients or for forecasts, and calculate predicted values. Understand the relationship between R2

and adjusted R2. Understand terminology and implications associated with multicollinearity,

heteroskedasticity, and serial correlation. The flow chart on page 156 of Book 1 should help you

synthesize this material.

Time Series Analysis

A successful candidate will be able to understand how to forecast based on an autoregressive

model that may contain a seasonable lag component. Understand the difference between a trend

model and a lagged model. The flow charts on page 198-199 should be extremely helpful in

grasping the “big picture” flow of the material. You should know how to calculate a time series trend,

determine whether a model is covariance stationary (including calculating the appropriate t-test

statistic) or has a unit root, and test for lags in terms of t-statistics and autocorrelation. Make sure

you can calculate one-step-ahead and two-step-ahead forecasts for out-of-sample forecasts.

Portfolio Concepts

This material contains two main themes: single-factor models (e.g., CAPM) and multiple factor

models (e.g., statistical factor models, macroeconomic factor models, and fundamental factor

models). For single-factor models, you need to know how to calculate expected return, variance,

covariance, and correlation; construct and interpret the efficient frontier and the impact of correlation

on its shape; and understand the construction of and terminology associated with the capital market

line and the capital asset pricing model. Remember, a capital allocation line is nothing more than the

capital market line constructed from a limited number of possible assets, rather than the entire

market.

The ability to exploit arbitrage relationships is a key topic for multiple factor models. Tracking error is

big across the curriculum, and the topic of applications for construction of a tracking portfolio ties in

nicely with portfolio management (benchmark error), debt, derivatives (tracking error of synthetic

positions compared to the index), and alternative investments. Understand the difference between a

factor portfolio and a tracking portfolio.

There has been some confusion over unit roots and random walks, so here is some clarification and new

information that might help. First, for a simple linear regression time series (time is the only independent

variable), a random walk has a unit root, so random walk and unit root are effectively the same thing. Also,

the coefficient cannot be greater than 1.0.

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For a multiple regression time series (several independent variables) none of the coefficients can be equal

to or greater than 1.0. That is, none of the independent variables can have a unit or explosive root. Also, you

cannot use a t-test to determine whether a coefficient is statistically different from 1.0. For example, a

coefficient of 0.8 with a standard error of 0.2 would be significantly different from zero (t = 4.0) but

insignificant from 1.0 using a t-test (t =1.0). Don’t worry about this concept. For the exam just be concerned

with whether the coefficient is different from zero (t-test) and is not 1.0 or greater.

Portfolio ConceptsArbitrage Portfolios (Book 1, Page 240)

An arbitrage portfolio has the following characteristics:

Factor sensitivities of zero to all factors (no risk).

Positive expected cash flow.

An initial investment of zero.

Arbitrage portfolios are formed by simultaneously going short in one portfolio and long by the same dollar

amount in another. The portfolios have the same factor sensitivities, but the expected return on the short

portfolio is less than the expected return on the long portfolio.

Deriving an APT Equation

An arbitrage opportunity exists if we can create an arbitrage portfolio by going long in one portfolio (positive

weights) and short in another (negative weights).

Example:

The figure below shows three sample portfolios with sensitivities for a one-factor model. Determine the

parameters of the one-factor model that are consistent with these expected returns and factor sensitivities.

Expected Returns and Factor Sensitivities

PortfolioExpected

Return

Factor Sensitivity

(βp,1)

X 14.35% 1.25

Y 11.35% 0.8

Z 13.60% 1.1

Expressing the expected returns in the form of a one-factor model, we have three equations and two

unknowns. We need to do a little math to solve for the two unknowns (RF and λ1). The three equations are:

E(RX) = RF + 1.2λ1 = 14.35%

E(RY) = RF + 0.8λ1 = 11.35%

E(RZ) = RF + 1.1λ1 = 13.60%

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To solve for the value of λ1, we subtract equation 2 from equation 1:

0.4λ1 = 3.0% → 1.0λ1 = 7.50%

Plugging this value into equation 3 yields the value for RF:

RF + 1.1(7.5%) = 13.6% → RF = 5.35%

The APT equation is, therefore:

E(Rp) =5.35 + (7.50%)βp,1

Note: βp,1 is the sensitivity of the portfolio to the single factor, λ1.

Identifying Arbitrage Opportunities

Example:

Portfolio A has an expected return of 12% and a factor sensitivity of 1.07. Determine whether an arbitrage

opportunity exists, and discuss how this opportunity can be exploited.

Answer:

Using the arbitrage equation we derived, we calculate the expected return for A:

E(RA) = 5.35 + (7.50%)1.07 = 13.4%

The consensus expected return for A is 12% and our APT model says it should be 13.4%, so A is overpriced

relative to this risk factor.

Exploiting Arbitrage Opportunities

To take advantage of this arbitrage opportunity, we will first find a combination of portfolios X and Y that has

the same factor sensitivity (1.07) as portfolio A*. Because this other portfolio will also be consistent with the

APT, it should have a return equal to 13.4%. Then we can create an arbitrage portfolio by going short in A

and long in the other portfolio.

Expected Returns and Factor Sensitivities

PortfolioExpected

Return

Factor Sensitivity

(βp,1)

X 14.35% 1.25

Y 11.35% 0.8

Z 13.60% 1.1

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First we find a combination of X and Y that has a factor sensitivity of 1.07. This is a combination of two-thirds

(0.666) X and one-third (0.333) Y:

βx+y,1 = (0.666)(1.2) + (0.333)(0.8) = 1.07

E(Rx+y) = (0.666)(14.35%) + (0.333)(11.35%) = 13.4%.

* Note: Only portfolios X and Y were used to simplify the mathematics. You would no doubt be given the

correct combination on the exam. Also, I took minor liberties in rounding.

Portfolio XY has the same factor sensitivity as A (1.07) but a higher expected return (13.4% percent versus

12%). Assume you short $50,000 of A and invest the entire proceeds in XY for one year. The net (risk-less)

cash flow to this costless strategy is:

Cash Flow to Arbitrage Portfolio

Factor

Sensitivity

(β1)

Initial Cash

Flow

Cash Flow in One

Year

Short

Portfolio A–1.07 $50,000

–$50,000 × 1.120 = –

$56,000

Long

Portfolio XY1.07 –$50,000

$50,000 × 1.134 =

$56,700

Total 0.00 $0 $700

Factor Portfolios (Book 1, Page 243)

A factor portfolio is a portfolio with a factor sensitivity of one to one factor and zero for all other factors. It

represents a pure bet on that factor. In order to create a factor portfolio, three relationships must hold:

The sum of the portfolios’ weights in the factor portfolio must equal one.

The weighted average of the factor sensitivities to the factor we want to gain exposure to must equal

one.

The weighted average of the factor sensitivities to the other factor we do not want exposure to must

equal zero.

Example: Calculating Factor Weightings for a Factor Portfolio

Assume the two-factor (real interest rates and GDP) APT equation is:

E(Rp) = 3.0% + 5.0%βp,GDP + 6.0%βp,INT

Given the factor sensitivities for each portfolio below and the APT equation, calculate the expected returns of

a factor portfolio, which takes a bet on GDP growth without taking on any interest rate risk. That is, construct

the portfolio with a factor sensitivity of 1.0 to GDP and 0.0 to interest rates.

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Portfolio Expected Returns and Factor Sensitivities

PortfolioExpected

Return

GDP Factor

Sensitivity

(βp,GDP)

Int. Rate Factor

Sensitivity (βp,INT)

D 20.10% 1.02 2.00

E 14.00% 0.88 1.10

F 12.05% 1.15 0.55

Answer:

Equation 1: wD + wE + wF = 1.0

Equation 2: 1.02wD + 0.88wE + 1.15wF = 1.0

Equation 3: 2.00wD + 1.10wE + 0.55wF = 0.0

To find the combination (weights of D, E, and F in the factor portfolio) and then calculate its required return,

you would have to solve the system of equations. I find it hard to believe AIMR would ask you to do that, but

you can look at the appendix for Book 1 for an example of how to solve a system of three simultaneous

equations. What is more likely for the exam is that you would be asked to set up the equations as above. You

will notice that equation:

1 forces the weights of the portfolios to in the factor portfolio to equal 1.0

2 forces the weighted average factor sensitivity to GDP equal to 1.0

3 forces the weighted average factor sensitivity to interest rates to 0.0

Market Indexes & Global Equity: Study Session 5Know the differences in methodology for price-weighted, market value-weighted, and unweighted

(equal-weighted) indexes and their built-in biases. For example:

Changes in the prices of higher priced stocks have more of an impact on a price-weighted index

than do changes in lower priced stocks.

Firms with a greater market value have the greater impact on value-weighted indexes.

Use of the geometric average return for an unweighted index causes a downward bias.

Adjusting the divisor to calculate the value of a price-weighted index is unlikely for the exam, but know why it

is done. Also, be able to determine the proper type of benchmark index to use, given the construction of the

managed portfolio.

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I can’t imagine you’ll have to actually calculate an index or the return on an index for the exam. I would be

more concerned with knowing the construction methodologies and any biases incorporated into the indexes.

Remember, for benchmarking you need to select an appropriate index (i.e., one constructed in the same

manner as your managed portfolio).

Global Equity

You should be able to discuss the following topics:

The arguments for and against international diversification.

The difference between country and industry factors as they relate to portfolio diversification.

Barriers to global investing, such as political barriers, inefficient markets, differing market

regulations, low trading volume, and lack of information.

Benefits and difficulties associated with investing in emerging markets.

Check out the summary table on page 315 of Book 1 of the Schweser Study Notes.

The return to an international investment is approximately the sum of the return on the investment in its

currency (the local currency) and the currency return. This is a fairly easy concept and is covered on page

288 of Book 1. International investing barriers are important for the test (page 298). There seems to be a

move toward global and away from international (i.e., be able to discuss why it’s not enough to diversify by

country alone). Industry factors are becoming more and more important. The emerging markets material is

always popular, but of course evidence about whether correlations increase or decrease in crisis is

conflicting. Be able to discuss how international economies are becoming more correlated over time.

Debt Securities: Study Session 6-7Debt Securities will comprise about 10 percent of the exam and will probably be tested in the item set format

in the afternoon session of the exam. Prior to entering the exam center, you should be familiar with the

following:

International Bond Portfolios

Be prepared to calculate the local bond excess and currency returns as part of an analysis to determine

which strategy should be used in the international bond markets (i.e., no hedge, full hedge, proxy hedge,

cross-hedge).

Start by determining which bond promises the greatest excess return above its local risk-free rate and then

determine the optimal hedging strategy using that bond. See Book 2, pages 135 – 142.

Breakeven Analysis

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Be able to conduct a breakeven analysis to determine the necessary change in the spread between two

bonds, either both domestic or one domestic and the other foreign. You should be able to perform this

calculation from the perspective of either bond.

When performing the calculation, don’t worry about whether the sign of the numerator is positive or negative.

The sign has no effect on the absolute size of the yield change. Just remember this: For the bond at the

disadvantage, the necessary price change is positive, meaning its yield change must be negative. For the

bond at the advantage, the necessary price change is negative, meaning its yield change must be positive. In

either case, you’ll find the spread must widen for the total return on the two bonds to be equal (breakeven).

See Book 2, pages 144 – 150.

Downside Risk Measures

Downside risk measures as applied to bonds include target semivariance, shortfall risk, and value at risk. Be

able to discuss the benefits and criticisms of each. I have a gut feeling VAR will be on this year’s exam. Be

able to calculate and interpret historical and statistical VAR (using Z-values). See Book 2, pages 42 – 49.

Debt securities will comprise about 10 percent of the exam and will probably be tested in item set format

during the afternoon exam session. Prior to entering the exam center, you should be familiar with the topics of

bond management techniques, duration and leverage, and managing funds against liabilities.

Bond Management Techniques

You should know the pros and cons of various bond management techniques, especially bond indexing

(Book 2, page 88) and enhanced indexing (Book 2, page 95), and know the conditions that lead to increased

tracking error risk (Book 2, page 32).

The benefits to indexing include diversification, lower costs, and stable performance. Be able to discuss the

effects on these characteristics as you move from pure bond indexing to full blown active management.

Duration and Leverage

Be able to calculate the effects of leverage (Book 2, page 58) on the duration of both domestic and

international bond portfolios. You will want to read and know the fixed-income review in Book 2, starting on

page 41.

Managing Funds Against Liabilities

Immunization against a single obligation is the best bet for calculations on the exam (Book 2, page 72). Know

the rules that underlie simple immunization and contingent immunization procedures, including construction,

rebalancing, and extensions.

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For multiple obligations, be ready to contrast immunization with other strategies, such as cash matching and

dedication (Book 2, page 79).

Surplus Management

Be able to calculate economic surplus and changes in economic surplus for given interest rate changes

(Book 2, page 33). If it is included in the data, be sure to include convexity in calculating the percentage

change in asset and liability values:

dP/P = –(effective duration)(dy) + (convexity)(dy)2

International Investing: Computing Excess Returns

Note: In this context, excess return means above a risk-free rate of return.

It is possible to decompose the domestic currency return derived from any foreign asset into three parts:

The risk-free rate in the domestic currency, cd. (Note: This is not the risk-free rate in the foreign

currency.)

The return the foreign asset earns, ri, over the foreign risk-free rate, ci.

The expected currency return versus the domestic currency. (At the end of the investment the

manager will have to convert back into the domestic currency.)

These three components are shown in the unhedged strategy that follows. (The first two terms are the same

in all four strategies.)

Hedging Strategies

Unhedged: Rd,i = cd + (ri – ci) + (ed,i – fd,i)

You will note that the last expression in the equation, ed,i – fd,i, measures what the manager expects the

currency differential to be, ed,i versus the market’s expectations, i.e. the current forward differential, fd,i.

In the unhedged strategy, the manager feels the foreign currency will appreciate more than what is currently

priced by the market as shown in the forward rate. Note: He could also feel the foreign currency will

depreciate less than the current forward rate implies.

Standard hedge: Rd,i = cd + (ri – ci) + 0

All currency risk has been eliminated using forward contracts (i.e., the third term disappears). ·

Crosshedge: Rd,i = cd + (ri – ci) + (ed,j – fd,j)

The manager actually sells the foreign currency forward into a third currency. You will note the exposure to

currency i is no longer in the equation. Instead, the manager is now betting on the third currency (i.e., the

second foreign currency, currency j). He feels currency j will appreciate more than the market predicts as

indicated by the forward rate between currency j and the domestic currency. Remember, he will eventually

have to exchange currency j for the domestic currency.

Proxy hedge: Rd,i = cd + (ri – ci) + [(ed,i – ed,j) – fj,i]

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ed,i = expected change in foreign currency i relative to the domestic currency.

ed,j = expected change in foreign currency j relative to the domestic currency.

fj,i = actual forward premium or discount for currency i relative to currency j.

The manager is effectively betting on currency i versus currency j. That is, he feels i will appreciate against

the domestic currency more than j will.

Alternative Investments: Study Session 8Readings 6, 7a, and 7b are new this year. As such, you should consider them likely to be represented on the

exam. There is not much quantitative material in these readings, but there are a lot of buzz words to learn

such as impaired class, blocking position, cramdown, etc. Know the risks and advantages of distressed debt

investing. Understand the use of commodity futures.

Marketability and minority interest discounts could easily show up as part of an individual’s scenario that

would need to be addressed in an investment policy statement (IPS). For example, an individual’s portfolio

might be full of a stock that represents a large portion of their wealth but a minority interest in a private firm.

That means it would be subject to a discount in value due to both lack of control and marketability.

Hedge funds are always a favorite. The summary tables on pages 239-243 of Book 2 of the Schweser Study

Notes will be a great study aid here. If you’d like to practice, you will find hedge fund Question 12 from the

2003 exam, Question 8 from the 2002 exam, and Question 12 from the 2001 exam in the old exam questions

starting on page 290 of our Book 2. (Did you notice that there has been a hedge fund question for the last

three years?)

Market neutral (zero beta), equitization, and long-short strategies are important topics. Be able to

calculate the variance approach to tracking error for long-only versus long-short strategies (page 259, Book

2). All of this could easily be incorporated into an institutional portfolio management case. As an example,

look at Question 9 from the 2002 exam on page 297.

Valuing a real estate investment is a long shot that could show up (easy points!). Know how to interpret,

calculate, and utilize a reversionary value in the discounted cash flow valuation technique. Remember, the

reversionary value is nothing more than a terminal value at a point in time (an estimate of the value at that

time). See pages 189 and 190 in Book 2.

Long-short strategies are important, as they are used to create market-neutral positions. Know how to

calculate tracking error for long and long-short strategies (see page 259 of Book 2). The distressed debt

material is new, so pay attention to it. Also, the bankruptcy material, including the absolute rule of priority

(page 268), is important. There is no math, but you should know the material. Also, I like commodity futures

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for the exam. They’re a different type of futures contract, because they behave differently than financial

futures to changes in inflation and other macro variables. Hedge funds are always an AIMR® favorite. Know

the difference between a classic hedge fund and a current hedge fund. The most obvious difference is the

approach to risk. Current funds are far more speculative (i.e., long positions in excess of 100 percent and net

short positions). The risks of hedge funds (pages 241-242) are an easy AIMR target.

Derivatives: Study Session 12-13The derivatives material can be a bit daunting at times, so don’t try to conquer it all in one sitting. Take your

time and master each section before going to the next. Learning and mastering the basics is critical. For

example, you should be very familiar with all the characteristics of futures before studying the material on

adjusting the portfolio duration or beta using index futures.

Controlling Interest Rate Risk With Derivatives

Level 3 assumes you are familiar with the basics of call and put options, including their payoff/profit graphs.

Accordingly, the curriculum this year includes a review section on options beginning on page 73 of Book 3.

Be sure you are up-to-date on calls and puts and the various strategies presented.

Dollar duration is the primary concern in the risk management material. Be able to calculate the dollar

duration of a portfolio and for a futures contract (page 31, Book 3). To hedge a bond portfolio (dollar duration

= 0), the number of futures contracts to buy/sell is determined by the portfolio duration, the dollar duration of

the CTD bond, and its conversion factor. In the equations below, yield beta measures the relationship

between changes in the yield on a bond or portfolio of bonds and changes in the implied yield on the futures

contract. For example, a yield beta of 1.35 would indicate that the portfolio yield tends to change 35 percent

more than the change in the futures yield.

Note that some reference texts show the denominator as a product of the DDCTD and the conversion factor,

which is incorrect. Use the equation as I have presented it above. Also, since the target duration is zero, the

change in portfolio duration is –DDcurrent (i.e., that’s the amount the portfolio duration must fall). Generally, to

increase the dollar duration, buy futures. To decrease the dollar duration, sell futures. Therefore, hedging a

long portfolio will require shorting futures.

To adjust the duration of the bond portfolio using futures, we must determine the current MD, the target MD,

and the MD of the cheapest to deliver bond, CTD. Again, if the target duration is zero (complete hedge), the

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numerator becomes

–MDcurrent:

Note that the calculations for adjusting a portfolio beta are identical (except there is no yield beta) to adjusting

the portfolio duration. See page 35, Book 3.

Refresher Note on Portfolio Duration

The modified duration of a portfolio is the weighted sum of the individual bond modified durations, but the

dollar duration of the portfolio is the simple sum of the individual dollar durations. The contribution of an

individual bond to the modified duration or dollar duration of the portfolio is its component contribution in the

equation:

Breakeven Analysis

This single topic has caused more confusion than any other, so I’m going to present the BK method for

breakeven analysis! First the equation:

Note: The percentage change in the bond’s price (the numerator) is simply the number of basis points

expressed as a percent. For example, if the bond needs to increase 200 bp (2 percent) in value, the

numerator is +2. If the price of the bond must decrease 150 bp (1.5 percent) the numerator is –1.5, etc.

The confusion in the calculation is determining whether the numerator in the equation should be positive or

negative, and that will be determined by the bond being examined and the direction of the necessary change

in its price (either negative or positive). Also, if you are working with two bonds, one domestic and one

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foreign, always calculate the effective yield spread before anything else. Effective yield spread is my name for

the yield spread after consideration of any expected currency differential.

Example: Breakeven Spread Change

Bond A: Domestic bond; yield = 7%; modified duration = 5

Bond B: Foreign bond; yield = 8%; modified duration = 4

Expected currency depreciation (Bond B vs. Bond A) 200 bp

The yield spread shows Bond A at a 100 bp disadvantage (8% – 7%).

To determine the necessary spread change, first calculate the effective spread (i.e., the yield spread

after considering the expected currency differential).

The effective yield for Bond B = 8% – 200 bp = 6%.

The effective spread shows Bond A at a yield advantage of 100 bp (1%). The yield for Bond

A is still 7%, but the effective yield for Bond B is now 6% because of its currency

depreciation.

Determine the direction of the necessary price change.

The price of Bond A will have to decrease because it has the yield advantage.

Therefore, the sign of the numerator is negative (i.e., –1).

The price of Bond A must decrease 1% (100 bp).

This indicates the spread will have to widen by 20 bp due to the yield on Bond A increasing

20 bp.

The price of Bond B would have to increase for the capital gain to offset Bond B’s yield disadvantage:

The yield of Bond B will decrease 25 bp (i.e., the effective yield spread must widen 25 bp).

Important Note: For two domestic bonds, the existing yield spread must always widen for the bonds to

breakeven. For one domestic and one foreign bond, as long as you work with the effective yield spread, the

spread will also widen.

Options & Swaps Strategies

Put and Call Options

AIMR® has included a topic section on puts and calls, including their payoff and profit graphs, as well as

various strategies using either or both (see page 73, book 3). My opinion is that they wouldn’t put so much

review material in if they weren’t intending to test it, and that they don’t intend to ask for payoffs for individual

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put or call options! If you’re lucky they will ask for the payoff to a covered call (long the stock and short the

call) or protective put (long the stock and long the put). These option strategies would be fairly easy to

reproduce for the exam.

The spread strategies would be somewhat more difficult to remember and reproduce. For the exam I like the

straddle because of its symmetrical payoff (see page 93). They could have a financial advisor saying

something like, “the stock isn’t expected to move much, so let’s put together a short straddle.” You would then

have to say whether the statement is correct or not and why. From their payoffs, you can see the long

straddle is good if you expect large price movements, and the short is good if you expect less movement.

Remember, even though I recommend knowing the straddle, don’t neglect the other strategies!

The Greeks

This could be the year of the Greeks! I would know delta (see characteristics at the bottom of page 117) and

delta hedging, but I imagine they’ll only ask you to apply delta (see our example on page 116). You may be

asked indirectly to define gamma and vega as well. Again, you could see an analyst making statements that

you would have to verify or dispute.

Swaps

Do not enter the exam room without understanding and being able to calculate the cash flows associated with

a plain-vanilla interest-rate swap (page 145) or being able to outline the cash flows of a currency swap (page

158). Also, since the calculations are so similar to adjusting a portfolio beta or duration, be able to change the

duration of a portfolio using swaps (page 152). I think you should know the mechanics for an interest rate

swaption (page 169), but I don’t feel you’ll have to do any calculations for one.

Credit Derivatives

This is new material and quite relevant for today’s business environment. I would know and be able to

describe the cash flows for credit options. However, my gut tells me you won’t have to do many (if any)

calculations.

Review of DerivativesCredit Derivatives

A credit derivative is similar to insurance in that it specifies a transaction that takes place if and when a

specific event occurs, such as when a borrower declares bankruptcy or just fails to make a payment. Most

credit derivatives fall into one of four categories:

1. Credit swaps. To protect against default on a loan, the protection buyer (e.g., a bank) makes periodic

payments to the protection seller, and receives a payment if a credit event occurs.

2. Total return swaps. The protection buyer passes on the total return on a risky position (e.g., the principal

and interest on a loan) to the protection seller in return for some cash flow that is usually based upon LIBOR.

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3. Credit spread options. The protection buyer receives a payment based upon a credit spread, such as the

difference between AA corporates and U.S. Treasury bonds (e.g., payment = max [0, (AA yield – Treasury

yield) – 50 bp]). Here the credit derivative kicks in only if the spread exceeds 50 bp.

4. Credit-linked notes are loans or bonds that allow the issuer to reduce the payment of interest and/or

principal if a credit event occurs.

Credit Call Options

A credit call option allows investors to call for additional coupon payments. Typically, credit call options are

tied to a borrower’s credit rating and protect against some initial credit downgrades, and (unlike stock options)

credit call options are not usually just in- or out-of-the-money. A credit spread call option, for example, has a

value that is an increasing function of the credit spread.

In the expression for the payoff of the credit spread, we see the option has value only if the spread is greater

than the specified “strike” spread. Further, we can see that the credit spread call option payoff increases as

the spread increases:

OVt = MAX {[(RSt – SS)(NP)(RF)], 0}

where:

OVt = option value at time t

RSt = actual spread over the benchmark rate at time t

SS = specified strike spread over the benchmark rate

NP = notional principal

RF = the risk factor (duration), or any adjustment for interest rate sensitivity

Note:

The word “MAX” in front of the expression simply means that the value of the option is the larger of 0

or . So if is negative (i.e., the strike spread is greater than the actual spread), the value of the option

is 0. Calculating the credit spread option payoff this way means the payoff will never be negative.

RF is an adjustment factor, usually duration. Since the value of the asset held will change when the

spread changes, the factor makes the value of the notional principal (NP) in the equation change,

also.

Example:

Let’s assume the strike spread is 300 bp, the notional principal is $10,000,000, and the duration of the bond

portfolio is 3.6. Calculate the option payoff if the spread changes to 250 and 375 bp.

Answer:

At 250 bp:


= (0.0250 – 0.0300)(10,000,000)(3.6) = –$180,000

Since the value of the option is –$180,000, there is no payoff (i.e., the payoff is 0).

At 375 bp:

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= (0.0375 – 0.0300)(10,000,000)(3.6) = $270,000

The option buyer will receive a payment (extra coupon, etc.) of $270,000 from the seller to increase the

effective coupon rate.

Credit Put Options

A credit put option allows the investor to put the bonds back to the issuer at face value if a certain condition

exists (e.g., a credit rating falls below investment grade). If the bond remains rated as investment grade, the

value of the put is zero.

If the bonds are subsequently rated as noninvestment grade, the value of the put is the difference between

the par value and the market value. This option protects the bondholder from any decrease in value due to a

widening credit spread, which could be caused by a downward credit revision.

Credit put options are also not generally specified in binary terms. Rather, they are valued in the following

way:

option valuet = (St – Vt) × NP

where:

NP = the notional principal

Vt = value of the bond at time t, expressed as a percent of par

St = strike price of the option at time t, expressed as a percent of par

Example:

Suppose that LIBOR is 5.0 percent, and a firm sells 5-year, 7.10 percent annual coupon notes (a spread of

210 bp over LIBOR). The yield is currently 7.10 percent. The bonds are issued along with a credit spread put

with a strike price determined by a 300 bp spread over LIBOR.

When the bonds are issued they are worth:

N = 5; I/Y = 7.10; PMT = 7.10; FV = 100; CPT PV = 100

The credit put strike price is:

N = 5; I/Y = 8.00; PMT = 7.10; FV = 100; CPT PV = 96.41

Since the bond price is greater than the strike price, the option is out-of-the-money.

Now suppose that one year later (technically, the day after the first coupon payment for computational

simplicity) LIBOR is 5.75 percent and the yield on the bond is 9.10 percent. Calculate the value of the credit

put option.

The bonds are now worth:

N = 4; I/Y = 9.10; PMT = 7.10; FV = 100; CPT PV = 93.53

The credit put strike price is:

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N = 4; I/Y = 8.75; PMT = 7.10; FV = 100; CPT PV = 94.62

The option is now in-the-money, because the strike price is greater than the bond’s price. Note also that both

the bond price and the strike price change when LIBOR changes. Suppose that a portfolio manager holds

$10 million face value of the bonds. He can put the bonds to the seller of the credit option at 94.62 percent of

par value. Therefore, the value of the put is:

option value1 = (S1 – V1) × NP

option value1 = (0.9462 – 0.9353) × 10,000,000 = $109,000

Creating a Synthetic Equity Index from Treasury Bills

Since an investor could simultaneously buy the stock of an equity index and sell futures on that index, the

combination of the two must yield the risk-free rate. The price of the index today must be:

FT = S0(1 + RF)T – dividends

That is, the futures price for a contract maturing at time T must be the future value of today's stock prices (at

the risk-free rate) less the dividends that are not received when you purchase the futures contract. That's why

we discount at the dividend rate to arrive at the synthetic position in equity created with the purchase of the

index.

Example data (expanded example from Book 3, page 40): (Note: You may find some slight rounding

differences as you work through this example).

A manager currently holds $120,000,000 T-bills:

RF = 3%; PF = 1,100; multiple = 250; div yield = 2%; T = 6 months

In six months the bills will be worth:

$120,000,000(1.03)1/2 - $121,786,989

The manager will purchase 443 futures contracts:

N = [($121,786,989)/(1,100)(250)] = 442.86 = 443

(Must be a round number)

443 contracts will actually equitize $120,037,739.30:

[(443((1,100)(250)/1.031/2)] = $120,037,739.30

(We assume the manager purchases an additional $37,739.30 in T-bills)

443 contracts are equivalent to holding 109,658.84 “units” of stock in the index:

[(443)(250)/1.021/2] = 109,658.84

Had these units actually been purchased, they would receive dividends (at 2%) and grow to 110,750

units in six months (assuming reinvestment of the dividends):

109,658.84(1.02)1/2 = 110,750

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Because of convergence, the futures price (per unit) in six months will be ST, and the total futures

price will be 110,750(ST) (i.e., the number of units times the price per unit).

In six months the T-bills will be worth:

$120,037,739.30(1.03)1/2 = $121,825,000

Cash flows in six months on the futures contracts (assumes reversing out of the futures contracts):

Deliver the agreed upon futures price (i.e., $121,825,000).

Sell the same contracts and receive the value of 110,750 units of the index stocks [i.e.,

110,750(ST)].

So, the manager’s payoff on the futures contracts is:

payoffFutures = 110,750(ST) – $121,825,000

Note that since the manager doesn’t actually want delivery of the T-bills in the futures

contracts, he can simply reverse out of the contracts. In that case, he will receive or pay the

net position (i.e., the difference between the agreed upon futures price and the current

price).

Since the manager now holds the T-bills and has earned the payoff on the futures position, his net

position is:

$121,825,000 + [110,750(ST) – $121,825,000] = 110,750(ST) .

So, the manager started with T-bills valued at $120,000,000 and ended up with a total value of

110,750(ST), the value of the stocks in the index.

He thus earns the return on the stocks in the index.

Portfolio Management – Individual Investors: Study Session 9Portfolio Management, individual and institutional, is without question the most important material for the

Level 3 exam. Portfolio management will be 50 to 60 percent of the exam and will dominate the morning

(essay) portion of the exam. This week I will focus on individual portfolio management.

I strongly recommend that you read and reread our study notes and try as many old exam questions as

possible. Learning the patterns in answering AIMR® essay questions is paramount. By the way, as you do

the old exam questions, be aware that the guideline answers are not what AIMR expects for the exam.

Typically, you can use about half of what AIMR includes in their guideline answers and get full credit. As you

read their answer, give thought to how much you could leave out.

Here are a few suggestions for answering essay questions:

Get to the point. Be as brief as possible while fully answering the question.

Don’t feel you have to say a lot to say enough

NEVER add anything that does not relate directly to the question asked.

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Don’t give the grader excuses to deduct points by making unnecessary comments or

assumptions.

Even if AIMR gives you a full page for a one-line answer, just write the one line!

Determine the time horizon(s) first.

The various horizons will be clear from the case.

Working years (pre-retirement).

Intermediate goals, such as college for kids.

Retirement.

Post-retirement.

Given the time horizons and their required cash flows, determine the required return.

Consistency, consistency, consistency.

Be sure your final recommendation agrees with your goals and constraints.

Even if you recommend the wrong portfolio (by choosing one from among four or five), if

you have been consistent throughout the answer, you will get some points.

If you are not consistent and recommend the wrong portfolio, you will miss all the points.

If the client’s willingness to accept risk (as stated in the case) does not agree with his or her

ability to accept risk (as determined by wealth, income, goals, and time horizon), go with

the client’s desires unless doing so will place the portfolio at undue risk.

If you recommend less risk, be sure to make a note in your answer to explain why

you are not taking as much risk as the client wants.

It is almost always safe to recommend risk/return education.

You can usually recommend legal counsel, too, especially if there are any unusual

circumstances or complications. Examples include special trusts set up at before

or after death, large charitable contributions, etc.

Make logical assumptions.

Inflation of 3% is reasonable.

Protection of principal is reasonable (i.e., don’t meet cash flows out of principal,

unless specifically stated in the case). For example, the client may want to make

an immediate donation to charity. The donation must be deducted from the

portfolio before determining time horizons and associated returns/cash flows

Behavioral Investing

Look for “The Psychology of Investing” (beginning on page 63, Book 4) to show up in cases for individual

investors. (I wouldn’t be surprised to see item set questions, also!) It would be very simple for AIMR to have

the client make certain statements that demonstrate overconfidence, snake bite, fear of regret, house money,

etc. If you detect any psychological traits that place constraints on the portfolio that are not in the client’s best

interest, be ready to point them out and explain why the client needs education on the topic.

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Portfolio Management – Institutional Investors (Study Session 10)This material, which focuses primarily on employer-sponsored pension plans and insurance companies, has

been in the curriculum for a while and is usually tested in essay format. Having said that, however, be aware

that it would be very easy for AIMR® to test pensions, both defined benefit and defined contribution, in the

item set format. If pension plans show up on the exam, I would expect calculations and explanations (essay

format) to be more relevant for defined benefit pension funds. Defined contribution plans would more

appropriately be tested as item set, since the major institutional problems associated with them typically

center on the firm’s fiduciary duty to the employees (beneficiaries).

Look over thoroughly and be able to answer questions related to the summary table on page 122 of Book 4.

Don’t just memorize the table, however. Remember, Level 3 is all about being able to look at the material

from one perspective and answer from another. For example, for a defined benefit pension plan, the table

states the amount of risk tolerance, “depends upon surplus, age of work force, time horizon, and company

balance sheet.”

Be able to explain each component of the statement. For example, “The risk tolerance of the defined benefit

pension plan depends upon the average age of the work force, because average age determines the time

horizon and the associated pension liability. High average age implies a short time horizon and high pension

liability. A short time horizon usually means low risk tolerance, especially when accompanied by a large

liability. ”

Surplus: The larger the surplus the more risk the plan can take. However, a safety net (minimum) return

should be determined. If the return on the fund’s assets hits the safety net return, sometimes referred to as a

trigger return, the fund manager should immunize. (Remember contingent immunization? It is discussed on

page 76 of Book 2.)

Age of work force: Generally, the younger the work force, the longer until they retire, and an older average

age work force indicates a shorter horizon. How do surplus and work force age relate? The younger the work

force, the longer the planning horizon, and the smaller the necessary surplus (i.e., the more time to make up

for short term underperformance).

Time horizon: Time horizon is an extremely important variable to pinpoint. Without first determining the time

horizon, meaningful required and safety net returns are impossible to determine with any validity.

Company balance sheet: By now you’ve noticed the circularity of the characteristics already discussed. Any

pension fund planning means next to nothing if the company is in financial difficulty. Of course, given a fairly

sound firm, the stronger the balance sheet (the greater the equity of the firm) the more risk that can be taken,

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because the firm is better able to make special contributions to the fund. If the firm is unable to do that, the

pension fund manager must be very careful not to accept undue risk in the plan’s assets.

Comparing Institutional and Individual Investors

Other than the obvious differences associated with size and the firm’s fiduciary duty to its employees, legal

and time horizon issues are important differences for the institutional investor versus the individual investor.

For example, the time horizon for the institutional investor is usually infinite with continuing liabilities to current

retirees while the individual’s time horizon is finite, because even if the individual intends to leave money to

charity or relatives, the investor has a finite life.

Strategies for Asset Allocation (Study Session 11)The summary points on page 165 are very important for the exam. Again, don’t just memorize the points;

know what they mean. For example, take the statement:

“A constant mix strategy will outperform buy and hold and CPPI strategies in a flat but oscillating market.”

The buy and hold strategy does nothing in a flat, oscillating market, so the value of the portfolio oscillates

with the market, but neither transactions costs nor profits or losses associated with trading are incurred.

CPPI assumes readjustment of the portfolio according to a formula. As the portfolio value falls (oscillates

downward) and approaches the floor value, the portfolio manager sells equities. As such the portfolio

manager sells low. Then, as the market oscillates back up, the portfolio manager will buy equities at

increased prices (buys high).

In a constant mix strategy, the manager will continually buy low and sell high. As the portfolio increases in

value, due to increases in the value of equities held, the manager will be forced to sell equities to maintain the

constant percentage mix of debt and equity. Then, as the market falls and the percentage of equities in the

portfolio falls with it, the manager must buy equities to return to the set percentage.

Bottom line, when the market oscillates but is generally flat, the buy and hold strategy will experience no

transactions costs, profits, or losses associated with trading. In the CPPI, the manager buys high and sells

low, continually generating losses. In the constant mix, the manager buys low and sells high, continually

generating profits. Hence the constant mix strategy outperforms both the buy and hold and CPPI strategies in

a flat, oscillating market.

Portfolio Management: The Tracking Error Question (Study Session 14)From Study Session 14:

Tracking error = standard deviation of monthly excess returns.

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Excess return = alpha = the difference between the portfolio return and the index (benchmark) return.

Earlier in the curriculum:

Tracking error = the difference between the portfolio return and the index return.

Tracking error risk = the standard deviation of the tracking error over time.

The confusion:

Tracking error = the difference between the portfolio and index returns (i.e., a single measurement at one

point in time).

Tracking error = the standard deviation of the difference between the portfolio and index returns over time

(i.e., the standard deviation of many measurements).

Alpha = excess return = the difference between the portfolio and index returns, (i.e., a single measurement at

one point in time). This means alpha is the same as one of the tracking error definitions!

For the exam:

If there is a silver lining to this dark cloud, it is that AIMR® must realize the confusion as well. On the exam

they will have to be very explicit in what they ask. For example:

Bounty Funds has experienced a tracking error of 28% over the past twelve months, and the

average excess return (alpha) during the period was 6%. Calculate Bounty’s information ratio.

The information ratio is defined as:

IR = (average excess return, or alpha) / (standard deviation of excess returns) = 0.06/0.28 = 0.214

In this example, we know they must be using tracking error defined as the standard deviation of

excess returns over the period, because it was presented as a measure over several periods.

Using the data provided in Figure 1, calculate Bounty Fund’s average tracking error over the last

twelve months.

Figure 1: Benchmark and Portfolio Returns

MonthReturn

Tracking ErrorPortfolio Benchmark

1 0.010 0.009 +0.001

2 0.008 0.002 +0.006

3 0.014 0.011 +0.003

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4 0.006 0.010 –0.004

5 –0.001 0.006 –0.007

6 0.005 0.007 –0.002

7 0.002 –0.009 +0.011

8 0.011 0.010 +0.001

9 0.007 0.007 +0.000

10 0.010 0.006 +0.004

11 0.001 –0.001 +0.002

12 0.002 0.008 –0.006

Average = +0.00075

By the way the data was presented and the question was asked, we know they calculate tracking error as the

simple difference between portfolio and benchmark returns and they want the average of that difference for

the past twelve months.

Using the data in Figure 1 (and assuming a standard deviation of 0.009), calculate the information

ratio for Bounty Funds.

IR = (average excess return, or alpha) / (standard deviation of excess returns) =0.00075/0.009 =

0.0833

The question was phrased such that you know exactly what you need to do (i.e., what form of

tracking error was to be used). In this question tracking error was presented as the standard

deviation of excess returns.

Risk Considerations: VAR (Study Session 15)The two methods for calculating value at risk (VAR) are analytical and historical:

Analytical VAR

Using the analytical method to express VAR in percentage terms:

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Note: On page 18 of Book 5, currency VAR is presented as:

By multiplying by the value of the portfolio, this equation turns the percentage VAR into dollars (currency).

IMPORTANT NOTE: Both forms of the equation are found in the CFA curriculum this year. The first equation,

however, subtracts the absolute (positive) value of z times the portfolio standard deviation, and the second

adds the actual (negative) value of z times the portfolio standard deviation. Both expressions, therefore,

subtract z(s) from the expected return.

Analytical VAR is based upon past variance and covariance measures (i.e., the analyst must assume past

variances and covariances are representative of the future). Also, since you are only concerned with

downside risk, VAR is a one-tail measure. As such, we do not necessarily work with the z-values we used to

create confidence intervals (CI).

In the back of Book 5 are two tables: the cumulative z-table and the alternative z-table. The alternative z-

table, which could also be used to generate VAR, is what you used to generate confidence intervals. The

cumulative z-table, however, is actually better for measuring VAR, because it measures one tail rather than

two. All you have to do is find the level of significance you desire in the body of the table.

Aside: The graphic at the top of the table might confuse you, because it seems to measure the upper tail.

Since the distribution is symmetrical, however, the z-values actually measure either tail.

Figure 1 has a few VAR significance levels and their corresponding z-values from the cumulative z-table. Be

sure you are confident in finding these values:

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Once you have located the desired significance value (actually as close to it as possible), you add the

corresponding values for z along the left margin and across the top. Looking for 0.9000, for example, you will

find a value of 0.8997. We add the corresponding values for z and get 1.2 (row heading) + 0.08 (column

heading) = 1.28. This means we will use z = 1.28 to define the 90 percent VAR.

Try it with a 95 percent VAR: 95 percent implies 5 percent in the tail or a value in the body of the table of

0.9500. Searching through the table, 0.9505 is about as close as you can get, so z = 1.6 + 0.05 = 1.65.

Example:

Let’s assume we want a 90 percent annual VAR for a portfolio with an expected return of 15 percent and a

standard deviation of 9 percent. Since we want 10 percent of the possible returns to fall in the lower tail, the

z-value is 1.28, and:

If we now assume the portfolio is worth $1,000,000,

There are two interpretations of these answers:

There is 95% probability the annual return will be greater than 0.0348 or $34,800.

There is 5% probability of an annual return less than 0.0348 or $34,800.

Note: Figure 2 shows z-values using the alternative z-table, just in case that is your preference. You will

notice that, in each case, the values in the table are those in Figure 1 less 0.5000.

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Historical VAR

Historical VAR would also be easy to ask on the exam. Historical VAR is based upon actual past returns, not

their distribution; hence, it is not dependent upon past measures of variance and covariance.

Example:

Estimate the 90 percent 1-week VAR for Bounty Funds. Figure 3 presents the past 20 weekly returns for

Bounty Funds, in no particular order:

Answer:

First, we rank the returns in descending order from the highest 1-week return: 0.0032, 0.0028, 0.0021,

0.0017, 0.0015, 0.0012, 0.0011, 0.0010, 0.0009, 0.0008, 0.0007, 0.0006, 0.0004, 0.0004, 0.0002, –0.0010, –

0.0013, –0.0015, –0.0021, –0.0027.

Ninety percent VAR implies 90 percent or 0.90(20) = 18 of the returns are above the 90 percent VAR and

0.10(20) = 2 returns are below. From the ranking, we see that the two lowest returns are –0.21 percent and –

0.27 percent.

We can say two things:

There is 90% probability that the lowest 1-week return will be –0.21%.

There is 10% probability that the 1-week return will be lower than –0.21%.

Note: VAR must always have a time dimension (e.g., in our first example the VAR was stated for a 1-year

period, and in the second, VAR was stated for a 1-week period). VAR must also be stated with a set

percentage. We used 90 percent in both the examples. Although you might see any value used on the exam,

I would expect that you will have to calculate a 95 percent VAR. From Figure 1, you can see that z = 1.65 is

associated with a 95 percent VAR.

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Performance Evaluation, Attribution, and GIPS® (Study Session 17)This material is part of the 40–60 percent allocation to portfolio management. You will see a performance

presentation that you will have to analyze—either a prepared presentation or statements related to its

construction.

GIPS

Every year AIMR® has used at least one question related to performance presentation. Be sure to focus on

old exam questions as an indicator of what you will see in this area on the exam. Know the requirements—

especially the disclosures. In recent years, you needed to identify errors in presentation along with omissions.

The omissions almost always relate to missing required disclosures. See page 197, Book 5, for a complete

list and discussion of required disclosures.

Start with our coverage of GIPS in Study Session 17 (Book 5) and the example on page 219. Next, go to the

problem set associated with our Study Session 17 review, which starts on page 225. Once you feel fairly

comfortable with the material, work through the old exam questions, starting on page 236 with 2002 Question

4.

Performance Evaluation

The Sharpe and Treynor measures and Jensen’s Alpha, starting on page 101 (in Study Session 16,

Evaluation of Portfolio Performance) in Book 5, are always important topics. The Sharpe measure, for

example, has been on almost every Level 3 exam in recent history, and candidates have been asked to

compare evaluation results using the three measures.

First, know when each measure is appropriate to use. As a rule of thumb, just remember that for an accurate

assessment of return relative to risk, you must consider the actual risk of the investment over the period,

whether systematic only, unsystematic only, or some combination of the two:

The Sharpe ratio measures excess return (above the risk-free rate) per unit of total risk, which is

measured with standard deviation. In this fashion, the analyst makes one of two assumptions:

The portfolio is completely diversified, so the only risk present is systematic risk, or…

The asset is stand-alone, so total risk is the appropriate measure of risk.

The Treynor measure uses beta to measure risk, so it measures return per unit of nondiversifiable

(systematic) risk, only. Treynor is appropriate only when the portfolio is fully diversified (i.e., when

there is no unsystematic risk in the investment).

The CAPM methodology used to calculate Jensen’s Alpha assumes returns of the portfolio are

determined by the market portfolio, and the expected value of the error term is zero. The error term

in the CAPM regression measures unsystematic risk (variability in the portfolio’s returns that is not

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explained by the market), so the analyst utilizing Jensen’s Alpha is implicitly assuming only

systematic risk is present. Also, the R2 for the Jensen regression indicates the percentage of

variability in the dependent variable (the portfolio’s excess returns) that is explained by the market’s

excess returns. A very low R2 would indicate significant unsystematic variability (lack of

diversification).

Using Sharpe and Treynor to Rank Portfolios

If a portfolio was not well-diversified over the measurement period, it may be ranked higher using Treynor

than using Sharpe, because Treynor considers only the systematic risk (beta) of the portfolio over the period.

When the Sharpe ratio is calculated for the same portfolio, the increased risk (standard deviation captures

both systematic and unsystematic risk) due to using total risk may cause a lowering in the rankings.

When a portfolio drops in ranking using the Sharpe ratio as compared to the Treynor ratio, it is not as

diversified as the other portfolios, and its Treynor measure, which considers only systematic risk, is not

catching the actual total risk over the measurement period.

If a portfolio rises in ranking using the Sharpe ratio, it was more diversified than the comparison portfolios

(i.e., the comparison portfolios’ standard deviations contained more unsystematic risk, so they dropped in

rank).

The Information Ratio

The information ratio compares the performance of the portfolio to the risk undertaken to achieve the

performance. When portfolio performance is compared to its benchmark, any returns over the benchmark are

considered surplus return. (Note: This is also referred to as tracking error elsewhere in the curriculum.)

The information ratio is the surplus return divided by its standard deviation; therefore, it compares the surplus

generated by the portfolio manager to the risk taken to achieve the surplus:

Again, the information ratio is defined as average tracking error divided by the standard deviation of the

tracking error:

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Remember, tracking error is also defined as the standard deviation of the portfolio excess return over the

period, which would be the same as the denominator in the above expression. That is, the difference between

portfolio and benchmark returns is also referred to as excess return (same as the numerator above). Ugh!

This confusion was discussed in my April 22nd tip.

Performance Attribution

Portfolio managers seek to outperform their benchmark by either selecting undervalued securities (selection

effect) or shifting allocation among asset classes at the right time (allocation effect, a.k.a. sector rotation or

market timing). Allocation skill involves shifting money out of sectors that are expected to perform poorly into

those sectors that are expected to perform well. Performance attribution tries to identify the source of a

manager’s performance as superior selection skill, superior allocation skill, or both.

The allocation effect identifies the return attributed to the manager’s decision to change the weights of asset

classes in the portfolio as compared to their weights in the benchmark. In other words, the manager tries to

time the market by weighting heavily in entire sectors he expects to outperform, while lowering the weights of

sectors expected to underperform.

The security selection effect captures the difference in returns caused by the selection of individual assets

within the asset classes. This measure captures the manager’s ability to select superior individual properties,

securities, etc. within the sectors in the portfolio.

Read the equations carefully:

You’ll notice that the first equation, for allocation effect, multiplies the difference in weights (portfolio weight

less benchmark weight) of each asset class (sector) by the excess return earned by the asset class. The

excess return here is measured as the return for the asset class minus the total benchmark return. So, the

equation measures the portion of the return attributable to the manager’s ability to select outperforming asset

classes (sectors).

The second equation, for selection effect, multiplies the weight of the asset class in the portfolio times the

excess return earned by the asset class. The excess return is defined as the return for the asset class in the

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portfolio as compared to the same asset class in the benchmark. It measures the manager’s ability to select

superior properties/assets from all those available in the sector.

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Documents

Study Session 2 – Quantitative Analysis · Web viewThey could have a financial advisor saying something like, “the stock isn’t expected to move much, so let’s put together