978-0078034695 Chapter 18 Solution Manual

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Chapter 18 – Portfolio Performance Evaluation

CHAPTER 18

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Chapter 18 – Portfolio Performance Evaluation

PORTFOLIO PERFORMANCE EVALUATION

a. Possibly.Alpha alone does not determine which portfolio has a larger Sharpe

ratio. Sharpe measure is the primary factor, since it tells us the real return per

b. Yes. It is possible for a positive alpha to exist, but the Sharpe measure declines.

Thus, we would experience inferior performance.

2. Maybe. Provided the addition of funds creates an efficient frontier with the existing

3. No. The M-squared is an equivalent representation of the Sharpe measure, with the

4. Definitely the FF model. Research shows that passive investments (e.g., a market index

E(r)  

Portfolio A

11%

10%

b. If you hold only one of the two portfolios, then the Sharpe measure is the

appropriate criterion:

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Chapter 18 – Portfolio Performance Evaluation

SA =

E( r A )－ r f

.11－ .06

.1 0

= .5

SB=

E( rB ) － r f

.14 － .06

.31

= .26

Therefore, using the Sharpe criterion, Portfolio A is preferred.

6. We first distinguish between timing ability and selection ability. The intercept of the

scatter diagram is a measure of stock selection ability. If the manager tends to have a

positive excess return even when the market’s performance is merely “neutral” (i.e., the

market has zero excess return) then we conclude that the manager has, on average,

made good stock picks. In other words, stock selection must be the source of the

positive excess returns.

We can therefore classify performance ability for the four managers as follows:

a. Actual: (.70  .02) + (.20 .01) + (.10 .005) = .0165 = 1.65%

b. Asset Allocation:

(1) (2) (3) (4) (5) = (3)

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Chapter 18 – Portfolio Performance Evaluation

(4)

Market Actual

Weight

Benchmark

Weight Excess Weight Index Return Contribution

Equity

.70

.60

.10

2.5%

.25%

Summary

Security selection –.39%

Chapter 18 – Portfolio Performance Evaluation

13. Primo return

0.6 17% 0.15 24% 0.25 20% 18.8%= ´ + ´ + ´ =

Benchmark return

0.5 16% 0.4 26% 0.1 18% 20.2%= ´ + ´ + ´ =

Primo – Benchmark = 18.8% − 20.2% = -1.4% (Primo underperformed benchmark)

(.17 .16) (.6) (.24 .26) (.15) (.2 0.18) (.25) 0.8%– ´ + – ´ + – ´ =

14. Because the passively managed fund is mimicking the benchmark, the

of the

regression should be very high (and thus probably higher than the actively managed

fund).

15. a. The euro appreciated while the pound depreciated. Primo had a greater stake in the

euro-denominated assets relative to the benchmark, resulting in a positive currency

allocation effect. British stocks outperformed Dutch stocks resulting in a negative

16.

a. SP =

E( rP ) － rf

.102 － .02

.37

= .2216

SM =

E( rM )－ r f

－ .22 5－ .02

.44

= – .5568

b. To compute

measure, blend the Miranda Fund with a position in T-Bills

such that the “adjusted” portfolio has the same volatility as the market index.

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Chapter 18 – Portfolio Performance Evaluation

.102 .02 .225 .02

.0745 .245

1.10 1.00

P f

Miranda S P

r r T T

–– – –

® = = = =–

d. αP =E(rP) – {rf +βP[E(rM) –rf]} = .102 – [.02 + 1.10 – .225 – .02)] = .3515

17. The spreadsheet below displays the monthly returns and excess returns for the

Vanguard U.S. Growth Fund, the Vanguard U.S. Value Fund and the S&P 500.

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Chapter 18 – Portfolio Performance Evaluation

a. The excess returns are noted in the spreadsheet.

b. The standard deviations for the U.S Growth Fund and the U.S. Value Fund are

4.21% and 4.05%, respectively, as shown in the Excel spreadsheet above.

c. The betas for the U.S. Growth Fund and the U.S. Value Fund are 1.02 and 1.03,

respectively, as shown in the Excel spreadsheets below.

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Chapter 18 – Portfolio Performance Evaluation

d. The formulas for the three measures are below and results listed above.

E( rP ) － rf

Current stock price = S0 = $1.0

Exercise price = X = (1 + rf) = 1.01

Standard deviation =  = .055

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Chapter 18 – Portfolio Performance Evaluation

Risk-free interest rate = rf = .01

Time to maturity of option = T = 1

Recall that ln(l + y) is approximately equal to y, for small y, and that

19.

a. Using the relative frequencies to estimate the conditional probabilities P1 and P2

for timers A and B, we find:

Timer A Timer B

78/135 = 0.58

86/135 = 0.64

P257/92 = 0.62 50/92 = 0.54

P* = P1 + P2 – 1 0.20 0.18

The data suggest that timer A is the better forecaster.

b. Use the following equation and the previous answer to value the imperfect timing

services of Timer A and Timer B:

CFA 1

Answer:

d. Russell 2000 Index

CFA 2

Answer:

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Chapter 18 – Portfolio Performance Evaluation

a. αA = .24 – [ .12 + 1.0 ( .21 – .12)] = 3.0%

αB = .30 – [ .12 + 1.5 ( .21 – .12)] = 4.5%

b. (i)The managers may have been trying to time the market. In that case, the SCL

CFA 3

Answer:

a. Indeed, the one year results were terrible, but one year is a poor statistical base

b. The sample of pension funds held a much larger share in equities compared to

c. Over the five-year period, Alpine’s alpha, which measures risk-adjusted

d. Note that, over the last five years, and particularly the last one year, bond

performance has been poor; this is significant because this is the asset class that

e. A trustee may not care about the time-weighted return, but that return is more

indicative of the manager’s performance. After all, the manager has no control

over the cash inflow to the fund.

CFA 4

Answer:

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Chapter 18 – Portfolio Performance Evaluation

Alpha (): αi = E(ri) – {rf +βi [E(rM) –rf]} Expected excess return: E(ri) –rf

αA = .20 – [ .08 + 1.3  ( .16 – .08)] = 1.6% .20 – .08 = 12%

The residual variances are:

b. To construct the optimal risky portfolio, we first determine the optimal active

portfolio. Using the Treynor-Black technique, we construct the active

portfolio:

－

2 (e)

－－ 2( e)

－ α i－ 2 ( e i)

.0476

–0.6136

Do not be disturbed by the fact that the positive alpha stocks get negative

weights and vice versa. The entire position in the active portfolio will turn out

to be negative, returning everything to good order.

With these weights, the forecast for the active portfolio is:

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Chapter 18 – Portfolio Performance Evaluation

Here, again, the levered position in stock B [with the high 2(e)] overcomes the

diversification effect, and results in a high residual standard deviation. The

optimal risky portfolio has a proportion w* in the active portfolio, computed as

follows:

w0 =

－－ 2( e)

[E( r M )－ r f ]/ 2 M

－ .1690/2.18082

. 08/ .232

= – .05124

The negative position is justified for the reason given earlier.

The adjustment for beta is:

w* =

w 0

1+ (1－－) w 0

－ . 05124

1 + (1－2.08 )－( － . 05124 )

= – .0486

Because w* is negative, we end up with a positive position in stocks with

positive alphas and vice versa. The position in the index portfolio is:

1 – (–0.0486) = 1.0486

c. To calculate Sharpe’s measure for the optimal risky portfolio we compute the

appraisal ratio for the active portfolio and Sharpe’s measure for the market

portfolio. The appraisal ratio of the active portfolio is:

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