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Chapter 18 - Portfolio Performance Evaluation
CHAPTER 18
18-1
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 18 - Portfolio Performance Evaluation
PORTFOLIO PERFORMANCE EVALUATION
1.
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
5.
a.
E(r)
Portfolio A
11%
10%
.8
b. If you hold only one of the two portfolios, then the Sharpe measure is the
appropriate criterion:
18-2
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 18 - Portfolio Performance Evaluation
SA =
E( r A )－ r f
A
=
.11－ .06
.1 0
= .5
SB=
E( rB ) － r f
B
=
.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:
7.
a. Actual: (.70 .02) + (.20 .01) + (.10 .005) = .0165 = 1.65%
b. Asset Allocation:
(1) (2) (3) (4) (5) = (3)
18-3
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
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
2
R
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
P
=
.102 － .02
.37
= .2216
SM =
E( rM )－ r f
M
=
－ .22 5－ .02
.44
= – .5568
b. To compute
2
M
measure, blend the Miranda Fund with a position in T-Bills
such that the “adjusted” portfolio has the same volatility as the market index.
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
Chapter 18 - Portfolio Performance Evaluation
c.
&
.102 .02 .225 .02
.0745 .245
1.10 1.00
P f
Miranda S P
P
r r T T
b
-- - -
® = = = =-
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.
18-6
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
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.
18-7
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
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
18-8
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
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
P1
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:
18-9
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
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:
a.
18-10
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
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)
A
.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:
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
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:
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in
whole or part.
