Note: Question numbers here are based on 10th/11th edition.
8.
a.
The alphas for the two portfolios are:
αA = 12% – [5% + 0.7 × (13% – 5%)] = 1.4%
αB = 16% – [5% + 1.4 × (13% – 5%)] = –0.2%
Ideally, you would want to take a long position in Portfolio A and a short position in
Portfolio B.
b.
If you will hold only one of the two portfolios, then the Sharpe measure is the
appropriate criterion:
SA 
.12  .05
 0.583
.12
SB 
.16  .05
 0.355
.31
Using the Sharpe criterion, Portfolio A is the preferred portfolio.
9.
a.
(i)
Alpha = regression intercept
Stock A
1.0%
(ii)
Information ratio =
0.0971
0.1047
0.4907
0.3373
8.833
10.500
(iii) *Sharpe measure =
P
 (eP )
rP  rf
(iv) **Treynor measure =
P
rP  rf
P
Stock B
2.0%
* To compute the Sharpe measure, note that for each stock, (rP – rf ) can be computed
from the right-hand side of the regression equation, using the assumed parameters rM
= 14% and rf = 6%. The standard deviation of each stock’s returns is given in the
problem.
** The beta to use for the Treynor measure is the slope coefficient of the regression
equation presented in the problem.
b.
(i) If this is the only risky asset held by the investor, then Sharpe’s measure is the
appropriate measure. Since the Sharpe measure is higher for Stock A, then A is the
best choice.
(ii) If the stock is mixed with the market index fund, then the contribution to the
overall Sharpe measure is determined by the appraisal ratio; therefore, Stock B is
preferred.
(iii) If the stock is one of many stocks, then Treynor’s measure is the appropriate
measure, and Stock B is preferred.
11.
a.
Bogey: (0.60 × 2.5%) + (0.30 × 1.2%) + (0.10 × 0.5%) = 1.91%
Actual: (0.70 × 2.0%) + (0.20 × 1.0%) + (0.10 × 0.5%) = 1.65%
Underperformance:
0.26%
b.
Security Selection:
Market
(1)
Differential return
within market
(Manager – index)
(3) = (1) × (2)
Manager's
Contribution to
portfolio weight
performance
–0.5%
0.70
–0.2%
0.20
0.0%
0.10
Contribution of security selection:
Equity
Bonds
Cash
c.
(2)
−0.35%
–0.04%
0.00%
−0.39%
Asset Allocation:
Market
Equity
Bonds
Cash
(1)
Excess weight
(Manager – benchmark)
(2)
Index
Return
0.10%
2.5%
–0.10%
1.2%
0.00%
0.5%
Contribution of asset allocation:
Summary:
Security selection –0.39%
Asset allocation
0.13%
Excess performance –0.26%
(3) = (1) × (2)
Contribution to
performance
0.25%
–0.12%
0.00%
0.13%
12.
a.
Manager: (0.30 × 20%) + (0.10 × 15%) + (0.40 × 10%) + (0.20 × 5%) = 12.50%
Bogey:
(0.15 × 12%) + (0.30 × 15%) + (0.45 × 14%) + (0.10 × 12%) = 13.80%
Added value:
–1.30%
b.
Added value from country allocation:
Country
U.K.
Japan
U.S.
Germany
c.
(1)
Excess weight
(Manager – benchmark)
(2)
Index Return
minus bogey
0.15
−1.8%
–0.20
1.2%
−0.05
0.2%
0.10
−1.8%
Contribution of country allocation:
(3) = (1) × (2)
Contribution to
performance
−0.27%
–0.24%
−0.01%
−0.18%
−0.70%
Added value from stock selection:
Country
U.K.
Japan
U.S.
Germany
(1)
Differential return
within country
(Manager – Index)
(2)
(3) = (1) × (2)
Manager’s
country weight
Contribution to
performance
0.08
0.30%
0.00
0.10%
−0.04
0.40%
−0.07
0.20%
Contribution of stock selection:
Summary:
Country allocation –0.70%
Stock selection
−0.60%
Excess performance –1.30%
2.4%
0.0%
−1.6%
−1.4%
−0.6%
15.
a. The manager’s alpha is: 10% – [6% + 0.5 × (14% – 6%)] = 0
b. From Black-Jensen-Scholes and others, we know that, on average, portfolios
with low beta have historically had positive alphas. (The slope of the empirical security
market line is shallower than predicted by the CAPM.) Therefore, given the manager’s
low beta, performance might actually be sub-par despite the estimated alpha of zero.
17.
The within sector selection calculates the return according to security selection. This is
done by summing the weight of the security in the portfolio multiplied by the return of the
security in the portfolio minus the return of the security in the benchmark:
Large Cap Sector: 0.6  (.17-.16)= 0.6%
Mid Cap Sector: 0.15  (.24 - .26)  -0.3%
Small Cap Sector: 0.25  (.20-.18)= 0.5%
Total Within-Sector Selection = 0.6% - 0.3%  0.5%  0.8%
18.
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)
To isolate the impact of Primo’s pure sector allocation decision relative to the benchmark,
multiply the weight difference between Primo and the benchmark portfolio in each sector
by the benchmark sector returns:
(0.6  0.5)  (.16)  (0.15  0.4)  (.26)  (0.25  0.1)  (.18)  2.2%
To isolate the impact of Primo’s pure security selection decisions relative to the
benchmark, multiply the return differences between Primo and the benchmark for each
sector by Primo’s weightings:
(.17  .16)  (.6)  (.24  .26)  (.15)  (.2  0.18)  (.25)  0.8%
19.
Because the passively managed fund is mimicking the benchmark, the R 2 of the regression
should be very high (and thus probably higher than the actively managed fund).
20.
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
market allocation effect for Primo. Finally, within the Dutch and British investments,
Primo outperformed with the Dutch investments and under-performed with the British
investments. Since they had a greater proportion invested in Dutch stocks relative to
the benchmark, we assume that they had a positive security allocation effect in total.
However, this cannot be known for certain with this information. It is the best choice,
however.
21.
a.
rP  rf
P
 SMiranda 
.102  .02
 .2216
.37
SS &P 
.225  .02
 .5568
.44
b. To compute M 2 measure, blend the Miranda Fund with a position in T-Bills such that
the “adjusted” portfolio has the same volatility as the market index. Using the data, the
position in the Miranda Fund should be .44/.37 = 1.1892 and the position in T-Bills
should be 1 – 1.1892 = -.1892. (assuming borrowing at the risk free rate)
The adjusted return is: rP*  (1.1892)  10.2%  (.1892)  2%  .1175  11.75%
Calculate the difference in the adjusted Miranda Fund return and the benchmark:
M 2  rP*  rM  11.75%  (22.50%)  34.25%
[Note: The adjusted Miranda Fund is now 59.46% equity and 40.54% cash.]
c.
rP  rf
P
 TMiranda 
.102  .02
 .0745
1.10
TS & P 
.225  .02
 .245
1.00
d.  P  rP  [rf   P (rM  rf )]
 0.102  [0.02  1.10  (0.225  0.02)]
 .3515  35.15%
CFA Problems
4.
Treynor measure =
5.
6.
17  8
 8.182
1.1
Sharpe: (24-8)/18 = 0.889
a.
Treynor measures
Portfolio X:
(10  6)
 6.67
0.6
S&P 500:
(12  6)
 6.00
1.0
Sharpe measures
(.10  .06)
(.12  .06)
 0.222
S&P 500:
 0.462
0.18
.13
Portfolio X outperforms the market based on the Treynor measure, but underperforms
based on the Sharpe measure.
Portfolio X:
14.
b.
The two measures of performance are in conflict because they use different measures
of risk. Portfolio X has less systematic risk than the market, as measured by its lower
beta, but more total risk (volatility), as measured by its higher standard deviation.
Therefore, the portfolio outperforms the market based on the Treynor measure but
underperforms based on the Sharpe measure.
a.
Sharpe ratio =
SWilliamson :
rP  rf
P
22.1%  5.0%
24.2%  5.0%
 1.02 S Joyner :
 0.95
16.8%
20.2%
Treynor measure =
TWilliamson :
b.
rP  rf
P
22.1%  5.0%
24.2%  5.0%
 14.25 TJoyner :
 24.00
1.2
0.8
The difference in the rankings of Williamson and Joyner results directly from the
difference in diversification of the portfolios. Joyner has a higher Treynor measure
(24.00) and a lower Sharpe ratio (0.95) than does Williamson (14.25 and 1.202,
respectively), so Joyner must be less diversified than Williamson. The Treynor
measure indicates that Joyner has a higher return per unit of systematic risk than does
Williamson, while the Sharpe ratio indicates that Joyner has a lower return per unit of
total risk than does Williamson.