21. a.
Miranda S&P
.102 .02 .225 .02
.2216 .5568
σ .37 .44
P f
P
r r S S
–– – –
® = = = =
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. 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 = -0.1892 (assuming borrowing at the risk-free rate).
The adjusted return is:
*
(1.1892) 10.2% (.1892) 2% .1175 11.75%
P
r= ´ – ´ = =
Calculate the difference in the adjusted Miranda Fund return and the benchmark:
*
2
11.75% ( 22.50%) 34.25%
M
P
M r r= – = – – =
[Note: The adjusted Miranda Fund is now 59.46% equity and 40.54% cash.]
c.
Miranda S&P
.102 .02 .225 .02
.0745 .245
β 1.10 1.00
P f
P
r r T T
–– – –
® = = = =-
d.
22. This exercise is left to the student; answers will vary.
CFA PROBLEMS
1. a. Manager A
Strength. Although Manager A’s one-year total return was somewhat below the
Weakness. Manager A has an obvious weakness in the currency management area.
Manager B
α [ β ( )]
0.102 [0.02 1.10 ( 0.225 0.02)]
.3515 35.15%
P P f P M f
r r r r= – + –
= – + ´ – –
= =
Strength. Manager B’s total return exceeded that of the index, with a marked positive
Weakness. Manager B had a marked shortfall in local market return. Therefore,
b. The following strategies would enable the fund to take advantage of the strengths
of each of the two managers while minimizing their weaknesses.
1. Recommendation: One strategy would be to direct Manager A to make no
Justification: This strategy would mitigate Manager A’s weakness by hedging
all currency exposures into index-like weights. This would allow capture of
Manager A’s country and stock selection skills while avoiding losses from
2. Recommendation: Another strategy would be to combine the portfolios of
Justification: This recommendation would capture the strengths of both Manager
2. a. Indeed, the one year results were terrible, but one year is a poor statistical base from
b. The sample of pension funds had a much larger share invested in equities than did
Alpine. Equities performed much better than bonds. Yet the trustees told Alpine to
c. Alpine’s alpha measures its risk-adjusted performance compared to the market:
d. Note that the last five years, and particularly the most recent year, have been bad for
bonds, the asset class that Alpine had been encouraged to hold. Within this asset
e. A trustee may not care about the time-weighted return, but that return is more
3. a. Method I does nothing to separately identify the effects of market timing and
b. Method II is not perfect but is the best of the three techniques. It at least attempts to
focus on market timing by examining the returns for portfolios constructed from bond
market indexes using actual weights in various indexes versus year-average weights.
c. Method III uses net purchases of bonds as a signal of bond manager optimism. But
such net purchases can be motivated by withdrawals from or contributions to the
4. Treynor measure =
17 8 8.182
1.1
–=
5. Sharpe measure =
6. a. Treynor measures
(10 6) (12 6)
Portfolio X: 6.67 S&P 500: 6.00
0.6 1.0
– –
= =
Sharpe measures
(.10 .06) (.12 .06)
Portfolio X: 0.222 S&P 500: 0.462
0.18 .13
– –
= =
b. The two measures of performance are in conflict because they use different measures
10. d.
11. Time-weighted average return =
1/2
(1.15 1.1) 1 12.47%´ – =
[The arithmetic mean is:
15% 10% 12.5%
2
+=
]
To compute dollar-weighted rate of return, cash flows are:
CF0 = −$500,000
Dollar-weighted rate of return = 11.71% (Solve for IRR in financial calculator).
12. a. Each of these benchmarks has several deficiencies, as described below.
Market index:
A market index may exhibit survivorship bias. Firms that have gone out of business
A market index may exhibit double counting that arises because of companies
It is often difficult to exactly and continually replicate the holdings in the market
Benchmark normal portfolio:
This is the most difficult performance measurement method to develop and calculate.
The normal portfolio must be continually updated, requiring substantial resources.
Consultants and clients are concerned that managers who are involved in
Median of the manager universe:
It can be difficult to identify a universe of managers appropriate for the investment
style of the plan’s managers.
b. i. The Sharpe ratio is calculated by dividing the portfolio risk premium (i.e., actual
portfolio return minus the risk-free return) by the portfolio standard deviation:
Jensen’s alpha is calculated by subtracting the market risk premium, adjusted for
risk by the portfolio’s beta, from the actual portfolio excess return (risk premium).
α [ β ( )]
P P f P M f
r r r r= – + –
ii. The Sharpe ratio assumes that the relevant risk is total risk, and it measures excess
return per unit of total risk. The Treynor measure assumes that the relevant risk is
13. i. Incorrect. Valid benchmarks are unbiased. Median manager benchmarks, however,
are subject to significant survivorship bias, which results in several drawbacks,
including the following:
The performance of median manager benchmarks is biased upwards.
ii. Incorrect. Valid benchmarks are unambiguous and can be replicated. The median
manager benchmark is ambiguous because the weights of the individual securities in
Valid benchmarks are also investable. The median manager benchmark is not
iii. The statement is correct. The median manager benchmark may be inappropriate
14. a. Sharpe ratio =
σ
P f
P
r r–
22.1% 5.0% 24.2% 5.0%
: 1.02 : 0.95
16.8% 20.2%
Williamson Joyner
S S
– –
= =
Treynor measure =
β
P f
P
r r–
22.1% 5.0% 24.2% 5.0%
: 14.25 : 24.00
1.2 0.8
Williamson Joyner
T T
– –
= =
b. 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