CHAPTER 24: PORTFOLIO PERFORMANCE EVALUATION
1.
a.
Arithmetic average:
%
10
r
ABC
=
;
%
10
r
XYZ
=
b.
Dispersion:
σ
ABC
= 7.07%;
σ
XYZ
= 13.91%
Stock XYZ has greater dispersion.
(Note: We used 5 degrees of freedom in calculating standard deviations.)
c.
Geometric average:
r
ABC
= (1.20
×
1.12
×
1.14
×
1.03
×
1.01)
1/5
– 1 = 0.0977 = 9.77%
r
XYZ
= (1.30
×
1.12
×
1.18
×
1.00
×
0.90)
1/5
– 1 = 0.0911 = 9.11%
Despite the fact that the two stocks have the same arithmetic average, the
geometric average for XYZ is less than the geometric average for ABC.
The
reason for this result is the fact that the greater variance of XYZ drives the
geometric average further below the arithmetic average.
d.
In terms of “forward looking” statistics, the arithmetic average is the better
estimate of expected rate of return.
Therefore, if the data reflect the
probabilities of future returns, 10% is the expected rate of return for both
stocks.
5.
a.
Stock A
Stock B
(i)
Alpha = regression intercept
1.0%
2.0%
(ii)
Information ratio =
α
P
/
σ
(e
P
)
0.0971
0.1047
(iii)
*Sharpe measure = (r
P
– r
f
)/
σ
P
0.4907
0.3373
(iv)
**Treynor measure = (r
P
– r
f
)/
β
P
8.833
10.500
*
To compute the Sharpe measure, note that for each stock, (r
P
– r
f
) can be
computed from the righthand side of the regression equation, using the assumed
parameters r
M
= 14% and r
f
= 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.
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 Summer '08
 STAFF
 Finance, Valuation, Sharpe, Manager B

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