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Chapter 24  Portfolio Performance Evaluation
241
CHAPTER 24: PORTFOLIO PERFORMANCE EVALUATION
PROBLEM SETS
1.
As established in the following result from the text, the Sharpe ratio depends on both
alpha for the portfolio (
∀
P
) and the correlation between the portfolio and the market
index (
ρ
):
M
P
P
P
f
P
S
r
r
E
ρ
σ
α
+
=
−
)
(
Specifically, this result demonstrates that a lower correlation with the market index
reduces the Sharpe ratio. Hence, if alpha is not sufficiently large, the portfolio is inferior
to the index. Another way to think about this conclusion is to note that, even for a
portfolio with a positive alpha, if its diversifiable risk is sufficiently large, thereby
reducing the correlation with the market index, this can result in a lower Sharpe ratio.
2.
The IRR (i.e., the dollarweighted return) can not be ranked relative to either the
geometric average return (i.e., the timeweighted return) or the arithmetic average
return. Under some conditions, the IRR is greater than each of the other two averages,
and similarly, under other conditions, the IRR can also be less than each of the other
averages. A number of scenarios can be developed to illustrate this conclusion. For
example, consider a scenario where the rate of return each period consistently increases
over several time periods. If the amount invested also increases each period, and then
all of the proceeds are withdrawn at the end of several periods, the IRR is greater than
either the geometric or the arithmetic average because more money is invested at the
higher rates than at the lower rates. On the other hand, if withdrawals gradually reduce
the amount invested as the rate of return increases, then the IRR is less than each of the
other averages. (Similar scenarios are illustrated with numerical examples in the text,
on page 824, where the IRR is shown to be less than the geometric average, and in
Concept Check 1, where the IRR is greater than the geometric average.)
3.
It is not necessarily wise to shift resources to timing at the expense of security selection.
There is also tremendous potential value in security analysis. The decision as to whether
to shift resources has to be made on the basis of the macro, compared to the micro,
forecasting ability of the portfolio management team.
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242
4.
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.
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This note was uploaded on 04/03/2010 for the course FEAS 311.01 taught by Professor Attilaodabaşı during the Spring '10 term at Boğaziçi University.
 Spring '10
 AttilaOdabaşı

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