CHAPTER 24: PORTFOLIO PERFORMANCE EVALUATION
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
α
) and the correlation between the portfolio and the market
index (ρ):
M
P
P
P
f
P
S
r
r
E
ρ
σ
+
=

)
(
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increases each period, and then all of the proceeds are withdrawn at the end of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, 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.
241