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CHAPTER 26
EVALUATION OF PORTFOLIO PERFORMANCE
Answers to Questions
1.
The two major factors would be: (1) attempt to derive riskadjusted returns that exceed a
naive buyandhold policy and (2) completely diversify  i.e., eliminated all unsystematic
risk from the portfolio. A portfolio manager can do one or both of two things to derive
superior riskadjusted returns. The first is to have
superior timing
regarding market
cycles and adjust your portfolio accordingly. Alternatively, one can consistently
select
undervalued stocks.
As long as you do not make major mistakes with the rest of the
portfolio, these actions should result in superior riskadjusted returns.
2.
Treynor (1965) divided a fund’s excess return (return less riskfree rate) by its beta. For a
fund not completely diversified, Treynor’s “T” value will understate risk and overstate
performance. Sharpe (1966) divided a fund’s excess return by its standard deviation.
Sharpe’s “S” value will produce evaluations very similar to Treynor’s for funds that are
well diversified.
Jensen (1968) measures performance as the difference between a fund’s
actual and required returns. Since the latter return is based on the CAPM and a fund’s
beta, Jensen makes the same implicit assumptions as Treynor  namely, that funds are
completely diversified.
The information ratio (IR) measures a portfolio’s average return
in excess of that of a benchmark, divided by the standard deviation of this excess return.
3.
For portfolios with R
2
values noticeably less than 1.0, it would make sense to compute
both measures. Differences in the rankings generated by the two measures would suggest
lessthancomplete diversification by some funds  specifically, those that were ranked
higher by Treynor than by Sharpe.
4.
Jensen’s alpha (
α
) is found from the equation R
jt
– RFR
t
==
α
j
+
β
j
[R
mt
– RFR
t
] +e
jt
. The
a
j
indicates whether a manager has superior (
α
j
> 0) or inferior (
α
j
< 0) ability in market
timing or stock selection, or both. As suggested above, Jensen defines superior (inferior)
performance as a positive (negative) difference between a manager’s actual return and his
CAPMbased required return. For poorly diversified funds, Jensen’s rankings would
more closely resemble Treynor’s. For welldiversified funds, Jensen’s rankings would
follow those of both Treynor and Sharpe. By replacing the CAPM with the APT,
differences between funds’ actual and required returns (or “alphas”) could provide fresh
evaluations of funds.
5.
The Information Ratio (IR) is calculated by dividing the average return on the portfolio
less a benchmark return by the standard deviation of the excess return. The IR can be
viewed as a benefitcost ratio in that the standard deviation of return can be viewed as a
cost associated in the sense that it measures the unsystematic risk taken on by active
26  1
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View Full Documentmanagement. Thus IR is a costbenefit ratio that assesses the quality of the investor’s
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