Chapter 26

Portfolio Management
Evaluation of Portfolio
Performance
• A large percentage of investments are made by professional managers.
• Professionally managed funds include mutual funds, pension funds, college
endowments, and discretionary accounts, among others.
• It is important for an investor utilizing one of these managers to evaluate how
well the fund has done relative to other funds, understand the fund’s general
policies, and to be able to tell how well the fund has followed them.
• How diversified is the fund? How actively does it try to pursue short-run
aberrations in prices? What is the bond–stock mix, and how much does it
vary?
• For the individual investor to understand the risks he is undertaking, the fund’s
policies and how strictly the manager adheres to them.
• For the institution that has engaged a professional manager, examining the
manager’s policies enables the institution to evaluate not only the risks it is
undertaking but also the costs of any restrictions it might have placed on the
fund manager.
• To the individual making investment decisions, it is important to understand
what caused the performance.
• Were there extra benefits from market timing or only extra transaction costs? Was
stock selection superior?
EVALUATION TECHNIQUES
• The evaluation of portfolio performance is essentially concerned with

comparing the return earned on some portfolio with the return earned on one
or more other portfolios.
• It is important that the portfolios chosen for comparison are truly comparable.
• This means that they not only must have similar risk but also must be bound
by similar constraints.
• For example, an institution that restricts its managers to investing in bonds rated AA or
better should not evaluate its managers by comparing their performance to the
performance of portfolios that are unconstrained
Measures of Return
• If a security paid dividends of $3.00 and had a capital gain of $7.00 on an investment of
$100, the return was;
• When evaluating a portfolio, generalizing our simple idea of return requires care.
• A problem occurs because there are many inflows and outflows of funds to the portfolio,
and very different amounts of money are invested at different points in time.
Measures of Return
• If we just looked at the ending value

compared to the beginning value over
the full period, fund A’s performance
would look superior.
• However, the period-by-period return

is identical and (ignoring risk for the
moment) so is the manager’s
performance.
• We eliminate the effect of having different amounts of funds available if we calculate the rate of return in
each time period and then compound the return to determine it in the overall period.
• When the rate of return is calculated this way, it is called the time-weighted rate of return.
Measures of Risk
• There are two possible measures of risk that can be used: total risk or non-diversifiable
risk.
• Total risk is normally measured by standard deviation of return, whereas non-diversifiable
risk is normally measured by the beta coefficient.
Direct Comparisons
• One way to compare portfolios is to examine the return earned by alternative portfolios of
the same risk. This is the procedure used by Friend, Blume, and Crockett (1970) in their
examination of mutual funds.
• Mutual funds underperform randomly selected portfolios of the same risk.

• They also show that the population of securities, or more specifically, the weighting of the
securities in random portfolios, can affect the evaluation results.
Direct Comparisons
• Most professional evaluation services chose as a benchmark not random portfolios but
rather the performance of portfolios administered by other managers.
Direct Comparisons
• The return comparisons in Table 26.4a are not generally being made between
funds of the same risk.
• Thus, although both return and risk measures are included as part of all
evaluation services, it is often difficult to form an overall opinion about fund
performance.
• Only in the two cases where risk and return are both adverse or good is it
possible to form an overall opinion.
• There is no consistent pattern of return over time, and often the risk pattern
varies as well.
• Thus, the return pattern cannot be used to form an overall opinion about fund
performance.
• The risk information may be useful in determining whether the manager has followed
guidelines on risk.
One-Parameter Performance Measures
• Three different one-parameter performance measures have been proposed in
the literature and are widely used in practice.
• These measures differ in their definition of risk and their treatment of the
ability of the investor to adjust the risk level of any fund in which she might
invest.
• All of these measures implicitly make the assumption that the investor can
both lend and borrow at the risk-free rate of interest.
The Excess Return to Variability Measure
This ratio is often referred to as Sharpe measure, an excess return to variability measure.
The Excess Return to Variability Measure
Figure 26.3 is the plot of individual mutual fund
performance and the Dow-Jones Industrial index
as presented in Sharpe’s classic 1966 article.
The Sharpe measure looks at the decision from

the point of view of an investor choosing a
mutual fund to represent the majority of his
investment.
An investor choosing a mutual fund to represent

a large part of her wealth would likely be
concerned with the full risk of the fund, and
standard deviation is a measure of that risk.
The Treynor Measure: Excess Return to Non-diversifiable
Risk
Treynor (1965) measure examines differential
return when beta is the risk measure.
This may be more appropriate if one manager

among many is being evaluated or a part of the
total portfolio is being evaluated.
The Jensen Measure: Differential Return When Risk Is
Measured by Beta
If the manager’s choice is to actively manage the
fund, then one measure of the manager’s
performance is the difference in return earned
by actively managing the fund, compared to
what would have been earned if the manager
had passively invested in the market portfolio
and riskless asset to achieve the same risk level.
The differential return is the actual return less

the return on the portfolio of identical beta, but
lying on the line connecting the riskless asset
and the market portfolio.
The differential return can be viewed as the difference in return earned by the fund compared
to the return that the capital asset pricing line implies should be earned.
TIMING
The question is how successful managers have been in timing the market, and also how timing
is measured.
Timing involves a change in the sensitivity of a portfolio to one or more systematic influences
in anticipation of future movement in these influences.
There are three ways a manager can change the beta in his portfolio.
The manager can sell stocks and buy debt instruments if he believes that the stock
market will perform poorly.
Second, the manager can sell high beta stocks and buy low beta stocks, if he believes
the market will underperform.
A third way, and one which involves less transaction costs, is for the manager to write
stock index futures.
TIMING
The easiest way to examine the effectiveness of attempts to market time is to graphically
examine market movements versus the bond–stock mix or average beta.
If the fund has a well-specified policy regarding the average beta or the bond–stock mix, then
it is more illuminating to examine the relationship between deviations from the policy and
changes in the market.
TIMING
Another measure of a manager’s timing ability is to look at a plot of portfolio beta or bond–
stock mix compared to the market return. If there is significant timing ability, then there
should be a relationship between these variables, and this should be apparent from the plot.
A third way to measure market timing is to look directly at the fund return compared to the
market return.
If the fund did not engage in market timing, then the average beta on the overall portfolio should be fairly
constant.
If there was no diversifiable risk in the portfolio, then the portfolio return would be a constant fraction of
the market return
TIMING
In the case of successful timing through changing beta, when the market increased
substantially, the fund would have a higher than normal beta and would tend to do better than
it would have otherwise done.
Likewise, if the manager were able to anticipate a market decline, he or she would reduce the
beta and have a portfolio that declined less than it would otherwise.

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Chapter 26

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Portfolio Management

• The evaluation of portfolio performance is essentially concerned with

• If we just looked at the ending value

• However, the period-by-period return

• Mutual funds underperform randomly selected portfolios of the same risk.

The Sharpe measure looks at the decision from

An investor choosing a mutual fund to represent

This may be more appropriate if one manager

The differential return is the actual return less

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