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measure of 0.5.
But if we take the eight-quarter sequence as a single measurement period, instead of two
independent periods, and measure the portfolio™s mean and standard deviation over that full
period, we get an average excess return of 5% and standard deviation of 13.42%, resulting
in a Sharpe measure of only 0.37, apparently inferior to the passive strategy!

What happened? Sharpe™s measure does not recognize the shift in the mean from the first
four quarters to the next as a result of a strategy change. Instead, the difference in mean returns
Bodie’Kane’Marcus: VI. Active Investment 20. Performance Evaluation © The McGraw’Hill
Essentials of Investments, Management and Active Portfolio Companies, 2003
Fifth Edition Management

20 Performance Evaluation and Active Portfolio Management

F I G U R E 20.4
Rate of return (%)
Portfolio returns




in the two years adds to the appearance of volatility in portfolio returns. The change in mean
returns across time periods contributed to the variability of returns over the same period. But
in this case, variability per se should not be interpreted as volatility or riskiness in returns. Part
of the variability in returns is due to intentional choices that shift the expected or mean return.
This part should not be ascribed to uncertainty in returns. Unfortunately, an outside observer
might not realize that policy changes within the sample period are the source of some of the
return variability. Therefore, the active strategy with shifting means appears riskier than it re-
ally is, which biases the estimate of the Sharpe measure downward.
For actively managed portfolios, therefore, it is crucial to keep track of portfolio composi-
tion and changes in portfolio mean return and risk. We will see another example of this prob-
lem when we talk about market timing.
Finally, we must be careful in assigning value to the performance of the most successful
mutual fund over a given period. In assessing the significance of such performance we must
account for the fact that even if all mutual funds were equally well managed, a winner would
emerge by sheer chance every period. When thousands of funds compete for investor savings,
we should expect spectacular performance by the winner. This principle is explained in the
nearby box.

Rather than focus on risk-adjusted returns, practitioners often want simply to ascertain which
decisions resulted in superior or inferior performance. Superior investment performance de-
pends on an ability to be in the “right” securities at the right time. Such timing and selection
ability may be considered broadly, such as being in equities as opposed to fixed-income secu-
rities when the stock market is performing well. Or it may be defined at a more detailed level,
such as choosing the relatively better-performing stocks within a particular industry.
Portfolio managers constantly make both broad-brush asset market allocation decisions as
well as more detailed sector and security allocation decisions within markets. Performance at-
tribution studies attempt to decompose overall performance into discrete components that may
be identified with a particular level of the portfolio selection process.
Bodie’Kane’Marcus: VI. Active Investment 20. Performance Evaluation © The McGraw’Hill
Essentials of Investments, Management and Active Portfolio Companies, 2003
Fifth Edition Management

The Magellan Fund and Market Efficiency:
Assessing the Performance of Money Managers
contestants, the probability is greater than 40% that the
Fidelity™s Magellan Fund outperformed the S&P 500 in
individual who emerges as the winner would in fact flip
eleven of the thirteen years ending in 1989. Is such per-
heads eleven or more times. (In contrast, a coin chosen
formance consistent with the efficient market hypothe-
at random that resulted in eleven out of thirteen heads
sis? Casual statistical analysis would suggest not.
would be highly suspect!)
If outperforming the market were like flipping a fair
How then ought we evaluate the performance of
coin, as would be the case if all securities were fairly
those managers who show up in the financial press as
priced, then the odds of an arbitrarily selected manager
(recently) superior performers. We know that after the
producing eleven out of thirteen winning years would
fact some managers will have been lucky. When is the
be only about 0.95%, or 1 in 105. The Magellan Fund,
performance of a manager so good that even after ac-
however, is not a randomly selected fund. Instead, it is
counting for selection bias”the selection of the ex post
the fund that emerged after a thirteen-year “contest”
winner”we still cannot account for such performance
as a clear winner. Given that we have chosen to focus
by chance?
on the winner of a money management contest, should
we be surprised to find performance far above the
mean? Clearly not.
Once we select a fund precisely because it has out- SELECTION BIAS AND
performed all other funds, the proper benchmark for PERFORMANCE BENCHMARKS
predicted performance is no longer a standard index
such as the S&P 500. The benchmark must be the ex- Consider this experiment. Allow fifty money managers
pected performance of the best-performing fund out of to flip a coin thirteen times, and record the maximum
a sample of randomly selected funds. number of heads realized by any of the contestants. (If
Consider as an analogy a coin flipping contest. If markets are efficient, the coin will have the same prob-
fifty contestants were to flip a coin thirteen times, and ability of turning up heads as that of a money manager
the winner were to flip eleven heads out of thirteen, we beating the market.) Now repeat the contest, and
would not consider that evidence that the winner™s coin again record the winning number of heads. Repeat this
was biased. Instead, we would recognize that with fifty experiment 10,000 times. When we are done, we can

Attribution analysis starts from the broadest asset allocation choices and progressively
focuses on ever-finer details of portfolio choice. The difference between a managed portfolio™s
performance and that of a benchmark portfolio then may be expressed as the sum of the con-
tributions to performance of a series of decisions made at the various levels of the portfolio
construction process. For example, one common attribution system decomposes performance
into three components: (1) broad asset market allocation choices across equity, fixed-income,
and money markets; (2) industry (sector) choice within each market; and (3) security choice
within each sector.
To illustrate this method, consider the attribution results for a hypothetical portfolio. The
portfolio invests in stocks, bonds, and money market securities. An attribution analysis
appears in Tables 20.3 through 20.6. The portfolio return over the month is 5.34%.
The first step is to establish a benchmark level of performance against which performance
ought to be compared. This benchmark is called the bogey. It is designed to measure the
returns the portfolio manager would earn if she were to follow a completely passive strategy.
The return an
“Passive” in this context has two attributes. First, it means the allocation of funds across broad
investment manager
asset classes is set in accord with a notion of “usual” or neutral allocation across sectors. This
is compared to for
performance would be considered a passive asset market allocation. Second, it means that, within each
evaluation. asset class, the portfolio manager holds an indexed portfolio, for example, the S&P 500 index
for the equity sector. The passive strategy used as a performance benchmark rules out both
asset allocation and security selection decisions. Any departure of the manager™s return from

Bodie’Kane’Marcus: VI. Active Investment 20. Performance Evaluation © The McGraw’Hill
Essentials of Investments, Management and Active Portfolio Companies, 2003
Fifth Edition Management

compute the frequency distribution of the winning TA B L E 1
number of heads over the 10,000 trials. Probability Distribution of Number of Successful Years out
Table 1 (column 1) presents the results of such an of Thirteen for the Best-Performing Money Manager
experiment simulated on a computer. The table shows
Managers in Contest
that in 9.2% of the contests, the winning number of
heads was nine; in 47.4% of the trials ten heads would
be enough to emerge as the best manager. Interest-
Years 50 100 250 500
ingly, in 43.3% of the trials, the winning number of
heads was eleven or better out of thirteen. 8 0.1% 0 0 0
Viewed in this context, the performance of Magel-
9 9.2 0.9 0 0
lan is still impressive but somewhat less surprising. The
10 47.4 31.9 5.7 0.2
simulation shows that out of a large sample of man-
11 34.8 51.3 59.7 42.3
agers, chance alone would provide a 43.3% probability
that someone would beat the market at least eleven 12 7.7 14.6 31.8 51.5
out of thirteen years. Averaging over all 10,000 trials, 13 0.8 1.2 2.8 5.9
the mean number of winning years necessary to
Mean winning
emerge as most reliable manager over the thirteen-
years of best
year contest was 10.43.
performer 10.43 10.83 11.32 11.63
Therefore, once we recognize that Magellan is not a
fund chosen at random, but a fund that came to our
best-performing manager beats an efficient market) for
attention precisely because it turned out to perform so
other possible sample sizes. Not surprisingly, as the
well in competition with more than fifty managers, the
pool of managers increases, the predicted best per-
frequency with which it beat the market is no longer
formance steadily gets better. . . . By providing as a
high enough to constitute a contradiction of market ef-
benchmark the probability distribution of the best per-
ficiency. Indeed, using the conventional 5% confidence
formance, rather than the average performance, the
level, we could not reject the hypothesis that the con-
table tells us how many grains of salt to add to reports
sistency of its performance was due to chance.
of the latest investment guru.
The other columns in Table 1 present the frequency
distributions of the winning number of successful coin SOURCE: Alan J. Marcus, “The Magellan Fund and Market
Efficiency.” The Journal of Portfolio Management, Fall 1990.
flips (analogously, the number of years in which the

the passive benchmark must be due to either asset allocation bets (departures from the neutral
allocation across markets) or security selection bets (departures from the passive index within
asset classes).
While we™ve already discussed in earlier chapters the justification for indexing within sec-
tors, it is worth briefly explaining the determination of the neutral allocation of funds across
the broad asset classes. Weights that are designated as “neutral” will depend on the risk toler-
ance of the investor and must be determined in consultation with the client. For example, risk-
tolerant clients may place a large fraction of their portfolio in the equity market, perhaps
directing the fund manager to set neutral weights of 75% equity, 15% bonds, and 10% cash
equivalents. Any deviation from these weights must be justified by a belief that one or another
market will either over- or underperform its usual risk-return profile. In contrast, more risk-
averse clients may set neutral weights of 45%/35%/20% for the three markets. Therefore, their
portfolios in normal circumstances will be exposed to less risk than that of the risk-tolerant
clients. Only intentional bets on market performance will result in departures from this profile.
In Table 20.3, the neutral weights have been set at 60% equity, 30% fixed-income, and
10% cash equivalents (money market securities). The bogey portfolio, comprising invest-
ments in each index with the 60/30/10 weights, returned 3.97%. The managed portfolio™s
measure of performance is positive and equal to its actual return less the return of the bogey:
5.34 3.97 1.37%. The next step is to allocate the 1.37% excess return to the separate de-
cisions that contributed to it.

Bodie’Kane’Marcus: VI. Active Investment 20. Performance Evaluation © The McGraw’Hill
Essentials of Investments, Management and Active Portfolio Companies, 2003
Fifth Edition Management

E XC E L Applications www.mhhe.com/bkm

> Performance Measures

The Excel model “Performance Measures” calculates all of the performance measures discussed
in this chapter. The model that is available on the book website is built to allow you to compare
eight different portfolios and to rank them on all measures discussed in this chapter.
You can learn more about this spreadsheet model by using the interactive version available on
our website at www.mhhe.com/bkm.

1 Performance Measurement
M2 T2
5 Average Standard Beta Unsystematic Sharpe Treynor Jensen Appraisal
6 Fund Return Deviation Coefficient Risk Ratio Measure Alpha Measure Measure Ratio
7 Alpha 0.2800 0.2700 1.7000 0.0500 0.8148 0.1294 -0.0180 -0.0015 -0.0106 -0.3600
8 Omega 0.3100 0.2600 1.6200 0.0600 0.9615 0.1543 0.0232 0.0235 0.0143 0.3867
9 Omicron 0.2200 0.2100 0.8500 0.0200 0.7619 0.1882 0.0410 -0.0105 0.0482 2.0500
10 Millennium 0.4000 0.3300 2.5000 0.2700 1.0303 0.1360 -0.0100 0.0352 -0.0040 -0.0370
11 Big Value 0.1500 0.1300 0.9000 0.0300 0.6923 0.1000 -0.0360 -0.0223 -0.0400 -1.2000
12 Momentum Watcher 0.2900 0.2400 1.4000 0.1600 0.9583 0.1643 0.0340 0.0229 0.0243 0.2125
13 Big Potential 0.1500 0.1100 0.5500 0.0150 0.8182 0.1636 0.0130 -0.0009 0.0236 0.8667
14 S & P Index Return 0.2000 0.1700 1.0000 0.0000 0.8235 0.1400 0.0000 0.0000 0.0000 0.0000
15 T-Bill Return 0.06 0
17 Ranking By Sharpe


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