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Chapter 18 - Portfolio Performance Evaluation
CHAPTER EIGHTEEN
PORTFOLIO PERFORMANCE EVALUATION
CHAPTER OVERVIEW
This chapter presents various performance measures that are used for evaluation of portfolios.
The process of decomposing portfolio returns into the various components of the portfolio-
building process is presented. Performance measures of market timing, security selection and
adding securities to a diversified portfolio are introduced.
LEARNING OBJECTIVES
After studying this chapter, the student should be able to calculate various risk-adjusted return
measures, including Jensen’s alpha, the Sharpe and Treynor ratios, the M2 measure, and the
information ratio and know when to use each. The students should be able to decompose excess
returns into components attributable to asset allocation and security selection. Students should
also understand market timing, timing performance measures and the problems that timing causes
in performance measurement.
CHAPTER OUTLINE
1. Risk-Adjusted Returns
PPT 18-2 through PPT 18-16
Passive management consists of choosing a capital allocation between cash and the risky portfolio
and choosing the asset allocation within the risky portfolio. However, how passive the
management actually is varies from, “set it and forget it,” to changing allocations in according to
perceptions of risk to keep current with portfolio goals. Active management is a step beyond.
Active management involves forecasting future rates of return on either/both asset classes and
individual securities. Passive management, even if the portfolio is updated, is basically focused on
the level of risk of the portfolio in conjunction with the stated portfolio goals. Active
management is far more difficult. Risk levels are fairly stable but expected returns are not.
Successful forecasting of future prices and rates of return is very difficult in the highly competitive
markets we have. It requires either private information, or perhaps some better analytical or
instinctual method of analysis. A true market timer focuses on allocation between the risky and
riskless portfolios, although most actually change broad class allocations and reallocate within the
risky portfolio as well. It is a stretch to call a market timer a passive investor, so there is a bit of
ambiguity here.
The purpose of performance evaluation is to ascertain whether the returns earned are worth the
risk and the fees charged. The average return by itself is an insufficient measure of performance
because the average return may not equal the expected return, because you can earn higher
returns by taking on more risk and because much of the performance at any point in time is based
on overall market performance.
What is needed is a measure of abnormal performance. One can get more return in bull markets
by taking on more risk, this doesn’t mean the managers are adding value; can they generate good
returns consistently through time across different market cycles? It takes measures that
incorporate risk and it requires statistical work to make us believe the results are not just due to
Successful across asset allocations (time the market)
Superior allocation within each asset class (weight sectors)
oSectors or industries
oOverweight better performing sectors, underweight poorer performers
Individual security selection (pick stocks)
should a multi-index model be used? Second, most of the sound measures of risk-adjusted returns
require stability for the portfolio. Most portfolios are actively managed and the stability
assumptions are not met. Third, in competitive markets with significant volatility, identifying the
actual level of abnormal performance that is likely to occur is very difficult. The probability of a
Type 2 error is quite high.
Jensen’s alpha is a very widely understood measure of abnormal performance. It can be calculated
The Sharpe Measure is also widely accepted in industry. This measure indicates the slope of the
CAL and it is based on the portfolio risk premium and the total risk of the portfolio as measured
by standard deviation. The Treynor measure also calculates the excess return to variability ratio
but it uses the portfolio beta as the risk measure. The Sharpe and the Treynor measures should
risk.
18-2
fp
rr
Ratios Sharpe
Chapter 18 - Portfolio Performance Evaluation
This measure asks the question, “How much excess return does one get for the level of risk?” In a
Sharpe is easy to interpret but the Sharpe number is not. It was developed by Modigliani and
Modigliani; hence M2. One uses M2 to compare the performance of a managed portfolio (MP)
with a market index. The M2 measure creates a hypothetical complete portfolio that is composed
of T-bills and the MP that has the same standard deviation as the market index. This allows
comparing the portfolio return directly with the level of return of the market.
to find undervalued stocks, what strategy should a portfolio manager use in investing in those
stocks? The percentage of funds allocated to undervalued stocks depends, in part, on the ability
of the manager. If a manager has perfect foresight, theoretically all funds should be placed in the
most undervalued stocks. If the manager has substantial funds however, buying pressure could
make that impossible. The risk of such a strategy would be extreme in any case. Most portfolio
portfolios. The relevant measure of risk for the actively managed portfolio is its ratio of alpha to
nonsystematic risk.
18-3
Chapter 18 - Portfolio Performance Evaluation
This edition of the text goes much further in explaining alpha and its relationship to other
performance measures.
= Correlation between RP & RM
short sales and hedge out the risks.
Alpha and the Treynor measure
A positive alpha does not guarantee a higher Treynor ranking because one must know the beta as
18-4
2
p
P
2
MOptimal σ
α
SsqrtS
P
MMP )1(SSS
P
P
MP TT
Chapter 18 - Portfolio Performance Evaluation
Alpha Capture & Transport
If an analyst finds an undervalued security and invests in it, market moves may still wipe out any
transport.
To hedge out systematic risk, short sell βP dollars of the index for every dollar invested in the
portfolio, investing the proceeds in T-bills. The excess return on this zero beta position is:
The Sharpe ratio for Z, SZ, simplifies to the information ratio because ρ = 0 by construction
because with a zero beta, the correlation between Z and M = 0. Note that one could write alpha
as alpha p or alpha z.
indicates that it is difficult to find positive alphas, although it may be easier to find negative
alphas.
Evidence indicates one should use a multi-index model such as the Fama-French model (FF) (See
Chapter 7) to establish the expected return:
have positive alphas when calculated against the FF model, even when a fourth momentum factor
is added. This probably tells us we still don’t have the proper model of expected returns so all
performance evaluation should be viewed skeptically.
The assumptions of stability that underlie the measures of abnormal performance limit their
effectiveness. Actively managed portfolios are, by their nature, not stable. The beta of the
ptPMtPPt eαRβR
ptPZ eαR
P
ZαR
P
P
Z
P
P
MMZ S or )1(SSS
ptPHMLtHMLSMBtSMBMtPPt eαrβrβRβR
2. Style Analysis
PPT 18-17 through PPT 18-21
3. Morningstar’s Risk-Adjusted Rating
PPT 18-22 through PPT 18-23
4. Risk Adjustment with Changing Portfolio Composition
PPT 18-24 through PPT 18-25
Performance measures assume a fund maintains a constant level of risk. This assumption is
violated for most funds and is particularly problematic for funds that engage in active asset
know about the strategy change one would incorrectly state that the fund underperformed M.
In a large universe of funds, some funds will have abnormal performance in every period just by
chance. It requires statistical work to verify the significance of performance estimates.
Volatility is quite high and creates large errors in estimation so we have to be somewhat skeptical
5. Performance Attribution Procedures
PPT 18-26 through PPT 18-30
Decomposing overall performance into components allows the analyst to determine what aspects
of portfolio choices contributed to good or bad performance.
generated by overweighting investments in classes that perform better than the bogey. Ex post
one would have wanted to have 100% allocated to the highest performing class. The only way
this number can be negative is if one has a negative index return.
The second step is to calculate the contribution to performance of both sector and security
6. Market Timing
PPT 18-31 through PPT 18-36
If a portfolio manager could time general movements in the market, the performance would be
similar to a call option. When market returns are lower than money market instruments, the
manager would switch out of equities and into money markets. When stock returns will be higher
a large number of bull and bear markets in recent years. This reduces the accuracy of testing a
manager’s ability to call turns. If the manager of a portfolio can time the market, that manager
would increase the beta on the portfolio when the market is expected to rise. When the market
experiences lower returns or losses, the manager reduces the beta of the portfolio.
There is not much evidence of timing ability and this should be difficult to do in competitive
The timer doesn’t have to perfectly forecast the cash or the stock market, he or she just has to
know which one will do better. The time period is 82 years so part of the size of the numbers is
the long time period for compounding. As stated above, there isn’t much evidence of timing
ability but one can understand the lure of it with the size of gains that are possible.
Excel Applications
