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Investment Analysis and Portfolio Management

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Investment Analysis & Portfolio Management (FIN630)
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Lesson # 39
EVALUATION OF INVESTMENT PERFORMANCE
Framework for Evaluating Portfolio Performance:
When evaluating a portfolio's performance, certain factors must be considered. Assume that
in early 2004 you are evaluating the Go Growth mutual fund, a domestic equity fund in the
category of large growth (it emphasizes large-capitalization growth stocks). This fund
earned a total return of 20 percent for its shareholders for 2003. It claims in an
advertisement that it is the #1 performing mutual funds in its category. As a shareholder,
you are trying to assess Go Growth's performance.
SOME OBVIOUS FACTORS TO CONSIDER IN MEASURING PORTFOLIO
PERFORMANCE:
Differential Risk Levels:
Based on our discussion throughout this text of the risk-return trade-off that underlies all
investment actions, we can legitimately say relatively little about Go Growth's performance.
The primary reason is-that investing is always a two-dimensional process based on both
return and risk. These two factors are opposite sides of the same coin, and both must be
evaluated if intelligent decisions are to be made. Therefore, if we know nothing about the
risk of this fund, little can be said about its performance. After all, Go Growth's managers
may have taken twice the risk of comparable portfolios to achieve this 20-percent return.
Given the risk that all investors face, it is totally inadequate to consider only the returns
from various investment alternatives. Although all investors prefer higher returns, they are
also risk averse. To evaluate portfolio performance properly, we must determine whether
the returns are large enough given the risk involved. If we are to assess portfolio
performance correctly, we must evaluate performance on a risk-adjusted basis.
Differential Time Periods:
It is not unusual to pick up a publication from the popular press and see two different
mutual funds of the same type--for example, small-capitalization growth funds or balanced
funds--advertise themselves as the #1 performer. Each of these funds is using a different
time period over which to measure performance. For example, one fund could use the 10
years ending December 31, 2003, whereas another fund uses the five years ending June 30,
2003.GoGrowth could be using a one-year period ending on the same date or some other
combination of years. Mutual fund sponsors may emphasize different time periods in
promoting their performance. Funds can also define the group or index to which
comparisons are made.
Although it seems obvious when one thinks about it, investors tend not to be careful when
making comparisons of portfolios over various time periods. As with the case of differential
risk, the time element must be adjusted for if valid performance of portfolio results is to be
obtained.
Appropriate Benchmarks:
A third reason why we can say little about the performance of Go Growth is that it's 20
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percent return given its, risk, is meaningful only when compared to a legitimate alternative.
Obviously, if the average-risk fund or the market returned 25 percent in 2003, and Go
Growth is an average-risk fund, we would find its performance unfavorable. Therefore, we
must make relative comparisons in performance measurement, and an important related
issue is the benchmark to be used in evaluating the performance of a portfolio.
It is critical in evaluating portfolio performance to compare the returns, obtained on
the portfolio being evaluated with the returns that could have been obtained from a
comparable alternative. The measurement process must involve relevant and obtainable
alternatives; that is, the benchmark portfolio must be a legitimate alternative that accurately
reflects the objectives of the portfolio being evaluated.
An equity portfolio consisting of Standard & Poor's Composite 500 Index (S&P
500) stocks should be evaluated relative to the S&P 500 index or other equity portfolios
that could be constructed from the Index, after adjusting for the risk involved. On the
other hand, a portfolio of small-capitalization stocks should not be judged against the
benchmark of the S&P 500. Or, if a bond portfolio manager's objective is to invest in
bonds rated A or higher, it would be inappropriate to compare his or her performance
with that of a junk bond manager.
It may be more difficult to evaluate equity funds that hold some mid-cap and small
stocks while holding many S&P 500 stocks. Comparisons for this group can be quite
difficult.
Constraints on Portfolio Managers:
In evaluating the portfolio manager rather than the portfolio itself, an investor should
consider the objectives set by (or for), the manager and any constraints under which he or
she must operate. For example if a mutual fund's objective is to invest in small speculative
stocks investors must expect the risk to be larger than that of a fund invested in S&P 500
stocks with substantial swings in the annual realized returns.
It is imperative to recognize the importance of the investment policy statement pursued, by
a portfolio manager in determining the portfolio's results in many cases he investment
policy determines the return and/or the risk of the portfolio. For example, Brinson, Hood,
and Bee bower found that for a sample of pension plans the asset allocation decision
accounted for approximately 94 percent of the total variation in the returns to these funds. In
other words, more than 90 percent of the movement in a fund's returns, relative to the
market returns, is attributable to a fund's asset allocation policy.
If a portfolio manager is obligated to operate under certain constraints these must be taken
into account. For example, if a portfolio manager of an equity fund is prohibited from
selling short, it is unreasonable to expect the manager to protect the portfolio in this manner
in a bear market. If the manager is further prohibited from trading in options and futures the
only protection left in a bear market may be to reduce the equity exposure.
Other Considerations:
Of course, other important issues are involved in measuring the portfolio's performance,
including evaluating the manager as opposed to the portfolio itself if the manager does not
have full control over the portfolio's cash flows. It is essential to determine how well
diversified the portfolio was during the evaluation period, because, diversification can
reduce portfolio risk.
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All investors should understand that even in today's investment World of computers
and databases, exact, precise universally agreed-upon methods of portfolio evaluation
remain an elusive goal. One popular press article summarized the extent of the problem by
noting that "most investors ... don't have the slightest idea how well their portfolios are
actually performing." This article suggests some do-it-yourself techniques as well, as some
"store-bought solutions" and discusses some new trends in the money management industry
10 provide investors with better information.
Investors can use several "well-known, techniques to assess, the actual performance of a
portfolio relative to one or more alternatives. In the final analysis, when investors are
selecting money managers to turn their money over to, they evaluate these managers only
on the basis of their published performance statistics. If the published "track record" looks
good, that is typically enough to convince many investors to invest in, a particular mutual
fund. However, the past is no guarantee of an investment manager's future. Short-term
results may be particularly misleading.
Return and Risk Considerations:
Performance measurement begins with portfolio valuations and transactions translated
into rate of return. Prior to 1965, returns were seldom related to measures of risk. In. eval-
uating portfolio performance, however, investors must consider both the realized return
and the risk that was assumed. Therefore, whatever measures or techniques are used
these parameters must be incorporated into the analysis.
MEASURES OF RETURN:
When portfolio performance is evaluated, the investor should be concerned with the total
change in wealth. A proper measure of this return is the total return (TR), which captures
both the income component and the capital gains (or losses) component of return. Note that
the Performance Presentation Standards require the use of total return to calculate
performance.
In the simplest case, the market value of a portfolio can be measured at the beginning and
ending of a period, and the rate of return can be calculated as
Rp=VE -VB / VB
Where VE is the ending value of the portfolio and VB is its beginning value.
This calculation assumes that no funds were added to or withdrawn from the portfolio by
the client during the measurement period. If such transactions occur, the portfolio return as
calculated, Rp may not be an accurate measure of the portfolio's performance. For example,
if the client adds funds close to the end of the measurement period, would produce
inaccurate results, because the ending value was not determined by the actions of the
portfolio manager. Although a close approximation of portfolio performance might be
obtained by simply adding any withdrawals or subtracting any contributions that are made
very close to the end of the measurement period, timing issues are a problem.
Dollar-Weighted Returns:
Traditionally, portfolio measurement consisted of calculating the dollar-weighted rate of
return (DWR), which is equivalent to the internal rate of return (IRR) used in several
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financial calculations. The IRR measures the actual return earned on a beginning portfolio
value and on any net contributions made during the period. The DWR equates all cash
flows, including ending market value, with the beginning market value of portfolio. Because
the DWR is affected by cash flows to the portfolio it measures the rate of return to the
portfolio owner. Thus, it accurately measures the investor's return. However because the
DRW is heavily affected by cash flows, it is inappropriate to use when making comparisons
to other portfolios or to market indexes, a key factor in performance measurement. In other
words, it is a misleading measure of the manager's ability, because the manager does not
have control over the timing of the cash inflows and outflows. Clearly, if an investor with
$1,000,000 allocates these funds to a portfolio manager by providing half at the beginning
of the year and half at mid-year, that portfolio value at the end of the year will differ from
another manager who received the entire $1,000,000 at the beginning, of the year. This is
true even if both managers had the same two 6-month returns during that year.
Time-Weighted Returns:
In order to evaluate a manager's performance properly, we should use the time-weighted
rate of return (TWR). TWRs are unaffected by any cash flows to the portfolio; therefore,
they measure the actual rate of return earned by the portfolio manager.
We wish to determine how well the-portfolio manager performed regardless of the
size or timing of the cash flows. Therefore, the time-weighted rate of return measures the
compound rate of growth of the portfolio during the evaluation period. It is calculated by
computing the geometric average of the portfolio subperiod returns. That is, we calculate
the geometric mean of a set of return relatives (and subtract out the 1.0).
Which Measure to Use:
The dollar-weighted return and, the time-weighted return, can produce different results, and
at times these differences are substantial. In fact, the two will produce identical results only
in the case of no withdrawals or contributions during the evaluation period and with all
investment income being reinvested. The time-weighted return captures the rate of return
actually earned by the portfolio manager, whereas the dollar-weighted return captures the
rate of return earned by the portfolio owner.
For evaluating the performance of the portfolio manager, the time-weighted return should
be used, because he or she generally has no control over the deposits and withdrawals made
by the clients. The objective is to measure the performance of the portfolio manager
independent of the actions of the client, and this is better accomplished by using the time
weighted return.
RISK MEASURES:
Why can we not measure investment performance on the basis of a properly calculated rate
of return measure? After all rankings of mutual funds are often done this way in the popular
press, with one-year, three-year, and sometimes five-year returns shown. Are rates of return,
or averages, good indicators of performance?
Differences in risk will cause portfolios to respond differently to changes in the overall
market and should be accounted for in evaluating performance.
We now know that the two prevalent measures of risk used in investment analysis are total
risk and non-diversifiable or systematic risk. The standard deviation for a portfolio's set of
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returns can be calculated easily with a calculator or computer and is a measure of total risk.
As we know from portfolio theory, part of the total risk can be diversified away.
Beta, a relative measure of systematic risk, can be calculated with any number of software
programs, However, we must remember that Betas are only estimates of systematic risk.
Betas can be calculated using weekly, monthly, quarterly, or annual data, and each will
produce a different estimate. Such variations in this calculation could produce differences in
rankings which use beta as a measure of risk. Furthermore, betas can be unstable, and they
change over time.
Risk-Adjusted Measures of Performance:
Based on the concepts of capital market theory, and recognizing the necessity to incorporate
return and risk into the analysis, three researchers-- William Sharpe, Jack Treynor, and
Michael Jensen-- developed measures of portfolio performance in the 1960s. These
measures are often referred to .as the composite (risk-adjusted') measures of portfolio
performance, meaning that .they incorporate 'both realized return and risk into the
evaluation. These measures are often still used, as evidenced by Morningstar, perhaps the
best-known source of mutual fund information, reporting the Sharpe ratio explained below.
The Sharpe Performance Measure:
William Sharpe, whose contributions to portfolio theory have been previously discussed,
introduced a risk-adjusted measure of portfolio performance called the reward­to-variability
ratio (RVAR) based on his work in capital market theory. This measure uses a benchmark
based on the expost capital market line. This measure can be defined as:
RVAR = [TRp - RF] / SDp
= excess return / risk
TRp = the average TR for portfolio p during some period of time
RF = he average risk-free rate of return during the period
SDp = the standard deviation of return for portfolio p during the period
TRp ­ RF = the excess return (risk premium) on portfolio p
The Treynor Performance Measure:
At approximately the same time as Sharpe's measure was developed (the mid-1960s), jack
Treynor presented a similar measure called the reward-to-volatility ratio (RVOL) like
Sharpe, Treynor sought to relate the return on a portfolio to its risk. Treynor, however,
distinguished between total risk and systematic risk, implicitly assuming that portfolios
are well diversified; that is, he ignored any diversifiable risk. He used as a benchmark the
ex post security market line.
In measuring portfolio performance, Treynor introduced the concept of the characteristic
line which was used to partition a security's return into its systematic and non-systematic
components. It is used in a similar manner with portfolios, depicting the relationship
between the returns on a portfolio and those of the market. The slope of the characteristic
line measures the relative volatility of the fund's returns. As we know, the slope of this line
is the beta coefficient, which is a measure of the volatility (or responsiveness) of the
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portfolio's returns in relation to those of the market index.
Characteristic lines, can be estimated by regressing each portfolio's returns on the market
proxy returns using either raw returns for the portfolios and raw proxy returns or excess
portfolio returns and excess1 market proxy it turns where the risk-free rate has been
subtracted out: The latter method is theoretically better and is used here.
Treynor's measure relates the average excess return on the portfolio during some period
(exactly the same variable as in the Sharpe measure) to its systematic risk as measured by
the portfolio's beta. The reward-to-volatility ratio is:
RVOL = [TRp - RF] / βp
= Average excess return on portfolio p
βp = the beta for portfolio p
In this case, we are calculating the excess return per unit of systematic risk. As with RVAR,
higher values of RVOL indicate better portfolio performance. Portfolios can be ranked on
their RVOL, and assuming that the Treynor measure is a correct measure of portfolio
performance, the best performing portfolio can be determined.
Comparing the Sharpe and Treynor Measures:
Given their similarity, when should RVAR or RVOL be used, and. why? Actually, given
the assumptions underlying each measure, both can be said to be correct. Therefore, it is
usually desirable to calculate both measures for the set of portfolios being evaluated.
The choice of which to use could depend on the definition of risk. If an investor thinks it
correct to use total risk, RVAR is appropriate; however, if the investor thinks that it is
correct to use systematic risk, RVOL is appropriate.
What about the rankings of a set of portfolios using the two measures? If the portfolios are
perfectly diversified that is, the correlation coefficient between the portfolio return and the
market-return is l.0 the rankings ­will be identical. For typical large, professionally
managed portfolios, such as broad-based equity mutual funds, the two-measures often
provide identical, or almost identical, rankings.
As the portfolios become less well diversified, the possibility of differences in rankings
increases. This leads to the following conclusions about these two measures: RVAR takes
into account how well diversified a portfolio was during the measurement period.
Differences in rankings between the two measures can result from substantial differences in
diversification in the portfolio. If a portfolio is inadequately diversified, its RVOL ranking
can be higher than its RVAR ranking. The nonsystematic risk would not affect the RVOL
calculation. Therefore, a portfolio with a Jaw amount of systematic risk and a large amount
of total risk could show a high RV0L value and a low RVAR; value. Such a difference in
ranking results from the substantial difference in the amount of diversification of the
portfolio.
This analysis leads to an important observation about the Sharpe and Treynor measures.
Investors who have all (or substantially all) of their assets in a portfolio of securities should
rely more on the Sharpe measure, because it assesses the portfolio's total return in relation to
total risk, which: includes any unsystematic risk assumed by the investor. However for
those investors, whose portfolio constitutes only one (relatively) small part of their total
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assets that is, they have numerous other assets systematic risk may well be the relevant risk.
In these circumstances, RVOL Is appropriate, because it considers only systematic or non-
diversifiable risk.
Measuring Diversification:
Portfolio diversification is typically measured by correlating the returns on the portfolio
with the returns oh the market index, this is accomplished as part of the process of fitting a
characteristic, line whereby the' portfolio's returns are regressed: against the market's
returns. The square of the correlation coefficient produced as a part of the analysis, called
the coefficient of determination, or R2, is used to, denote the degree of diversification. The
coefficient, of determination indicates the percentage of the variance in the portfolio's
returns that is explained by the market's-returns. If the fund is totally diversified, the R2 will
approach 1.0, indicating that the fund's returns are .completely explained by the market's
returns: The lower the coefficient of determination, the less the portfolio returns are
attributable to the market's returns. This indicates that other factors, which could have been
diversified away, are being allowed to .influence-the portfolio's returns.
Jensen's Differential Return Measure:
A measure related to Treynor's RVOL is Jensen's differential return measure (or alpha).
Jensen's measure of performance like Treynor's measure is based on the capital asset pricing
model (CAPM). The expected return for any security (i) or, in this case, portfolio (p) is
given as;
E (Rpt) = RFt + βp (E (RMt) ­ RFt)
Problems with Portfolio Measurement:
Using the three risk-adjusted performance measures just discussed to evaluate portfolios is
not without problems. Investors should understand their limitations, and be guided
accordingly.
First, these measures are derived from capital market theory and the CAPM and are
therefore dependent on the assumptions involved with this theory. For example, it the
Treasury bill rate is not a satisfactory- proxy for the risk-free rate, or if investors cannot
borrow and lend at the risk-free rate this will have an impact on these measures of
performance.
An important assumption of capital market theory that directly affects the use of these
performance measures is the assumption of a marker portfolio that can be proxied by a
market index. We have used the S&P 500 Index as a market proxy, as is often. However,
there are potential problems.
Although a high correlation exists among most of the commonly used market proxies this
does not eliminate the problem that some may be efficient but others are not. According to
Roll, no unambiguous test of the CAPM has yet been conducted. This point should be kept
in mind when we consider performance measures based on the CAPM, such as the Treynor
and Jensen; measures.
The movement to global investing increases the problem of benchmark error. The efficient
frontier changes when foreign securities are added to the portfolio. The measurement of
beta will be affected by adding foreign securities. Given that a world portfolio is likely to
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have a smaller variance than the S&P 500 Index, any measure of systematic risk is likely to
be smaller.
A long evaluation period is needed to determine successfully performance that is truly
superior. Over short .periods, luck can overshadow all else, but luck cannot be expected to
continue. According to some estimates, the number of years needed to make such an
accurate determination is quite large.
OTHER ISSUES IN PERFORMANCE EVALUATION:
Monitoring Performance:
Portfolio evaluation of managed portfolios should be a continuing process. The results of
the portfolio must be calculated using some of the techniques discussed above. In addition,
a monitoring process should evaluate the success of the portfolio relative to the objectives
and constraints of the portfolio's owners.
Performance Attribution:
Most of this chapter has considered how to measure a portfolio manager's performance.
However, portfolio evaluations also to concern with the reasons why a manager did better or
worse than a properly constructed benchmark with complete risks adjustment. This part of
portfolio evaluation is called performance attribution, which seeks to determine, after the
fact, why a particular portfolio had a given return over some specified time period and,
therefore, why success or failure occurred.
Typically, performance attribution is a top-down approach; it looks first at the broad issues
and progresses by narrowing the investigation its purpose is to decompose the total
performance of a portfolio into specific components that can be associated with specific
decisions made by the portfolio manager.
.
Performance attribution often begins with, the policy statement that guides the management
of the portfolio; the portfolio normally would have a set of portfolio weight to be used. If
the manager uses a different set, this will account for some of the results. In effect, we are
looking at the asset allocation decision. If the manager chooses to allocate portfolio funds
differently than the weights that occur in the benchmark portfolio, what are the results?
After this analysis performance attribution might analyze sector (industry) selection and
security selection. Did the manager concentrate on or avoid certain sectors, and if so what
were the results? Security selection speaks for itself.
Part of this process involves identifying-a benchmark of performance to use in comparing
the portfolio results. This bogey is designed to measure passive results, ruling out both asset
allocation and security selection decisions. Any differences between the portfolio's results
and the bogey must be attributable to one or more of these decisions made by the portfolio
manager.
Another way to think about performance attribution is to recognize that performance
different from a properly constructed benchmark comes from one of two sources, or both:
1. Market timing
2. Security selection
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Techniques are available to decompose the performance of a portfolio into these two
components.
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