EVALUATION OF INVESTMENT PERFORMANCE

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Investment Analysis & Portfolio Management (FIN630)

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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