Evaluation Of Investment Performance-Investment Managment And Portfolio-Lecture Notes, Study notes of Investment Management and Portfolio Theory

Download Evaluation Of Investment Performance-Investment Managment And Portfolio-Lecture Notes and more Study notes Investment Management and Portfolio Theory in PDF only on Docsity! y g ( ) 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 percent return given its, risk, is meaningful only when compared to a legitimate alternative. docsity.com y g ( ) 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. docsity.com y g ( ) risk and non-diversifiable or systematic risk. The standard deviation for a portfolio's set of 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 reward–to-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 docsity.com y g ( ) 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 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] / p = Average excess return on portfolio p p = 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 docsity.com y g ( ) 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 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 + p (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. docsity.com