Example research essay topic: Portfolio Management Performance Measures Of Expected Rate Return - 2,189 words

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Portfolio management. PERFORMANCE MEASURES OF EXPECTED RATE OF RETURN. Expected rates of return are based on the main concept of risk vs. return.

Therefore, the higher the risks the higher the return should there be. If the two securities have the same risk, the security that offers more return based on the given risk should be accepted. Sharpe, Treynor and Jenson are some of the methods aimed at the measuring the processes used to determine the expected rates of return. Sharpe and treynor measures. The two leading portfolio performance measures were designed by William F.

Sharpe and Jack Treynor, and they are similar. 4 These measures are defined mathematically in Table A below. The only mathematical difference in the two measures is in their denominators. The Sharpe measure uses the standard deviation of periodic security returns, whereas the Treynor measure uses the security (or portfolio) beta. Despite their mathematical similarity, these two measures have an important conceptual difference. The Treynor index provides a measure of return relative to beta, a measure of systematic risk. It ignores any unsystematic risk that might be present.

Finance theory indicates that expected return is a function or necessary risk (systematic risk) only, and therefore the Treynor measure should be an appropriate risk measure for single securities, as well as portfolios. Table A. SHARPE AND TREYNOR PERFORMANCE MEASURE Sharpe measure = (R-Rf) /o Treynor Measure = (R-Rf) /? Where, R = average return Rf = risk-free rate O = standard deviation of returns? = beta The Sharpe measure, in contrast, measures return relative to total risk. In a well-diversified portfolio, total risk is predominately from systematic risk factors. The Sharpe measure can therefore be used effectively with a portfolio.

A single security, however, contains substantial unsystematic risk. It would not be appropriate, therefore, to apply the Sharpe measure in this case. Table B (Please see the addendum section) presents hypothetical return statistics over a year's time. The table shows both mean returns and mean excess returns (which have the prevailing Treasury bill rate subtracted). Two different risk measures are shown: (1) the standard deviation of return and (2) beta, the measure of systematic risk. Both the Sharpe and Treynor measures compute excess return per unit of risk.

The higher this ratio, the better. We can see directly from Table B in the addendum section that Fund C has the best risk-adjusted performance, as its ratio is higher than that of either Fund A or Fund B with both the Sharpe and Treynor performance measures. Figures A and B show these results graphically. The upward-sloping line in each figure shows the combinations of risk and return that are predicted by finance theory. Combinations that lie above this line are better than expected, and points below are substandard. Over the hypothetical year of Table C, Funds B and C out-performed the overall market as represented by the S&-P 500 stock market index, whereas Fund A underperformed the market.

Let us consider another example to further illustrate the message contained in risk-adjusted performance measurement. Look at Table D, which shows the first six years of data from Table A. Over this period, 44 Wall Street shows an annual mean return of 64. 6 percent, which is considerably higher than the 29. 2 percent earned by Mutual Shares. It is easy to jump to the conclusion that 44 Wall Street showed superior performance over these six years. It is certainly true that the fund made handsome gains over this period. This perspective, however, considers only the return.

It ignores the volatility of the fund. To compare the two funds properly, risk must be incorporated into the picture. For the sake of this example, assume that the T-bill rate was a constant 10 percent per year over this period. With this assumption, we can calculate risk-adjusted performance using the Sharpe measure, as in Table F. Table F RISK-ADJUSTED PERFORMANCE, 1975 TO 1980, AS DETERMINED BY SHARPE MEASURE 44 Wall Street: (. 646 -. 100) /. 560 = . 975 Mutual Shares: (. 292 -. 100) /. 173 = 1. 100 Mutual Shares shows a r return per unit of risk than 44 Wall Street during this six-year period.

This is that its risk-adjusted performance is superior to that of the other fund, even h 44 Wall Street showed average annual returns that were over twice as high. respite all this, many people take risk-adjusted performance measurement with n of salt. You would have a hard time convincing everyone that Mutual Shares outperformed 44 Wall Street over the period 1975 to 1980. The attitude that risk matters only if it hurts you prevails in the subconscious minds of most of us.

The words of a philosopher seem especially relevant here: "To prove a thing is not enough; you must convince someone to accept it. jensen measure Another traditional performance measure, the Jensen measure, is seldom used today. It stems directly from the implications of the Capital Asset Pricing Model: Rit-Rft = a[? (Rmt-Rft) ] Finance theory requires that the excess return on a security and the excess return on the market portfolio be directly related to the beta of the security, and that securities with a beta of 0 should have an excess return of 0. This means that in the previous equation, the constant term 0. should be 0. It this term is positive, it indicates the presence of an upward trend in security prices that is unexplainable by finance theory.

If it is negative, it indicates a downward trend. Michael Jensen proposed using this alpha term as a measure of performance. If a portfolio manager is a better-than-average stock picker and consistently earns returns above those predicted by beta, the alpha of the portfolio will be positive. Subsequent research has revealed several statistical and theoretical problems with the Jensen measure, and it is generally out of favor with today's managers and academic researchers. You still, however, frequently hear managers speak of the search for "positive alpha, " meaning above-average investment results. Some of the reference sources available on the Internet report an investment's alpha over past periods of time.

performance measurement In practice Academic Issues. A controversy is growing in academia about the value of the traditional portfolio measures. No one questions the need to view asset returns in a risk-adjusted framework. The issue is that their use is largely predicated upon the belief that the Capital Asset Pricing Model is the correct view of the world, yet evidence continues to accumulate that may ultimately lead to displacement of the CAPM paradigm. Efforts to develop the arbitrage pricing model, multi-factor Capm's, and an inflation-adjusted CAPM all have implications for proper performance evaluation. Until a better technique is discovered, however, the Sharpe and Treynor measures are likely to continue as popular methods in academic research.

Industry Issues and conclusive remarks. Virtually everyone who ever studied investment theory in a university classroom has read about the merits of the traditional performance measures. The sobering fact is that the investment industry has never really adopted them. A 1987 survey of three thousand investment practitioners found that over 80 percent agreed with the following statement: "Portfolio managers are hired and fired largely on the basis of realized investment returns with little regard to risk taken in achieving the returns. " When formal performance measurement is used in practice, the fund's performance is commonly compared with some similar benchmark. For instance, an all-equity fund might be compared with the S&-P 500, whereas a fund composed of both stocks and bonds might be compared with some weighted average of the S&P 500 and the Season Lehman Bond Index. Such a practice has intuitive appeal but can still lead to misleading results if careful attention is not paid to comparative beta and duration statistics.

In considering investment performance it can be useful to see why an investment performed better or worse than expected. One method for doing so is "Fama's decomposition, " named for Eugene Fama, a finance professor at the University of Chicago. Fama shows how realized investment performance can be segregated into several components that give more information on what the manager actually did. Figure C shows the performance of a manager whose portfolio had a set target level of systematic risk, Btarget Such a level of beta has a corresponding level of expected return, R target. The portfolio actually earned the level of return shown by point X and reflected systematic risk Btarget which is higher than the target.

Figure C Because the investor chose to take some risk, the investor should earn a return greater than the risk-free rate. This increment is labeled "Return from Investor's Risk. " The manager, we see, took on more risk than the target level, so again we expect the actual return to be higher than the target. The level of systematic risk marked "Bproxy " corresponds to a portfolio with the same level of total risk as the actual portfolio. You can find this value by remembering that Sigma portfolio = B^ 2 portfolio Sigma^ 2 market We see that the actual return, then, has three components: the return the investor chose to take, the added return the manager chose to bear, and return from the manager's good selection of securities. Bibliography: web for instance, reports alpha for mutual funds under the profile / performance selection. Strong; , Robert A. , "A Behavioral Investigation of' Three Paradigms in Finance, " Northeast' journal of Business and Economics, Spring/Summer 1988, 1 - 28.

Modern Portfolio Theory and Investment Analysis, 5 th edition, by Edwin J. Eicon and Martin J. Order for an excellent amplification of this aspect of performance evaluation. Chapter 24 Addendum: TABLE B SAMPLE INVESTMENT RESULTS Returns Excess 1 'euros A B C S&P T-bill A B C S&P January 2. 53 2. 07 3. 00 2. 30 0. 67 1. 86 1. 40 2. 33 1. 63 February - 4. 40 - 3. 90 - 6. 00 - 4. 00 0. 69 - 5. 09 - 4. 59 - 6. 69 - 4. 69 March - 1. 32 - 1. 08 - 1. 44 - 1. 20 0. 67 - 1. 99 - 1. 75 - 2. 11 - 1. 87 April 2. 42 1. 98 2. 64 2. 20 0. 70 1. 72 1. 28 1. 94 1. 50 May 1. 43 1. 17 1. 56 1. 30 0. 71 0. 72 0. 46 0. 85 0. 59 June 0. 50 3. 40 0. 48 0. 40 0. 69 - 0. 19 2. 71 - 0. 21 - 0. 29 July - 0. 33 - 1. 30 2. 00 - 0. 30 0. 73 - 1. 06 - 2. 03 1. 27 - 1. 03 August: 3. 00 2. 34 3. 90 2. 60 0. 75 2. 25 1. 59 3. 15 1. 85 September 4. 00 4. 79 4. 00 3. 10 0. 75 3. 25 4. 04 3. 25 2. 35 Oc tower - 5. 00 - 4. 50 - 3. 72 - 3. 10 0. 77 - 5. 77 - 5. 27 - 4. 49 - 3. 87 November 3. 19 2. 61 4. 48 2. 90 0. 74 2. 45 1. 87 3. 74 2. 16 December 5. 28 4. 32 5. 76 4. 80 0. 75 4. 53 3. 57 5. 01 4. 05 Mean % 0. 94 0. 99 1. 39 0. 92 0. 72 0. 22 0. 27 0. 67 0. 20 Standard deviation 3. 07 2. 91 3. 36 2. 53 0. 03 3. 07 2. 91 3. 36 2. 53 Beta 0. 00 1. 20 1. 06 1. 29 1. 00 Sharpe measure. 073. 094. 200. 079 Treynor measure. 183. 255. 519. 200 Monthly figures are in percentages. Figure A. Sharpe Measure Figure B.

Treynor Measure Figure C Table C COMPARAT 1 VE MUTUAL FUND RETURNS? ar 44 Wall Street Mutual Shares 75 + 184. 1 % + 24. 6 76 + 46. 5 + 63. 1 77 + 16. 5 + 13. 2 78 + 32. 9 + 16. 1 79 + 71. 4 + 39. 3 80 + 36. 1 + 19. 0 Mean + 64. 6 % + 29. 2 % St; innate deviation 56. 0 % 17. 3 % Table F RISK-ADJUSTED PERFORMANCE, 1975 TO 1980, AS DETERMINED BY SHARPE MEASURE 44 Wall Street: (. 646 -. 100) /. 560 = . 975 Mutual Shares: (. 292 -. 100) /. 173 = 1. 100

Research essay sample on Portfolio Management Performance Measures Of Expected Rate Return