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  1. 1. Investment Performance Evaluation Chapter 16
  2. 2. Introduction <ul><li>Chapter focuses on security selection decisions made by professional money managers, or institutional investors, such as: </li></ul><ul><ul><li>Bank trust departments </li></ul></ul><ul><ul><li>Mutual funds </li></ul></ul><ul><ul><li>Investment advisory services </li></ul></ul><ul><ul><li>Insurance companies’ investment management departments </li></ul></ul><ul><ul><li>Money management firms </li></ul></ul>
  3. 3. Sources of Funds <ul><li>Institutional money managers receive funds from various sources, including: </li></ul><ul><ul><li>Pensions </li></ul></ul><ul><ul><ul><li>Corporate </li></ul></ul></ul><ul><ul><ul><li>Government </li></ul></ul></ul><ul><ul><ul><li>Individual workers </li></ul></ul></ul><ul><ul><li>Wealthy individuals </li></ul></ul><ul><ul><li>Endowments </li></ul></ul><ul><ul><li>Foundations </li></ul></ul>
  4. 4. Selection of Money Manager <ul><li>These institutions/individuals must select a money manager </li></ul><ul><li>This chapter presents tools for measuring and ranking money managers’ performances </li></ul><ul><ul><li>Aids in the selection process </li></ul></ul><ul><ul><li>Money managers also use these tools to appraise and improve their skills </li></ul></ul>
  5. 5. Information Needed for Evaluation <ul><li>To evaluate an investment manager </li></ul><ul><ul><li>Need rates of return </li></ul></ul><ul><ul><ul><li>Many money manager services do not provide adequate data </li></ul></ul></ul><ul><li>Investment Company Act of 1940 requires every mutual fund in U.S. to disclose investment details </li></ul><ul><ul><li>Enables investors to effectively evaluate fund </li></ul></ul>
  6. 6. Investments Company Data <ul><li>Mutual fund investor redeem shares at the current Net Asset Value Per Share (NAVPS) </li></ul><ul><li>One-period rate of return for mutual fund: </li></ul>
  7. 7. Mutual Funds <ul><li>Investment goals </li></ul><ul><ul><li>Open-end investment companies must state the portfolio’s investment objective </li></ul></ul><ul><ul><ul><li> 33 categories of objectives </li></ul></ul></ul><ul><ul><li>Closed-end funds </li></ul></ul><ul><ul><ul><li>Differ from open-end funds in that: </li></ul></ul></ul><ul><ul><ul><ul><li>Cannot sell shares after initial offering </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Can borrow money, trade options and pursue different investment objectives </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Most shares are not redeemable at NAVPS </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Trade on stock exchanges—can trade at a premium or discount (more common) relative to NAVPS </li></ul></ul></ul></ul></ul>
  8. 8. Are Mutual Funds Markowitz Efficient Investments? <ul><li>The mutual funds are all inefficient investments </li></ul><ul><li>Funds tend to group into clusters corresponding to their investment goals </li></ul><ul><ul><li>Mutual funds are required to publish written goal statements </li></ul></ul><ul><ul><li>In a few cases fund’s stated objective and performance differed </li></ul></ul>This income and growth fund performed in the same league as the growth funds .
  9. 9. Scrutinizing Mutual Funds Goal Statements Portfolio’s SDs and Betas were better indicators of portfolio’s actual performance than their goal statements. 13.5% None 9.5% 13.8% 1 None 1 20 0.9 to 1.1 12.2% 10.0% 10.0% 11.2% 7 7 24 15 0.7 to 0.9 9.1% 9.7% 10.1% 6.9% 16 4 5 3 0.5 to 0.7 Income, Growth & Stability Income & Growth Growth & income Growth Income, Growth & Stability Income & Growth Growth & income Growth Beta Category’s average rate of return # of funds claiming each goal 13.5% 0.002304 0.992 22 0.9 to 1.1 High 10.6% 0.001543 0.786 53 0.7 to 0.9 Medium 9.1% 0.000877 0.619 28 0.5 to 0.7 Low Average Rate of Return Average Variance Average Beta # of funds Range of Betas Risk Class
  10. 10. Analyzing a Portfolio Manager’s Style <ul><li>In 1992 Sharpe introduced model to analyze a portfolio manager’s style ( i.e ., growth vs value investing, etc .) </li></ul><ul><ul><li>Uses modest amount of public information about funds </li></ul></ul><ul><ul><ul><li>Uses price indexes for 12 asset classes as explanatory variables for a mutual fund’s return </li></ul></ul></ul><ul><ul><ul><ul><li>Sample explanatory factors </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Soloman Brothers 90-day Treasury bill index </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Lehman Brothers Intermediate-Term Government Bond Index </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>FTA Japan Index </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Sharpe/BARRA Value Stock Index </li></ul></ul></ul></ul></ul>
  11. 11. Analyzing a Portfolio Manager’s Style <ul><ul><li>Uses factor analysis </li></ul></ul><ul><ul><ul><li>The factor loadings are estimates of the weights that a fund invests in the twelve asset categories </li></ul></ul></ul><ul><ul><ul><li>R 2 of 0.70 are common </li></ul></ul></ul><ul><li>Sharpe also suggests that same type of analysis could be done using a ‘rolling’ regression </li></ul><ul><ul><li>Repeating regression when new data is released—dropping oldest data and adding newest data </li></ul></ul>
  12. 12. Rolling Style Analysis <ul><li>Ibbotson Associates uses a rolling regression period of 60 months </li></ul><ul><ul><li>Deleting oldest month and adding new month as data becomes available </li></ul></ul>Some fixed-income securities entered this growth stock fund in mid 1990s—this is interesting because Magellan’s published investment objective is a growth stock fund.
  13. 13. Benefits From Using Quantitative Management Style Analysis <ul><li>Quantitative style analysis important due to: </li></ul><ul><ul><li>Investment holdings are usually not reported publicly until months after they are made—too late for investors to react in a timely manner </li></ul></ul><ul><ul><li>Mutual funds can report misleading investment goals </li></ul></ul><ul><li>Can also provide better forecasts of mutual fund’s risk/return than subjective comments in newspapers, etc . </li></ul>
  14. 14. Sharpe’s Portfolio Performance Measure <ul><li>May wish to rank portfolios’ performances </li></ul><ul><li>Need a measure that includes both risk and return </li></ul><ul><ul><li>Sharpe devised the reward to variability index </li></ul></ul>
  15. 15. SHARPE Example <ul><li>The Avon Fund earned an average return of 8% annually with a standard deviation of 16.6%, while the Blair Fund earned 13.00% annually with a standard deviation of 22.4%. During the same time period the average risk-free rate was 4%. </li></ul><ul><li>Which fund was the better performer? </li></ul>Since SHARPE Blair > SHARPE Avon , Blair was the better performer on a risk-adjusted basis.
  16. 16. SHARPE Example Avon RFR 13% 8% 22.4% 16.6% Standard Deviation of Returns Expected Return, E(r) Blair Slope is 0.4018 for REVAR Blair Slope is 0.241 for REVAR Avon
  17. 17. Treynor’s Performance Measure <ul><li>Treynor devised measure to evaluate performance that uses systematic risk (beta) rather than total risk (standard deviation) </li></ul>Calculated by estimating the fund’s characteristic line via regression.
  18. 18. TREYNOR Example <ul><li>The Avon Fund earned an average return of 8% annually (Characteristic Line AVON : Alpha: -0.00125; Beta: 0.8125), while the Blair Fund earned 13.00% annually (Characteristic Line BLAIR : Alpha: 0.014; Beta: 1.156). During the same time period the average risk-free rate was 4%. </li></ul><ul><li>Which fund was the better performer? </li></ul>Since TREYNOR Blair > TREYNOR Avon , Blair was the better performer on a risk-adjusted basis.
  19. 19. TREYNOR Example <ul><li>TREYNOR measures the desirability of fund in a SML context </li></ul>Avon RFR 13% 8% 1.156 .8125 Beta Expected Return, E(r) Blair TREYNOR Blair = 0.0778 TREYNOR Avon = 0.049 SML
  20. 20. An Investment’s Alpha <ul><li>Jensen modified the characteristic line equation </li></ul><ul><ul><li>Rather than using periodic rates of return , he uses periodic risk-premiums </li></ul></ul><ul><li>With expected values of </li></ul>
  21. 21. Explanation of an Investment’s Alpha <ul><li>Jensen’s alpha represents excess returns from asset </li></ul><ul><ul><li>Can be +, 0 or – </li></ul></ul><ul><ul><li>If asset is correctly priced, Jensen’s alpha = 0 </li></ul></ul><ul><ul><li>If alpha > 0 , asset has earned return greater than appropriate for its level of undiversifiable risk (beta) </li></ul></ul><ul><ul><ul><li>Asset is underpriced </li></ul></ul></ul><ul><ul><li>If alpha < 0 , asset’s returns are lower than appropriate for its level of risk </li></ul></ul><ul><ul><ul><li>Asset is overpriced </li></ul></ul></ul>
  22. 22. Jensen’s Alpha Example <ul><li>Using data ( risk premiums, not returns ) from Table 16-7 for the Avon and Blair Funds: </li></ul><ul><li>Characteristic Line Avon </li></ul><ul><li>Jensen’s alpha: -0.00875 </li></ul><ul><li>Beta: 0.8125 </li></ul><ul><li>Characteristic Line Blair </li></ul><ul><li>Jensen’s alpha: +0.02062 </li></ul><ul><li>Beta: 1.1562 </li></ul>Blair earned positive excess returns.
  23. 23. Caveats About Alphas <ul><li>Jensen’s alpha cannot be used to rank performance of different assets unless it’s adjusted for the assets’ risks </li></ul><ul><ul><li>The appraisal ratio divides Jensen’s alpha by the standard error of the estimate (SE (u) ) which then allows for rankings </li></ul></ul><ul><li>The alpha calculated from the original characteristic line (Chapter 7) is not the same as Jensen’s alpha and should not be used for investment performance evaluation </li></ul>
  24. 24. Analyzing Performance Statistics <ul><li>Mutual funds with the highest average rate of return might not have the highest rank because </li></ul><ul><ul><li>A highly aggressive fund may earn higher returns than a less aggressive fund but the higher returns may not be sufficient to compensate for the extra risk taken </li></ul></ul>
  25. 25. Analyzing Performance Statistics While the Yak Fund earned twice as much as the Zebra Fund it is four times as risky. 0% 4% RFR 5% 15% Zebra Fund 20% 30% Yak Fund Standard Deviation Expected Return Possible Investments
  26. 26. Analyzing Performance Statistics <ul><li>By multiplying Zebra’s low SD by 4, we could create a new portfolio on Zebra’s Asset Allocation Line with the same high SD as Yak Fund </li></ul><ul><li>By borrowing 4 times as much as the initial equity, one could achieve the following E(r Zebra ): </li></ul>
  27. 27. Analyzing Performance Statistics The leveraged Zebra portfolio dominates the Yak Fund; thus Zebra is a better fund even though Yak has a higher average return. Yak RFR 48% 30% 20% 5% Standard Deviation Expected Return, E(r) Zebra Zebra’s SHARPE = 2.2 Yak’s SHARPE = 1.3 15% Yak’s AAL Zebra’s AAL
  28. 28. General Discussion of Performance Measurement Tools <ul><li>When investors analyze merits of alternative investments, usually concerned with </li></ul><ul><ul><li>Asset selection </li></ul></ul><ul><ul><ul><li>Portfolio manager’s ability to select good investments and to not select poor investments </li></ul></ul></ul><ul><ul><ul><ul><li>Sharpe, Treynor & Jensen’s Alpha are good tools to evaluate this issue </li></ul></ul></ul></ul><ul><ul><li>Market timing </li></ul></ul><ul><ul><ul><li>Portfolio manager’s ability to buy low/sell high and manager’s ability to react to changes in market’s direction </li></ul></ul></ul><ul><ul><ul><ul><li>Sharpe, Treynor & Jensen’s Alpha are not good tools for evaluating market timing unless theoretical framework is extended </li></ul></ul></ul></ul>
  29. 29. Evaluating Timing Decisions <ul><li>Treynor & Mazuy included a second-order term in the characteristic line to evaluate market-timing </li></ul>
  30. 30. Evaluating Timing Decisions <ul><li>A successful market timer will </li></ul><ul><ul><li>Shift into high beta securities when bull market begins </li></ul></ul><ul><ul><li>Shift into low beta securities when bear market begins </li></ul></ul><ul><ul><ul><li>If portfolio manager does this, beta 2,investment > 0 </li></ul></ul></ul><ul><ul><ul><li>If portfolio manager cannot outguess market turns, beta 2,investment = 0 (statistically) </li></ul></ul></ul><ul><ul><ul><li>If portfolio manager incorrectly predicts market turns, beta 2,investment < 0 </li></ul></ul></ul>
  31. 31. Do Winners Repeat? <ul><li>Are the best portfolio managers able to repeat their high performance? </li></ul><ul><ul><li>If security markets are perfectly efficient, there should be no consistency in high performance </li></ul></ul><ul><ul><li>When evaluating whether winners repeat, must be careful to not flaw study in terms of survivorship bias </li></ul></ul><ul><ul><ul><li>Market indexes only contain securities that have ‘survived’—not experienced bankruptcy, merger, etc . </li></ul></ul></ul><ul><ul><ul><li>Goetzmann & Ibbotson studied mutual funds </li></ul></ul></ul><ul><ul><ul><ul><li>Mitigated survivorship bias by comparing funds within-sample performances through time </li></ul></ul></ul></ul>
  32. 32. Goetzmann & Ibbotson Study <ul><li>Database </li></ul><ul><ul><li>Monthly total returns of several hundred mutual funds over a 13-year period </li></ul></ul><ul><ul><li>Management fees deducted, but load, exit fees and taxes were not considered </li></ul></ul><ul><ul><li>All cash flows reinvested monthly </li></ul></ul><ul><ul><li>Returns measured over 2-year within-sample period, beginning in 1976 to predict out-of-sample performance for subsequent 2-year period </li></ul></ul><ul><ul><li>Only funds in existence for entire 2-year interval included </li></ul></ul><ul><ul><li>Every mutual fund categorized as ‘winner’ or ‘loser’ based on whether it ranked above or below that 2-year sample’s median return </li></ul></ul>
  33. 33. Goetzmann & Ibbotson Study The combined results show that there is about a 60% chance a winner will be a winner the following period. But, the repeat-winners pattern didn’t persist during this subsample. 327 40.3% 486 59.9% Winners Combined Results Successive Period 71 104 1984-1985 Winners 38 110 1980-1981 Winners 484 59.7% Initial Losers 125 72 1984-1985 Losers 325 40.1% Initial Winners 72 125 1984-1985 Winners Losers 1986-1987 Losers 1986-1987 Winners 95 1982-1983 Losers 63 96 1980-1981 Losers 62 1982-1983 Winners 96 63 1980-1981 Winners 1984-1985 Losers 1982-1983 Losers 1982-1983 Winners 113 1978-1979 Losers 88 50 1976-1977 Losers 41 1978-1979 Winners 54 84 1976-1977 Winners 1980-1981 Losers 1978-1979 Losers 1978-1979 Winners
  34. 34. Goetzmann & Ibbotson Study <ul><li>However, these high-return mutual funds could continue to have high-ranking returns due to high risk, not because they were winners </li></ul><ul><li>G&I replicate study using risk-adjusted returns </li></ul><ul><ul><li>Computed Jensen’s Alpha for each fund </li></ul></ul><ul><ul><li>Classified fund as a winner or loser if fund’s alpha > or < period’s median alpha </li></ul></ul><ul><ul><ul><li>Results show that winners tend to repeat in all 5 subsamples </li></ul></ul></ul><ul><li>Also, divided sample into growth funds and found similar results </li></ul><ul><li>Also, used 1-year subsamples rather than 2-year </li></ul><ul><ul><li>Similar, but weaker, support for the repeat winners hypothesis </li></ul></ul>
  35. 35. Other Studies <ul><li>Malkiel argues that while repeat winners phenomenon existed in 1970s, it was not present during 1980s </li></ul><ul><li>Carhart finds that winning funds tend to have a winning performance the following year, but not afterwards </li></ul><ul><ul><li>Losers have a strong tendency to persist with the worst performers persisting for years </li></ul></ul>
  36. 36. The Bottom Line <ul><li>About mutual fund investments </li></ul><ul><ul><li>Average American buying round lots can afford only about 7 different stocks </li></ul></ul><ul><ul><ul><li>Not enough to minimize diversifiable risk </li></ul></ul></ul><ul><ul><li>Mutual funds are usually able to reduce their diversifiable risk </li></ul></ul><ul><ul><li>Investors can maintain their desired risk-class by mutual fund investing </li></ul></ul><ul><ul><li>Most investors should focus on a mutual fund’s fees and favor funds charging smallest fees </li></ul></ul>
  37. 37. The Bottom Line <ul><li>About Portfolio Performance Measures </li></ul><ul><ul><li>To adequately evaluate a portfolio, must analyze both risk and return </li></ul></ul><ul><ul><li>SHARPE measures risk-premium per unit of total risk </li></ul></ul><ul><ul><li>TREYNOR measures risk-premium per unit of systematic risk </li></ul></ul><ul><ul><li>Jensen’s alpha measures risk-adjusted returns for both portfolios and individual assets </li></ul></ul><ul><ul><ul><li>All three measures tend to rank mutual funds similarly </li></ul></ul></ul><ul><ul><li>Additional tools are available for measuring a manager’s market timing skills </li></ul></ul>