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