1. Investments Chapter 22: Performance Evaluation

6. Scrutinizing Mutual Funds Goal Statements Portfolio’s SDs and Betas were better indicators of portfolio’s actual performance than their goal statements. There are some funds which claim they are growth funds, but get lower return than income funds. # of funds claiming each goal Category’s average rate of return Beta Growth Growth & income Income & Growth Income, Growth & Stability Growth Growth & income Income & Growth Income, Growth & Stability 0.5 to 0.7 3 5 4 16 6.9% 10.1% 9.7% 9.1% 0.7 to 0.9 15 24 7 7 11.2% 10.0% 10.0% 12.2% 0.9 to 1.1 20 1 None 1 13.8% 9.5% None 13.5% Risk Class Range of Betas # of funds Average Beta Average Variance Average Rate of Return Low 0.5 to 0.7 28 0.619 0.000877 9.1% Medium 0.7 to 0.9 53 0.786 0.001543 10.6% High 0.9 to 1.1 22 0.992 0.002304 13.5%

11. Performance Example (Francis & Ibbotson) 12/27/09 Year Avon Blair Market 1 10.0 10.0 10.0 2 30.0 40.0 30.0 3 -20.0 -20.0 -20.0 4 -10.0 -10.0 -10.0 5 20.0 40.0 20.0 6 10.0 20.0 30.0 7 0.0 -20.0 -10.0 8 30.0 20.0 20.0 9 -10.0 10.0 0.0 10 20.0 40.0 30.0 R 8.0 13.0 10.0  16.6 22.4 17.9  0.8125 1.156 1

13. SHARPE Example 12/27/09 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

38. Analyzing Performance Statistics While the Yak Fund earned twice as much as the Zebra Fund it is four times as risky. Possible Investments Expected Return Standard Deviation Yak Fund 30% 20% Zebra Fund 15% 5% RFR 4% 0%

41. 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. Perhaps both Treynor and Jensen would give the same ranking in this case 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

47. 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. 1978-1979 Winners 1978-1979 Losers 1980-1981 Winners 1980-1981 Losers 1976-1977 Winners 84 54 1978-1979 Winners 110 41 1976-1977 Losers 50 88 1978-1979 Losers 38 113 1982-1983 Winners 1982-1983 Losers 1984-1985 Winners 1984-1985 Losers 1980-1981 Winners 63 96 1982-1983 Winners 104 62 1980-1981 Losers 96 63 1982-1983 Losers 71 95 Combined Results Successive Period 1986-1987 Winners 1986-1987 Losers Winners Losers 1984-1985 Winners 125 72 Initial Winners 486 59.9% 325 40.1% 1984-1985 Losers 72 125 Initial Losers 327 40.3% 484 59.7%