Annual total returns for nine years are shown below for eight mutual funds. Char

Question

Annual total returns for nine years are shown below for eight mutual funds. Characteristic lines are calculated using annual market returns. The ex post values are as follows: Fund (1) Rp (%) (2) p (%) (3) p (4) p (5) R2 A 17.0 20.0 7.53 0.88 0.82 B 19.0 17.8 11.70 0.65 0.57 C 12.3 25.0 3.12 0.83 0.47 D 20.0 24.5 9.00 1.00 0.72 E 15.0 17.4 6.15 0.79 0.88 F 19.0 18.0 10.11 0.83 0.89 G 8.6 19.0 1.37 0.91 0.95 H 20.0 21.5 9.52 0.93 0.78 where Rp p mean annual total return for each fund standard deviation of the annual yields the intercept of the characte p ristic line the slope p Using an 8.6 percent riskfree return, a. Calculate Sharpe’s measure for each of these eight funds and rank the eight funds from high to low performance. b. Calculate Treynor’s measure for each fund and perform the same ranking as in part a. c. Use the R2 in column 5 to comment on the degree of diversification of the eight mutual funds. Which fund appears to be the most highly diversified? Which fund appears to be the least diversified? Jones, Charles P.; Jensen, Gerald R.. Investments: Analysis and Management, 13th Edition (Page 600). Wiley. Kindle Edition.

Explanation / Answer

Part - A

Sharp Index = Return - Risk Free Return/ Standard Deviation

Part - 2

Treyner's Ratio =Return - Risk Free Return/Beta

Part - C

1. Fund B is Return 0.57 but alpha showing 11.70,Since Fund B mostly highly diversified

2.Fund G is Highest Return 0.95 but alpha is negative (i.e -1.37),Since Least diversified

Particulars Calculation Index Rank A 17-8.6/20 0.42 5 B 19-8.6/17.8 0.5843 1 C 12.3-8.6/25 0.148 7 D 20-8.6/24.5 0.4653 4 E 15-8.6/17.4 0.3678 6 F 19-8.6/18 0.5778 2 G 8.6-8.6/19 0 8 H 20-8.6/21.5 0.5302 3

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