Question

Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 7%, and the market's average return was 13%. Performance is measured using an index model regression on excess returns. Index model regression estimates R-square Residual standard deviation, o(e) Standard deviation of excess returns Stock A 1% + 1.2 (rm -rf) 0.629 11.2% 22.5% Stock B 2% + 0.8(rm -rf) 0.463 20% 26.7% a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.) StockA Stock B % i. Alpha Information ratio iii. Sharpe ratio iv. Treynor measure b. Which stock is the best choice under the following circumstances? i. This is the only risky asset to be held by the investor. This stock will be mixed with the rest of the investor's portfolio, currently composed solely of holdings in the market-index fund. iii. This is one of many stocks that the investor is analyzing to form an actively managed stock portfolio.

Answer 1

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L O Ax B 11:07 E. ENG 22-03-2020 E21 ... O X HA481 X ✓ fic GR GS GT GU - GV GW GG GY GZ HA 458 а Rm = 13%, Rf = 7% return on stock Rp - Rf 1% + 1.2(Rm-Rf) 1% + 1.2(13%-7%) 8.20% 2% + 0.8 (Rm-Rf) 2% + 0.8 (13%-7%) 6.80% SO APLHA 1.0000% 2.0000% 459 460 461 462 463 464 465 466 467 468 469 470 471 INFORMATION RATIO (alpha/residual sd) 0.0893 1%/11.2% 0.1000 2%/20% SHARPE RATIO (Rp - Rf)/SD(excess returns) 0.3644 8.20%/22.5% 0.2547 6.80%/26.7% 472 iv 8.5000 TREYNOR RATIO (Rp - Rf)/BETA 6.8333 8.2/1.2 6.8/0.8 473 474 475 476 477 478 479 480 481 (i) (ii) if this is the only risky asset, use sharpe measure, it is higher for A portfolio mixed with index fund, use appraisal ratio (information ratio), it is higher for B, one of the many portfolios, use treynor ratio, it is higher for B Ciii ... UTILITY, SHARPE, beta coNvexity DGM beta port future INDEX INTL CAP BUD SANDRINE LEASING PORTFOLO Q DIR right cleanYIELD bond portfolio ... + : IN