Treynor-Black Model Portfolio Construction Using the Single Index Model (BKM 12th edition Ch 8 Problem #17 &18) Micro Forecasts Asset Expected Return (%) Beta (against the benchmark, M) Residual Stdev (%) Stock a 20 1.3 58 Stock b 18 1.8 71 Stock c 17 0.7 60 Stock d 12 1.0 55 Macro Forecasts Asset Expected Return (%) Standard Deviation (%) T-bills 8 0 Passive equity portfolio 16 23 Calculate expected excess returns, alpha values, and residual variances for these stocks. Alphas, Expected excess return (dont worry about) i = ri [rf + i (rM rf)] E(ri) - rf a = .20 [.08+1.3(.16-.08)] = .016 under .20 .08 = .12 b = .18 [.08 +1.8(.16-.08)] = .044 over .18 .08 = .10 c = .17 [.08 +.7(.16-.08)] = 0.034 under .17 .08 = .09 d = 0.12 [.08 +1 (1.16 - .08)] = -0.04 .12 .08 = .04 Stocks a and c have positive alphas, whereas stocks b and d have negative alphas. The residual variances are: recommend to use decimals! 2(ea) = .3364 2(eb) = .5041 2(ec) = __.3600_ 2(ed) = _.3025___ Construct the optimal risky portfolio. To construct the optimal risky portfolio, we first need to determine the active portfolio. Using the Treynor-Black technique, we construct the active portfolio. a .0476 .0476/-.0775 = .6142 b .0873 -.0873/-.0775 = 1.1265 c 0.0994 .0944/-.0755 = -1.2181 d -0.1322 -.1322/ -0.0755 = 1.17058 Total .0775 1.0000