FORD APPLE GENERAL ELECTRIC MICROSOFT NIKE Risk-free return

E(ri)Daily 0.03% 0.04% 0.03% 0.02% 0.03% 0.01% E(ri) 8.29% 11.37% 7.55% 6.11% 6.71% 2.00% E(ri) - rf 6.29% 9.37% 5.55% 4.11% 4.71% Var(ri)Daily 0.001138 0.001160 0.000567 0.000370 0.000410 Var(ri) 0.287 0.292 0.143 0.093 0.103 i 0.5356 0.5406 0.3781 0.3052 0.3214 Sharpe ratio, Si 0.117 0.173 0.147 0.135 0.147 Portfolio lab

wFORD rFORD wAPPLE rAPPLE wGE rGE wMICROSOFT rMICROSOFT wNIKE rNIKE Weight 9.37% 32.24% 14.54% 11.86% 31.99% wFORD rFORD 9.37% 0.00252 0.00432 0.00127 0.00076 0.00192 wAPPLE rAPPLE 32.24% 0.00432 0.03038 0.00644 0.00391 0.01020 wGE rGE 14.54% 0.00127 0.00644 0.00302 0.00105 0.00298 wMICROSOFT rMICROSOFT 11.86% 0.00076 0.00391 0.00105 0.00131 0.00187 wNIKE rNIKE 31.99% 0.00192 0.01020 0.00298 0.00187 0.01057

wFORD wAPPLE wGE wMICROSOFT wNIKE Portfolio weights 9.37% 32.24% 14.54% 11.86% 31.99% E(rP) 8.4116814861015200% Var(rP) 0.117

(rP) 0.3424180076280860000

0 Sharpe ratio, SP 18.72%

Minimum variance portfolios

E(rP) FORD APPLE GENERAL ELECTRIC MICROSOFT NIKE (rP) 3% 0.004 -73.40% 30.49% 91.81% 50.71% 0.321 5% 3.71% -34.36% 24.59% 62.26% 43.79% 25.59% 7% 7.03% 4.68% 18.70% 32.71% 36.87% 27.95% 9% 10.34% 43.73% 12.80% 3.17% 29.96% 37.54% 11% 13.66% 82.77% 6.91% -26.38% 23.04% 50.39% 13% 16.98% 121.81% 1.01% -55.93% 16.13% 64.58%

Optimal risky portfolio

FORD APPLE GENERAL ELECTRIC MICROSOFT NIKE Portfolio weight 9.37% 32.24% 14.54% 11.86% 31.99% E(rP*) 8.41% Var(rP*) 0.117 (rP*) 34.24% Sharpe ratio, SP* 0.187

Optimal complete portfolio A 2 Analytical solution Numerical solution

y* 0.27 0.27

E(rP) 3.7530757885223400% 3.75307578637104

00% (rP) 9.36% 9.36% U 0.0288 0.0288

0.00% 2.00% 4.00% 6.00% 8.00% 10.00%

12.00% 14.00% 16.00%

0% 10% 20% 30% 40% 50% 60% 70% 80%

E(r)

Ef'icient frontier

E(rApple) 0.04%

Student ID 1:

E(rGE)Annual 7.55%

Student ID 2: (E(rMicrosoft) - rf)Annual 4.11%

Student ID 3:

Var(rFord) 0.001138

Name 1: Var(rNike)Annual 0.103

Name 2:

AppleAnnual 54.06%

Name 3:

Sharpe ratio, Smicrosoft 0.135

Members: 0

3% MV Portfolio, wFord 0.40% 5% MV Portfolio, wApple -34.36% 7% MV Portfolio, wGE 18.70% 9% MV Portfolio, wMicrosoft 3.17% 11% MV Portfolio, wNike 23.04% 13% MV Portfolio, 64.58%

Optimal Risky Portfolio, wFord 9.37%

E(rP*) 8.41% Var(rP*) 0.117 (rP*) 34.24% SP* 0.187

y* (analytical) 0.27 Utility (numerical) 2.88%