Answer:
Corer = 0.15, Cave = 0.15 × 0.32 × 0.23 = 0.01104
Compute risk premium, R1 = 15 — 5 = 10%; R2 = 9 — 5 = 4%; and R1 +R2 = 14%
Following weights distribution for optimal Sharpe ratio
WI = (0.10 × 0.23^2 — 0.04 × 0.01104) / (0.10 × 0.23^2 + 0.04 × 0.32^2 — 0.14 × 0.01104)
WI = 0.6184, W2= 1 - 0.6184 = 0.3816
Return on risky portfolio = 0.6184 × 0.15 + 0.3816 × 0.09 = 0.1271 or 12.71%
Variance of risky portfolio = 0.6184^2 × 0.32^2 + 0.3816^2 × 0.23^2 + 2 × 0.6184 × 0.3816 × 0.01104
Variance of risky portfolio = 0.052073353 = (0.228195864) ^2
SD of risky portfolio = 0.2282 or 22.82%
Sharpe ratio = (0.1271— 0.05) / 0.2282 = 033786
Given, return on complete portfolio is 10% and compute distribution of $2,000.
Suppose, y is invested in optimal risky portfolio and 1 — y is invested in risk-free asset.
Weight of investment in risk-free asset I — y
Weight of investment in asset 1: yW1
Weight of investment in asset 2: yW2
Return on complete portfolio = 0.05 × (1 — y) + y × 0.1271 = 0.10
y = (0.10 — 0.05) / (0.1271 — 0.05) = 0.6485; and I — y = 0.3515
Weight of investment in risk-free asset: I — y = 0.3515
Weight of investment in asset 1: yW1 = 0.6485 × 0.6184 = 0.4010
Weight of investment in asset 2: yW2 = 0.6485 × 0.3816 = 0.2475
Now, distribution of $2000 as below
For risk-free asset: 0.3515.2000 = $703
For asset 1: 0.4010.2000 = $802
For asset 2: 0.2475.2000 = $495
