Question

i've calculate the w1 for section a which is, w1=[(sd2)^2-sd1sd2p]/[sd1^2+sd2^2-2sd1sd2p], so now i wanna know the weights for section b, thx!

3. Two risky assets with returns r1, r2 and standard deviations 01, 02, and correlation p. Calculate the weights for the following two optimal portfolios. a. Minimum volatility (variance) portfolio minimizes the overall risk min on s.t. W1 + W2 = 1 w b. Maximum Sharpe Ratio portfolio delivers the highest expected return of unit of risk max Tip -ri w Op s.t. W1 + W2 = 1

Answer 1

b.

Optimal portfolio has Maximum Sharpe Ratio. We can compute the weights of optimal portfolio or Maximum sharpe ratio portfolio wih following equation:

(ri - rf) * o - (r2 - rf) * P1,2 * 01 * 02 (ri - rp) * o£ + (r2 - rp) * o - [(r1 - rp) +(r2 - rp)]**p1,2 * 01 * 02

where,

r1 = Return of Asset-1

r2 = Return of Asset -2

rf = risk free return

$\rho _{1,2}$ = Correlation between Asset-1 and Asset-2

$\sigma$ = Standard deviation

And,

W2 = (1 - 1)

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.