[ Questions 8-9] Consider the following three assets . Asset A\'s expected retur

Question

[ Questions 8-9] Consider the following three assets . Asset A's expected return is 5% and return standard deviation is 25%. Asset B's expected return is 8% and return standard deviation is 32%. Asset C is a risk-free asset with 2% return. The correlation between assets A and B is 0.3 8. Constructing a portfolio from assets A and B such that the expected return of the portfolio equals 7%, find the portfolio weights of assets A and B and compute the return standard deviation of the portfolio 9. Constructing a portfolio from assets A and C such that the expected return of the portfolio equals 2.5%, find the portfolio weights of assets A and C and compute the return standard deviation of the portfolio.

Explanation / Answer

8. for Expected return pn portfolio = 7% the equation is

E(Rp) = WA * RA + (1-WA ) * RB = So from here we get WA = 0.33 & WB = 0.67

Portfolio St dev = [w2A*?2(RA) + w2B*?2(RB) + 2*(wA)*(wB)*Cov(RA, RB)]^1/2. Now as we are given the correlation betwenn A &B so we need to replace Cov with Corr.

Corr(A,B) = Cov(A,B) / (?A * ?B)

Now using these formulae we get portfolio std dev = 20.53%.

9. now similarly for the portfolio of assets A and C. we get  WA = 0.167 and WC = 0.833

here now the std dev for the risk free asset = 0 hence the Cov term = 0 So the std dev for this portfolio is only based on the weight of the Asset A.

std dev = 4.175%

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