Question

Stocks A and B have the expected returns and standard deviations shown in the table below: Asset E(R) Std. deviation A 15% 30% B 20% 50% The correlation between A and B is 0.6. The risk-free rate is 3% and you have a risk-aversion parameter of 2. What is the proportion of your investment in A and B, respectively, in your optimal risky portoflio? A. 25.0% in A ; 75.0% in B B. 76.6% in A; 23,4% in B C. 20.0% in A; 80.0% in B D. 80.0% in A; 20.0% in B E. 62.5% in A; 37.5% in B

Answer 1

The correct answer is option D. i.e. 80.0% in A; 20.0% in B

Weight in asset A = (Ra-Rf) x (SDb)2 - (Rb-Rf) x cov(a,b)

                                       (Ra-Rf) x SDb2 +(Rb-Rf) x (SDa)2- {[(Ra-Rf)+(Rb-Rf)]X cov(a,b)]}

Where Ra = Return on asset A i.e. 15%

Rb = Return on asset B i.e. 30%

Rf = Risk free security i.e. 3%

SDa= Standard Deviation of asset A i.e. 20%

SDb= Standard Deviation of asset B i.e. 50%

Cov(a,b) = correlation (a,b) x SDa x SDb i.e. 0.6 x .20 x .50 = 0.06

Weight in asset A = (0.15-0.03) x (0.50)2 - (0.30-.03) x 0.06

                                (0.15-0.03) x (0.50)2 + (0.30-.03)x (.20)2- {[ (0.15-0.03) +(0.30-.03)]X 0.06]}

Weight in asset A = 0.03-0.0162

                                  0.03 +0.0108 – 0.0234

Weight in asset A = 0.0138/ 0.0174 = 80% (rounded off)

Weight in asset B = 100%-80% = 20%

Therefore, The correct answer is option D. i.e. 80.0% in A; 20.0% in B

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