Question

FB AMZN Expected Return 8.74% 6.09% Standard Deviation 11.62% 9.01% The covariance between FB and AMZN...

FB

AMZN

Expected Return

8.74%

6.09%

Standard Deviation

11.62%

9.01%

The covariance between FB and AMZN is -0.0034. Suppose that you invest 75% in AMZN and 25% in FB to form the optimal risky portfolio. Then you combine the optimal risky portfolio with one risk-free asset (the risk-free rate is 1%) to form the optimal complete portfolio. How much should you invest in the risk-free asset if your risk aversion index is A=5? What is the weight of AMZN in your optimal complete portfolio? Here assume that you can borrow at 1% as well.

114.67%; 75%

-125.40%; 169.05%

-14.67%; 86%

-180.49%; 210.37%
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Answer #1

Given,

risk aversion of the investor (A) = 5

standard deviation of portfolio (Sd) = 5.87%

Weight in the stock (W) = ?

Stock Return(Rm) = 7.16%
Risk free rate (Rf)= 1%

weight of the risky portfolio formula:

W = (Rm - Rf)/A*Sd^2

W = (7.16 - 1)/0.05*(5.87%)^2

W= 357%

The amount to be invested in Amazon is 357*0.594

=212%

Answer is -180.49%; 210.37%

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