Question

You invest $1,800 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 12% and a standard deviation of 15% and a Treasury bill with a rate of return of 4%. ____ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 9%.

Answer #1

As T-bill is a risk free investment the standard deviation will be
zero.

Standard deviation of the portfolio= X*Standard Deviation of T-bill
+ (1-X)*Standard Deviation of the risky asset

9%= X*0 + (1-X)*15%

=>9%=15%-15%*X

=>9%-15%=-15%*X

=>-6%=-15%*X

=>6%/15%=X

=>X=40.0%

So, the percentage of amount invested in risky asset is
1-40%=60%

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2)
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