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

Suppose the percentage of the investment in T-bill be X, so the percentage of the amount invested in risky asset =1-X
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%