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You invest $2,800 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 13% and a standard deviation of 20% and a Treasury bill with a rate of return of 8%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 12%.

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abdullahfarooqi

Answer:

60% of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 12%.

Explanation:

Let the % of investment in Treasury Bill be X. It is important to note that treasury bill is a risk free investment, hence standard deviation would be 0.

% invested in Risky Asset = 1-X

Expected Standard Deviation = X*Standard Deviation of X + (1-X)*Standard Deviation of Risky Asset

12% = X*0 + (1-X)*20%

12% = 20% - 20%X

X = (20% - 12%)/20% = 40%

% Investment in Risky Asset = 1-40% = 60%

Answer is 60%

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