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You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. ________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 9%.

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Answer: 45%

Explanation:

Standard deviation for the portfolio will be a weighted average of the standard deviations of the individual assets.

Risky asset has standard deviation of 20%. Assume the weight is x.

Treasury bills have a standard deviation of 0 as they have no risk. Assume their weight is y.

Target Standard deviation is 9%.

Formula would be:

9% = (x * 20%) + (y * 0%)

20%x = 9%

x = 9% / 20%

x = 45%

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