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%.
A) 100%
B) 90%
C) 45%
D) 10%

Question

Quizplus · Accepted Answer

We can use the formula for the standard deviation of a portfolio consisting of a risky asset and a risk-free asset (treasury bill):

σ_p = w_r * σ_r

where σ_p is the standard deviation of the complete portfolio, w_r is the weight of the risky asset in the portfolio, and σ_r is the standard deviation of the risky asset. Solving for w_r, we get:

w_r = σ_p / σ_r = 9% / 20% = 0.45 = 45%

Therefore, 45% of the complete portfolio should be invested in the risky asset, and the remaining 55% should be invested in the treasury bill. This will result in a complete portfolio with a standard deviation of 9%.

You Invest $1,000 in a Complete Portfolio