You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045.
-What percentages of your money must be invested in the risk-free asset and the risky asset,respectively,to form a portfolio with a standard deviation of 0.08?
A)301% and 69.9%
B)50.5% and 49.50%
C)60.0% and 40.0%
D)61.9% and 38.1%
E)cannot be determined

Question

Quizplus · Accepted Answer

Let x be the percentage invested in the risky asset, then (1-x) must be the percentage invested in the risk-free asset. 
Using the formula for portfolio standard deviation, we have:

0.08 = (0.21x)^2 + (0.045(1-x))^2 + 2(0.21)(0.045)(1-x)x

Solving for x, we get x = 0.381 or 38.1%, which means (1-x) = 0.619 or 61.9%. Therefore, the best choice is D.

You Invest $100 in a Risky Asset with an Expected