You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05.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 0.06?
A) 30% and 70%
B) 50% and 50%
C) 60% and 40%
D) 40% and 60%
E) cannot be determined

Question

Quizplus · Accepted Answer

Let X be the portion invested in the risky asset, and (1-X) be the portion invested in the risk-free asset.

The formula for the standard deviation of a portfolio is:

σP = XσR + (1-X)σF

where σR is the standard deviation of the risky asset, σF is the standard deviation of the risk-free asset (which is 0), and σP is the desired standard deviation of the portfolio.

Plugging in the values:

0.06 = X(0.15) + (1-X)(0)

Simplifying:

0.06 = 0.15X 
X = 0.4

So you should invest 40% in the risky asset and 60% in the risk-free asset.

You Invest $100 in a Risky Asset with an Expected