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?

Question

Quizplus · Accepted Answer

Let x be the percentage invested in the risky asset and (1-x) be the percentage invested in the risk-free asset.

To find the portfolio's standard deviation, we use the formula:

σp = sqrt(x^2σ^2 + 2xrρσT + (1-x)^2σT^2)

where 
σ = standard deviation of the risky asset 
σT = standard deviation of the risk-free asset 
ρ = correlation between the two assets 
r = expected rate of return of the risky asset (also equal to the portfolio's expected rate of return)

We know σp = 0.08, σ = 0.21, and σT = 0.

We can solve for x using the formula:

x = (σp^2 - (1-x)^2σT^2) / (2rρσ)

Substituting the given values, we get:

x = (0.08^2 - (1-x)^2(0)^2) / (2(0.11)(0.21)) 
x = 0.381 or 38.1%

Therefore, the answer is D: 61.9% and 38.1%.

You Invest $100 in a Risky Asset with an Expected