Question

You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 29%. The T-bill rate is 8%. Your client chooses to invest 65% of a portfolio in your fund and 35% in an essentially risk-free money market fund. What is the expected return and standard deviation of the rate of return on his portfolio? (Do not round intermediate calculations. Round "Standard deviation" to 1 decimal place.)

Answer 1

Answer:

13.85% and 18.9%

Explanation:

As in this exercise we have a free risk asset we will assume that the t-bill has a standard deviation of 0%, so let´s firts calculate the expected return:

$E(r)=r_{1}*w_{1} +r_{2}*w_{2} +....+r_{n}*w_{n}$

where E(r) is the expected return, $r_{i}$ is the return of the i asset and $w_{i}$ is the investment in i asset, so applying to this particular case we have:

$E(r)=17\%*65\%+8\%*35\%$

$E(r)=13.85\%$

the calculation of standar deviation follows the same logic of the previous formula:

$Sigma(r)=29\%*65\%+0\%*35\%$

$Sigma(r)=18.9\%$