Question

You manage an equity fund with an expected risk premium of 11.4% and a standard deviation of 28%. The rate on Treasury bills is 5.2%. Your client chooses to invest $50,000 of her portfolio in your equity fund and $150,000 in a T-bill money market fund. What is the expected return and standard deviation of return on your client’s portfolio? (Round your answers to 2 decimal places.)

Answer 1

Answer:

The Expected return of the Portfolio is 8.05% and the standard deviation is 7%

Explanation:

The computation is shown below:

Given that

T-bill rate or risk-free rate = 5.20%

The Expected Risk premium of fund = 11.40%

As we know that

Expected Return of Equity = Risk premium + Risk free rate

= 11.4%+5.2%

= 16.60%

Now  

Weight of equity fund is

= $50,000 ÷ ($50,000 + $150,000)

= 0.25

And,  

Weight of T-bills is

= $150,000 ÷ ($50,000 + $150,000)

= 0.75

Also the correlation between risk free and the fund would always be zero  

The Standard deviation of Equity fund= 28%

ANd, the Standard deviation of T-bills= 0

Now

Expected return Portfolio = (weight of fund × expected return) + (weight of risk free × rate of return)

= (0.25 × 16.60%) + (0.75 × 5.2%)

= 8.05%

And,

The standard deviation of the portfolio (σp) is

= √(wA × standard deviation of A )^2 + (wB × standard deviation of B ) ^2 + (2 × wA × wB × standard deviation of A  ×standard deviation of A ×  rBM)

= √((0.25 × 28%)^2 + (0.75 × 0%)^2 + (2 × 0.25 × 0.75 × 28% × 0% × 0))

= 7.00%

Hence, the Expected return of the Portfolio is 8.05% and the standard deviation is 7%