Question

Suppose the annual risk-free rate is 1%. The expected annual return on IBM stock and its standard deviation is 5% and 0.25%, respectively. If a portfolio consisting of the risk-free asset and IBM stock yields a 2% annual return, what is the risk of the portfolio as measured by standard deviation?

a. 0.0345%. b. 0.0425%. c. 0.0515%. d. 0.0625%. e. None of the above.

Answer 1

Ans) 0.0625%

Here annual risk free rate of return = 1%

Expected rate of return on IBM Stock = 5%

Expected return on portfolio= 2%

We first need to find weights

So let say proportion of amount invested in risk free asset = W₁ and proportion of amount invested in IBM Stock = (1-W₁)

Thus expected return on portfolio = annual risk free rate of return x W₁ + Expected rate of return on IBM Stock x W₂

2% = (1% x W₁) + (5% x (1-W₁))

2% = 0.01W₁ + (0.05 - 0.05W₁)

0.02 = 0.01W₁ + 0.05 - 0.05W₁

0.04W₁ = 0.03

W₁ = 75%

Thus proportion of amount invested in risk free asset = 75% and  proportion of amount invested in IBM Stock = (1-W₁) = (1-75%) = 25%

Now Standard deviation of portfolio = [W₁² x Standard deviation of risk free asset² + W₂² x Standard deviation of IBM stock² + 2W₁W₂Standard deviation of risk free asset Standard deviation of IBM stock]^0.5

W₁ = 75%

Standard deviation of risk free asset = 0

W₂ = 25%

Standard deviation of IBM stock = 0.25%

Since Standard deviation of risk free asset = 0 whole of 2W₁W₂Standard deviation of risk free asset Standard deviation of IBM stock = 0

Thus Standard deviation of portfolio = [ (0.25)² (0.25)²]^0.5

= [0.0625 x 0.0625]^0.5

= 0.00390625^0.5

= 0.0625 %