Question

Suppose you invest equal amounts in a risky asset with an expected return of 16% and a standard deviation of returns of 18% and a risk-free asset with an interest rate of 4%. Calculate the standard deviation of the returns on the resulting portfolio.

Answer 1

Answer:

The answer is "$10\%$".

Explanation:

You are equivalent investors in 16 percent of a portfolio and 4 percent of a risk-free asset. A weighted mean of these two will become the predicted return.

$= \text{(Portfolio weight} \times \text{Return portfolio)} + \text{(Portfolio weight}\times \text{risk-free)}$

$= (0.5 \times 16\%) + (0.5 \times 4\%)\\\\= (0.5 \times \frac{16}{100}) + (0.5 \times \frac{4}{100})\\\\= \frac{8}{100} + \frac{2}{100}\\\\= \frac{8+2}{100}\\\\= \frac{10}{100}\\\\= \frac{1}{10}\\\\= \frac{1}{10} \times 100\\\\=10\%$