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

The answer is "
`10\%`".

Step-by-step 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} * \text{Return portfolio)} + \text{(Portfolio weight}* \text{risk-free)}\\\\`

`= (0.5 * 16\%) + (0.5 * 4\%)\\\\= (0.5 * (16)/(100)) + (0.5 * (4)/(100))\\\\= (8)/(100) + (2)/(100)\\\\= (8+2)/(100)\\\\= (10)/(100)\\\\= (1)/(10)\\\\= (1)/(10) * 100\\\\=10\%`