Question

Suppose you borrow at the risk-free rate an amount equal to your initial wealth and invest in a portfolio with an expected return of 16% and a standard deviation of returns of 20%. The risk-free asset has an interest rate of 4%. Calculate the expected return on the resulting portfolio.

Answer 1

Answer: 28%

Explanation:

First, we have to make an assumption that the initial wealth is 100, then the weight of the risk free asset will be:

= Amount invested in risk free / Initial wealth

= -100/100

= -1

The weight of the portfolio will be calculated as:

= 1 - weight of risk free asset

= 1-(-1)

= 1 + 1

= 2

Therefore, the expected return on the resulting portfolio will be:

= 2 × 16 + [(-1) × 4]

= 32 - 4

= 28