Question

Suppose that the risk-free rate is 6 percent and the expected return on the market portfolio is 15 percent. An investor with $1.5 million to invest wants to achieve a 25 percent return on a portfolio combining the risk-free asset and the market portfolio. Calculate how much this investor would need to borrow at the risk-free rate in order to establish this target expected return. Provide your final answers up to two decimal points

Answer 1

Given that,

risk free rate Rf = 6%

Expected return on market portfolio Rm = 15%

An investor with $1.5 million to invest wants to achieve a 25 percent return on a portfolio combining the risk-free asset and the market portfolio.

Let weight of risk free asset be W, then weight of market portfolio is (1-W)

So, expected return on the portfolio is W*Rf + (1-W)*Rm

=> 25 = 6W + 15*(1-W)

=> W = -1.1111 or -111.11%

weight of risk free asset is -111.11%

So, Investor need to borrow 111.11% of amount available to invest

=> Amount borrowed = 111.11% of 1.5 = $1.67 million