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 portfolio Rp = 15%

Target return E(r) = 25%

let weight of investment in Market portfolio be w, then weight in risk free asset is (1-w)\

So, expected return of target portfolio is weighted average return on its assets

=> E(r) = w*Rp + (1-w)*Rf

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

=> 25 = 15w +6 - 6w

=> w = 19/9 = 2.1111 or 211.11%

So, weight in risk free asset = 1-w = 1 - 2.1111 = -1.1111 or -111.11%

its weight is negative as it is borrowing.

So, total amount borrowed at risk free rate = -111.11% of 1.5 million = -1666666.67

this investor would need to borrow $1666666.67 at the risk-free rate