Question

Suppose that the borrowing rate that your client faces is 9%. Assume that the S&P 500 index has an expected return of 14% and standard deviation of 21%. Also assume that the risk-free rate is r_f = 6%. Your fund manages a risky portfolio, with the following details: E(r_p) = 11%, σ_p = 17%.

What is the largest percentage fee that a client who currently is lending (y < 1) will be willing to pay to invest in your fund? What about a client who is borrowing (y > 1)?

y<1= ____%

y>1=_____%

Answer 1

Sharpe Ratio: How well an investment used risk to get return

=Effective return/ Standard deviation

Where effective return=(Expected portfolio return (E(r) -Risk Free Rate (Rf) - Lending Fee)

Case 1: For Lenders: Y<1, Risk free return = 6% & We will find fee as follows

(14-6)/21 = (11-6- Fee)/17

--- Fee= 1.47%

Case 2: For Borrower: Y>1, the borrowing rate i.e. 10% is the risk free return. We Will notice that even without the fee, the fund is inferior to the passive fund, since:

= (11-9)/21 = 0.095

& 0.095< (14-9)/21

i.e. 0.095<0.24