Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a rate of 6%. The probability distribution of the risky funds is as follows:

	Expected Return			Standard Deviation
Stock fund (S)		17	%		38	%
Bond fund (B)		12			17

The correlation between the fund returns is 0.13.

What is the Sharpe ratio of the best feasible CAL? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Sharpe ratio           

Answer 1

Use excel to solve the problem as it needs an optimizer (Solver add-in in excel) to maximize the sharpe ratio.

We need to build a portfolio using risk free asset and a combination of stock fund and bond fund.

We will first build a portfolio of risky assets (Rp) and then add risk free asset (Rf) to it.

Rs = 0.17, Ss = 0.38, Ws = ?

Rb = 0.12, Sb = 0.17, Wb = 1- Ws = ?

correlation co-efficient (Rho) = 0.13

Rp = Ws*Rs + (1-Ws) * Rb

Sp = sqrt [ Ws² * Ss² +(1 - Ws)² * Sb² + 2 * Ws * (1-Ws) * Rho * Ss* Sb]

Then we find the sharpe ratio as (Rp-Rf) / Sp

In order to find the weights use solver to maximize this sharpe ratio. I have added all these values in excel and solved using solve. The two screenshots one with formula and the other with values is copied below:

D F Sigma 0.38 0.17 Correlation 0.13 Weight ER) 0.256844231728643 0.17 1=1-B2 0.12 0.06 2 Stock fund 3 bond fund 4 Risk free 5 6 MVE =B2*C2+B3*C3 1=SQRT(B2^2*D2^2+B3^2*D3^2+2*B2*B3*D2*D3*E2) Maximize C7 using 7 Sharpe Ratio Solver = (C6-C4)/D6

А Sigma 2 Stock fund 3 bond fund 4 Risk free Weight 0.256844232 0.743155768 Correlation 0.38 0.13 0.17 0.12 0.06 5 6 MVE 0.132842 0.169389389 Maximize C7 using Solver 7 Sharpe Ratio 0.430028

Answer: Sharpe ratio is 0.4300