Question

A pension fund manager is considering three investment options. The first is a stock fund, the second is a corporate bond fund, and the third is a T-bill money market fund (the risk-free asset) that yields a sure rate of 5.5%. The probability distributions of the risky funds are:

                                        Expected return (%)           Standard Deviation (%)

Stock fund (S)                          15                                  32

Bond fund (B)                           9                                    23

The correlation between the fund returns is 0.15.

a. What is the portfolio weight for the stock fund in the minimum-risk portfolio?

b.What is the portfolio weight for the stock fund in the optimal risky portfolio?

c. What is the standard deviation of the optimal risky portfolio?

d.What is the Sharpe ratio for the best feasible CAL?

e.Suppose now that you have a risk aversion coefficient A=3 and want to construct a complete portfolio on the best feasible CAL.

f. For the complete portfolio you derived part e, what is the standard deviation of the complete portfolio?

g. For the complete portfolio you derived in part e, what is the proportion invested in the stock fund?

Answer 1

Given:

Expected return(Bonds), E(B) = 9%

Expected return(Stocks), E(S) = 15%

Standard deviation of bonds, (B) = 23%

Standard deviation of stocks, (S) = 32%

, Correlation = 0.15

Answer 1) Min Risk Portfolio is given by:

also, Cov (B,S) = * (S) *(B)

Putting in values,

Wmin(S) = [ (0.23)^2 - 0.15 * 0.23 * 0.32 ] / [ (0.23)^2 +  (0.32)^2 - 2*0.15*0.23*0.32]

Wmin(S) = 0.04876 / 0.13322

Wmin(S) =  31%

Wmin(B) = 69%

Formula to be used

Using this:

Expected Return

Variance

Standard Deviation

10.86%

0.03502633

0.187

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Answer 2)

We will also find the Sharpe Ratio for getting the efficient portfolio

Sharpe Ratio = (Portfolio Return - Risk Free return ) / Portfolio Variance

We will be using excel Solver to Maximize the Sharpe Ratio

Formula used:

Weight of S	59%
Weight of B	41%
Sum of weight	1
Return of portfolio	0.125107967
Variance portfolio	0.044164624
SD	0.210153809
Risk Free Rate	5.5%
Excess Premium	0.070107967
Sharpe Ratio	0.333603122

% in S	% in B	Expected Return	Variance	Standard Deviation
0%	100%	9.00%	0.0529	0.23
20%	80%	10.20%	0.037952	0.195
31%	69%	10.86%	0.03502633	0.187
40%	60%	11.40%	0.035428	0.188
56%	44%	12.36%	0.04235408	0.21
80%	20%	13.80%	0.067652	0.26
100%	0%	15.00%	0.1024	0.32

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