The manager of a large pension fund is planning to invest in equity funds manage
ID: 2817941 • Letter: T
Question
The manager of a large pension fund is planning to invest in equity funds managed by the pension fund’s investment company. To evaluate the funds, the manager regressed five- years of monthly return data for each fund against the returns on the S&P 500 to obtain the following regression parameter estimates:
1.1
1.9
100
2. Value
1.3
0.75
75
3. Growth
1.1
1.25
125
4. Large Cap
0.95
0.90
50
5. Low P/E
0.75
1.75
75
The pension fund’s economic expert forecast an expected return on the S&P 500 of 8% and an expected standard deviation of (RM) = 12.25% or (Variance(RM) = 150). Using the Single-Index Model (where the returns on each fund are related only to the market, i.e., E(r) = + E(RM)), determine the expected returns, variance and standard deviations for each fund. What information is contained in the variance-covariance matrix? How is this information relevant for portfolio formation? Generate a variance-covariance matrix for the five funds presented above. Rank the two asset combinations (best to worst) in terms of portfolio risk reduction. Explain your results.
funds j j Variance () 1. Small Cap1.1
1.9
100
2. Value
1.3
0.75
75
3. Growth
1.1
1.25
125
4. Large Cap
0.95
0.90
50
5. Low P/E
0.75
1.75
75
Explanation / Answer
Statement Showing Expected return,Variance and Sd Funds aj Bj Variance Sd= SQR of Variance E(M) Expected Return ( alpha + Beta( E[M]) Small Cap 0.01 1.90 100.00 10.00 0.08 0.16 Value 0.01 0.75 75.00 8.66 0.08 0.07 Growth 0.01 1.25 125.00 11.18 0.08 0.11 Large Cap 0.01 0.90 50.00 7.07 0.08 0.08 Low PE 0.01 1.75 75.00 8.66 0.08 0.15
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