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:
|
Funds
|
αj
|
βj
|
V(ε)
|
|
1. Small Cap
|
1.1
|
1.9
|
100
|
|
2. Value
|
1.3
|
0.75
|
75
|
|
3. Growth
|
1.1
|
1.25
|
125
|
|
4. Large Cap
|
0.95
|
0.9
|
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 s(RM) = 12.25% (V(RM) = 150).
A) Using the Single-Index model (where the returns on each fund are related only to the market), determine the expected returns and standard deviations for each fund.
B) Generate a variance-covariance matrix for the five funds