You have 2 asset classes: bond and stock, and 3 mutual funds: fund X, fund Y, and
Question:
You have 2 asset classes: bond and stock, and 3 mutual funds: fund X, fund Y, and fund Z. The return on a mutual fund is modeled by,
The benchmark assigned by your client to you is: 50% in bond and 50% in stock.
You are given the following data:
The variance-covariance Matrix for bond and stock
| Bond | Stock |
Bond | 0.0500 | 0.0001 |
Stock | 0.0001 | 0.0300 |
The expected returns of bond and stock
| Expected return |
Bond | 4.00% |
Stock | 10.00% |
The sensitivities (or loadings) of the funds to bond and stock
| Bond | Stock |
Fund X | 0.5 | 0.5 |
Fund Y | 0.8 | 0.2 |
Fund Z | 0.3 | 0.7 |
The alphas of the funds
| Alphas | Tracking Error |
Fund X | 0.5% | 1% |
Fund Y | 2.0% | 3.0% |
Fund Z | 3.0% | 5.0% |
Suppose that you have a fund of funds portfolio which invests in 50% in fund X, 30% in fund Y, and 20% in fund Z.
Required
a. Compute 2 components in the expected excess return of the fund of funds portfolio.
b. Compute 2 components in the variance of the excess return of the fund of funds portfolio.
c. How are the components in (a) and (b) related in terms of risk-return trade off? Explain.
