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.

R = a + bRbond, + bR stock! + E