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

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

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,

$( R_{t}=alpha+b_{1} R_{text {bond }, t}+b_{2} R_{text {stock }, t}+varepsilon_{t} )$

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

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