Question

4. Asset Allocation (20%) Define mean/variance asset allocation optimization Include an objective function and two constraints in your answer (either in words or equations, both is better). An illustration is needed. b) Intuition is the key ingredient to answering this question effectively. If the expected return on stocks is 10% and the expected return on bonds is 5%, propose specific feasible portfolio weights (one set of two reasonable, defensible weights that total to 100%) of the two asset classes and explain why you proposed them. Be sure to utilize mean variance concepts, the stated expected returns and what you know about stock & bond risk. Bond Weight: Stock Weight: Why?

Answer 1

Answer:

4. Asset Allocation :

Mean/ Variance asset allocation optimization:

Mean median value of the expected return of asset and Variance means the deviation of mean from the expected return of the asset

When we optimize the mean/ Variance asset allocation then in this case we make a mix of investment in the assets of the portfolio in such a way that we will get maximum return from the portfolio assets.

Here it also noted that it depends on the expected return of the investor.

Objective function :

Objective function be denoted as optimum return from the portfolio asset mix

For example if there are Four assets in the portfolio with returns as follows:

Stock 1:A : 10% , Stock 2: B : 12% , Fixed deposit: C : 7.5% , Bonds : D : 4%

Here A , B ,C , D are the values to be invested in assets in portfolio

then Objective function be :

Maximize Z = 10% A + 12% B + 7.5% C + 4% D

Constraints :

These are the limitations to the objective function

Examples :

1. Minimum Investment Function

Investment in Stock 1 be 40% of Total Investment

we denoted this as

40% A $\geq$ A+B+C+D

2. Total expected return is not less than 8%

we denoted this as :

10% A + 12% B + 7.5% C + 4% D $\geq$ 8%

3. Non negative Constraint

A $\geq$ 0 , B $\geq$ 0, C $\geq$ 0 , D $\geq$ 0

b) If the expected return on stocks is 10% and bonds is 5%. propose specific feasible portfolio weights ( one set of two reasonable , defensible weights that total to 100% ) of the two asset classes and explain why you proposed them. Be sure to utilize mean variance concepts, the stated expected returns and what you know about stock & bond risk.

Bond Weight: _( Investment in Bond / Total Investment ), Stock Weight : _( Investment in Stock / Total Investment )

We want most highest return from Portfolio investment from their optimal Investment mix :

Let Stock return weight be X , Bond Weight 5% be Y

Weight will be decided on the total investment and individual share of investment in each asset of Portfolio.

It will be calculated as follows :

= Investment in individual Asset / Total Investment

Therefore optimal return will be calculated as follows:

= Sum of ( Weight of asset X return on Asset ) of all asset in portfolio

Reasons :