Alex has money to invest in some combination of four investments (I1, I2, I3, an

Question

Alex has money to invest in some combination of four investments (I1, I2, I3, and I4). There are three scenarios (A, B, and C) that may occur, and each investment will give a different return under each scenario (see below table, where the numbers indicate the percent return under each scenario). The probability of scenario A is 0.35, the probability of scenario B is 0.25, and the probability of scenario C is 0.4.

a) Formulate and solve the Markowitzian mean-variance problem of determining the portfolio which minimizes variance while maintaining an expected return of at least 2.5%.

b) Formulate and solve the Markowitzian mean-variance problem of determining the portfolio which maximizes expected return while maintaining a variance of no more than 30.

A B C 1 12 -3 -1 2 3 1 2 3 8 -1 1 4 5 -1 3

Explanation / Answer

(a)

We use solver to solve this.

Here portfolio return is 2.5% & risk is 2.36% where as weights are:

(b)

for this max portfolio return is 3.05%, risk is 8.1% weights are:

Excel formula:

A B C 0.35 0.25 0.4 expected return from each asset weights for each portfolio 1 12 -3 -1 3.05 0% 2 3 1 2 2.1 33% 3 8 -1 1 2.95 0% 4 5 -1 3 2.7 67% sum= 100% Total return 2.5 %

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