Question

Consider the data in the table below and answer the following questions: Utility Score Portfolio L Utility Score Portfolio M Utility Score Portfolio H Investor Risk Aversion (A) Er) =.07: =.05 E(r)=.09: O= E(r)= 13: o = 2 13-4x2x.22 =.0900 107 _x2x.052 = .0675.09–5x2x. P = 0800 <3<.05º =.0663.00 – £x3x8 =.0750 13-_x3x.2° = 0700 2X4x.052 - 0650.09 -->x4x. 1° = -0700 13x4x.22 - 0500 1. The three risk aversion coefficients in the first column represent investors X, Y and Z. Which risky portfolio maximizes the utility of each investor? Give an explanation for your answer. Assume now that all the three risky portfolios L, M, H are uncorrelated (correlation is zero). In such situation, the variance of a portfolio is given by the following formula: W,2* 0,2 + W22* 02? + W,2* 032 2. Find the utility of each investor for an investment in a portfolio that holds L, M and H in equal proportion.

Answer 1

As there are multiple sub-parts, as HOMEWORKLIB's guideline only first 4 sub-parts are answered below:

1.Investor's utility = E(R) - 1/2 * A * . This formula deducts risk from expected return by applying a risk aversion factor to the risk. Since we reduce risk from expected return, we get risk free rate.for the investor.

Most preferred portfolio for investor X is H, for investor Y is M and for investor Z is M because the utility is the highest.

2. First we need to find the equal weighted portfolio's expected return and standard deviation

Portfolio = 1/3rd invested in L. H and M

E(R) = 1/3 * 0.07 + 1/3 * 0.09 + 1/3 * 0.13 = 0.0967

Standard deviation =  

= sqrt((1/3)²*0.05² + (1/3)²*0.1² + (1/3)²*0.2²) = 0.07638

Now, we will find the investor's utility using the formula E(R) - 1/2 * A * .

Investor X: U = 0.0967-1/2*2*0.07638 = 0.02032

Investor Y: U = 0.0967-1/2*3*0.07638 = -0.01787

Investor Z: U = 0.0967-1/2*4*0.07638 = -0.05606

Part 3: The question is misleading. Instead of investors will have separate utility for each of the portfolio (which it actually is), the question may have been investors will have separate risk aversion co-efficient.

Otherwise the answer is the same as part 2.

Part 4: Since the answer is same one cannot comment on the question as to why they are different.