Question

An investor has a quadratic utility function where U = E(R) – ½ A σ2. This...

An investor has a quadratic utility function where

U = E(R) – ½ A σ2. This investor has a coefficient of risk aversion of 2.0.

There are two risky assets and a risk-free asset available to this investor. Asset A has an expected return of 7% and a standard deviation of 16%. Asset B has an expected return of 14% and a standard deviation of 26%. Assets A and B have a correlation of 0.3. Rf is a risk-free investment with a return of 3%. Please answer the following questions:

  1. Would our investor prefer to invest all her money into asset A, asset B, or the risk-free asset (She cannot combine assets for this particular question)? Circle the correct answer (you don’t need to show your work).

A       B       Rf

  1. Find the Mean/Variance Efficient Portfolio (MVE) by combining assets A and B.

Proportion of A _________

Proportion of B _________

Expected Return of MVE ________

Standard Deviation of MVE _________

Slope of the CAL that passes through the MVE ____________

  1. Our investor has $1,000 to invest with us. Our job is to allocate her money among Assets A, B, and Rf so that it maximizes her utility. Short selling and borrowing at Rf are allowed. How much money will be invested in each asset and what level of utility will this give our investor? (Be sure to answer the first three parts in dollars and cents)

Money in A __________                 Money in B ___________

Money in Rf __________                Utility _________

  1. Find the Minimum Variance Portfolio (MVP) by combining assets A and B.

Expected Return of MVP ______________

Standard Deviation of MVP ___________

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Homework Answers

Answer #1

Efficient Portfolio

WA weightage of asset A

WB weightage of asset B

E(Ra) = 7%

E(Rb) = 14%

= (16%)^2 , = (26%)^2 &   = 0.3*16%*26%

Rf = 3%

Substituting these values in the above equation, we get

WA = 36.49% & WB = 63.51%

Portion of A = 36.49%

Portion of B = 63.51%

Expected return = 36.49%*7%+63.51%*14% = 11.45%

s(P) standard deviation of portfolio

s(P)^2 = (36.49%*16%)^2+(63.51%*26%)^2+2*36.49%*63.51%*0.3*16%*26% = 0.0364597

s(P) = 19.09%

Standard deviation = 19.09%

Slope of capital asset line = (11.45%-3%)/19.09% = 0.4423

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