Question

As an individual investor, you have three funds to invest into. The first is an equity fund, the second is a corporate bond fund, and the third is a T-bill money-market fund (your risk-free asset). Assume your personal risk aversion is 0.06 (A=0.06). The correlation between the equity fund and the bond fund returns is 0.1.

Fund	Expected return	Risk
Equity fund	16%	38%
Corporate bond fund	7%	25%
T-bill money market fund	3%

1. Find weights of the equity and corporate bond funds in the minimum variance portfolio.

2.Using weights calculated in Question 1, compute the expected return (E[r]) and the risk (standard deviation) of the minimum variance portfolio.

3.Find weights of the equity and corporate bond funds in the optimal portfolio.

4.Using weights calculated in Question 3, find the expected return (E[r]) and risk (standard deviation) of the optimal portfolio.

5.Compute the slope of the Capital allocation line (CAL) using the optimal portfolio from questions 3 and 4 as your risky portfolio.

6.Using your personal risk aversion (A=0.06) and the optimal portfolio as the risky portfolio, find the weights of the optimal portfolio and of the risk-free asset in the complete portfolio.

7.Using weights calculated in Question 6, compute the expected return (E[r]) and the risk (standard deviation) of your complete portfolio.

8.Calculate weight of the equity and corporate bond fund in the complete portfolio calculated in Questions 6 and 7.

Answer 1

Here, the correlation () is 0.1

E(r) equity = 16%

E(r) debt = 7%

risk () Debt = 25% and Equity = 38%

we can find COV(D,E) = = 0.1 x 25 x 38 = 95

1) Weights of minimum variance portfolio :

=

= 1349/1879 = 0.72 (approx)

= 1 - 0.72 = 0.28

2) Expected return :

= 0.72 X 7% + 0.28 X 16% = 9.52%

Expected Risk :

3) Weights in optimal risky portfolio:

= 1 - 0.37 = 0.63

4) Expected Return and Risk :

Formulas will be same as in question 2

E(r) = (0.63X16 + 0.37X7) = 12.67%

5) slope of the CAL :

= 12.67 - 3/26.51 = 0.365 ( approx)

6) Now as our optimal portfolio risk and return is 26.51% and 12.67% respectively. and Risk free rate is 3% with Aversion (A) = 0.06

so the weight in risky optimal portfolio will be :

So we will invest approx 23% in optimal risky asset and 77% in risk free asset

7) Expected return of complete portfolio will be = 3 + [ 0.23 X (12.67 - 3)] = 5.2241 (approx)

Risk of the complete portfolio will be = 0.23 X 26.51 = 6.09%

8) Weight of equity and bond and risk free in complete portfolio will be

in risk free = 77%

in Debt = 23% X 0.37 = 8.51%

in Equity = 23% x 0.63 = 14.49%

Hence solved:

please give feedback and rate the answer. I have solved it to the best of my knowledge. there may be deviations in actual answers to some one or two decimal points due to approximations but the formulas and methodology is right

thanku