In structor s Ma nual Chapter 12 Page 147

6. Using the optimal portfolio of AT&T and Microsoft stock when the correlation of their price movements is 0.5, along with the results in part f of question 12-5, determine:

a. the expected return and standard deviation of a portfolio which invests 100% in a money market fund returning a current rate

of 4.5%. Where is this point on the risk-reward trade-off line?

b. the expected return and standard deviation of a portfolio which invests 90% in the money market fund and 10% in the

portfolio of AT&T and Microsoft stock.

c. the expected return and standard deviation of a portfolio which invests 25% in the money market fund and 75% in the

portfolio of AT&T and Microsoft stock.

d. the expected return and standard deviation of a portfolio which invests 0% in the money market fund and 100% in the

portfolio of AT&T and Microsoft stock. What point is this?

SOLUTION:

a. E[r] = 4.5%, standard deviation = 0. This point is the intercept of the y (expected return) axis by the risk-reward trade-off line.

b. E[r] = 6.03%, standard deviation = .0231

c. E[r] = 15.9%, standard deviation = .173

d. E[r] = 19.75%, standard deviation = .2306. This point is the tangency between the risk-reward line from 12-5 part f and the risky asset

risk-reward curve (frontier) for AT&T and Microsoft.

7. Again using the optimal portfolio of AT&T and Microsoft stock when the correlation of their price movements is 0.5, take

$ 10,000 and determine the allocations among the riskless asset, AT&T stock, and Microsoft stock for:

a. a portfolio which invests 75% in a money market fund and 25% in the portfolio of AT&T and Microsoft stock. What is this

portfolio ' s expected return?

b. a portfolio which invests 25% in a money market fund and 75% in the portfolio of AT&T and Microsoft stock. What is this

portfolio 'edsretxuprenc?t

c. a portfolio which invests nothing in a money market fund and 100% in the portfolio of AT&T and Microsoft stock. What is this

portfolio ' s expected return?

SOLUTION:

a. $7,500 in the money-market fund, $285 in AT&T (11.4% of $2500), $2215 in Microsoft. E[r] = 8.31%, $831.

b. $2,500 in the money-market fund, $855 in AT&T (11.4% of $7500), $6645 in Microsoft. E[r] = 15.94%, $1,594.

c. $1140 in AT&T, $8860 in Microsoft. E[r] = 19.75%, $1,975.

8. What strategy is implied by moving further out to the right on a risk-reward trade-off line beyond the tangency point between the line and the risky asset risk-reward curve? What type of an investor would be most likely to embark on this strategy? Why? SOLUTION:

This strategy calls for borrowing additional funds and investing them in the optimal portfolio of AT&T and Microsoft stock. A risk-tolerant, aggressive investor would embark on this strategy. This person would be assuming the risk of the stock portfolio with no risk-free

s own component; the money at risk is not onl y from this person '

wealth but also represents a sum that is owed to some creditor (such as a margin account extended by the investor broker).