Question

You have $100,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 12.1 percent. Stock X has an expected return of 10.28 percent and a beta of 1.20, and Stock Y has an expected return of 7.52 percent and a beta of .80.

a. How much money will you invest in Stock Y? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b. What is the beta of your portfolio? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)
a. Investment in Stock Y
b. Portfolio beta

Answer 1

a. Amount to invest in Y

The amount that will be invested in Stock Y should be such that the expected return of the portfolio would equal 12.1%.

This would be determined by the weights of the stock.

Assume the weight to be invested in X is x.

Portfolio return = (weight of X * Return of X) + (weight of Y * Return of Y)

12.1% = (x * 10.28%) + ( (1 - x) * 7.52%)

0.121 = 0.1028x + 0.0752 - 0.0752x

0.121 - 0.0752 = 0.1028x - 0.0752x

0.0458 = 0.0276x

x = 0.0458 / 0.0276

= 1.6594

Weight in stock Y:

= 1 - 1.6594

= -0.6594

Amount to invest in Y:

= -0.6594 * 100,000

= -$65,940

b. Portfolio beta

It will be a weighted average of the betas of the two stocks:

= (Weight of stock X * Stock X Beta) + ( Weight of stock Y * Stock Y beta)

= (1.6594 * 1.20) + (-0.6594 * 0.80)

= 1.46