Question

63 multiply with $100,000) This is your total investment in a portfolio that has stock X and stock Y. Your goal is to create a portfolio that has an expected return equal to 17 percent. If Stock X has an expected return of 14.8 percent and a beta of 1.35, and Stock Y has an expected return of 11.2 percent and a beta of .90, how much money will you invest in Stock Y? How do you interpret your answer? What is the beta of your portfolio? comment on the systematic risk of your portfolio?

Answer 1

Data:

Total Investment = 63 * $100,000 = $6,300,000

Expected Return of Stock X, Rx = 14.8%

Expected Return of Stock Y, Ry = 11.2%

Beta of Stock X, Bx = 1.35

Beta of Stock Y, By = 0.90

Expected Return of Portfolio = 17%

Let proportion of investment in Stock X, Wx be x

Then proportion of investment in Stock Y, Wy = 1-x

Expected Return of Portfolio = RxWx + RyWy

17 = (14*x) + (11.2*(1-x))

17 = 14x + 11.2 – 11.2x

2.8x = 5.8

x = 5.8/2.8

x = 2.07142857 = 207.142857%

Proportion of investment in Stock X = 207.142857%

Proportion of investment in Stock Y = -107.142857% (1-207.142857%)

Money to be invested in Stock Y = -107.142857% ($6,300,000) = -$6,750,000

It can be interpreted that investment in Stock Y to be sold in order to earn the expected return on portfolio.

Beta of Portfolio

= BxWx + ByWy

= (1.35 * 207.142857%) + (0.90 * (-107.142857%))

= 2.7964285695 – 0.964285713

= 1.8321428565

Beta of portfolio = 1.83

The systematic risk of the portfolio, beta = 1.83. Since the portfolio earns higher expected return, it needs to take more risk.