Question

IV. You currently hold a diversified portfolio with a beta of 1.1. The value of your investment is $500,000. The risk-free rate is 3%, the expected return on the market is 8%.

a) Using the CAPM, calculate the expected return on your portfolio.

b) Suppose you sell $10,000 worth of Chevron stock (which is currently part of the portfolio) with a beta of 0.8 and replace it with $10,000 worth of JP Morgan stock with a beta of 1.6. What will be beta of your new portfolio?

c) Suppose one of the stocks currently in your portfolio has beta of -.1. What is the expected return on this stock? Compare this stock to the risk-free asset. Aren’t you better off selling this stock and replacing it with the risk-free asset? Why or why not?

d) Suppose one of the stocks currently in your portfolio has beta of 0. What is the expected return on this stock? Compare this stock to the risk-free asset. Aren’t you better off selling this stock and replacing it with the risk-free asset? Why or why not?

Answer 1

a) Using CAPM, E(R) = Rf + beta x (Rm - Rf) = 3% + 1.1 x (8% - 3%) = 8.50%

b) New Beta = Old Beta + (Beta (JPM) - Beta (Chevron)) x Value / Total

= 1.1 + (1.6 - 0.8) x 10,000 / 500,000 = 1.116

c) E(R) = 3% + -0.1 x (8% - 3%) = 2.50% < Risk-free rate = 3%

No, negative beta stock provides diversification to the portfolio and helps in reducing portfolio risk. In case, the market declines, these kind of stocks are likely to increase in value.

d) E(R) = 3% + 0 x (8% - 3%) = 3% = Risk-free rate

Zero beta stocks also provide diversification to the portfolio and helps in reducing portfolio risk.