Question

You already have a very well-diversified portfolio of common stock with a beta of 2, and you want to add stock AAA or BBB into the portfolio. AAA’s standard deviation is 0.2300 and its beta is 4. BBB’s standard deviation is 0.6500 and its beta is 0.5. How will the addition affect the portfolio’s risk?

If we add more factors into the one-factor asset pricing model, what happens to the required returns, increase or decrease? If the expected future cash flows of the financial securities remain the same, will that increase or decrease the current market price? Why?

Answer 1

(1): Here the firm specific risk will not matter as a stock is being added to a well-diversified portfolio. The factor that will matter is beta of the stock. Portfolio’s beta is 2 while beta of stock AAA is 4. Thus adding AAA to the portfolio will increase the beta of the stock and hence its risk. Beta of BBB is 0.5 and this is less than portfolio’s beta of 2 and so adding BBB to the portfolio will reduce the portfolio’s beta and hence its risk.

(2): When more factors are added into the one-factor asset pricing model then there will be more risk factors and these factors will be in addition to the market factor. Due to this the required return needs to be higher. If the expected future cash flow remains the same then discounting it with a higher rate will decrease the present value, which will decrease the price that investors would be willing to pay.