Suppose a three-factor model is appropriate to describe the returns of a stock.

Question

Suppose a three-factor model is appropriate to describe the returns of a stock. Information about those three factors is presented in the following chart:

Factor                 b            Expected Value            Actual Value
GDP             .006821                $14,011               $13,982
Inflation           .90                   2.80%                   2.6%
Interest rates   .32                   4.80%                   4.6%

a. What is the systematic risk of the stock return?

b. Suppose unexpected bad news about the firm was announced that causes
the stock price to drop by 1.1 percent. If the expected return on the stock is 12.8 percent, what is the total return on this stock?

Explanation / Answer

a. Systematic risk is risk related to economy/market-wide events like interest rates, recessions and wars. These types of events affect all stocks and cannot be diversified away. Generally, systematic risk factors are those factors that affect a large number of firms in the market. Note that those factors do not affect equally all the firms. The systematic factors in the list are GNP, inflation and interest rate. Syst. Risk = 0.006821(13982- 14011) – 0.9(2.6%- 2.8%) - 0.32(4.6% -4.8%) = = -0.197809 + 0.18 + 0.064 = 0.04619% b. Unsystematic risk is related to events that don't affect all companies, only your company is affected. Unsystematic risk is the type of risk that can be diversified away through portfolio formation. Unsystematic risk factors are specific to the firm or industry. Surprises in these factors will affect the returns of the firm in which you are interested, but they will have no effect on the returns of firms in a different industry and perhaps little effect on other firms in the same industry. Examples include your plant burns down, your product flops, or your product is a huge hit. The unexpected bad news about the firm that dampens the returns by 1.1% is an unsystematic risk, in this case the only one Unsystematic Risk = - 1.1% c. Total Return = expected return + Syst. Risk + Unsyst. Risk = 12.8% +0.04619% - 1.1% = 11.746%

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