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Problems 307

c. Would you expect the factor betas to remain constant over time? Discuss how and why these coefficients might change in response to changing market conditions.

3. You have been assigned the task of estimating the expected returns for three different stocks: QRS, TUV, and WXY. Your preliminary analysis has established the historical risk premiums associated with three risk factors that could potentially be included in your calculations: the excess return on a proxy for the market portfolio (MKT), and two variables capturing general macroeconomic exposures (MACRO1 and MACRO2). These values are: XMKT = 7.5%, XMACRO1 = -0.3%, and XMACRO2 = 0.6%. You have also estimated the following factor betas (i.e., loadings) for all three stocks with respect to each of these potential risk factors:

Factor Loading

Stock MKT MACRO1 MACRO2

a. Calculate expected returns for the three stocks using just the MKT risk factor. Assume a risk-free rate of 4.5%.

b. Calculate the expected returns for the three stocks using all three risk factors and the same 4.5% risk-free rate.

c. Discuss the differences between the expected return estimates from the single-factor model and those from the multifactor model. Which estimates are most likely to be more useful in practice?

d. What sort of exposure might MACRO2 represent? Given the estimated factor betas, is it really reasonable to consider it a common (i.e., systematic) risk factor?

4. Consider the following information about two stocks (D and E) and two common risk factors (1 and 2):

Stock ba bi2 E(Ri)

a. Assuming that the risk-free rate is 5.0%, calculate the levels of the factor risk premia that are consistent with the reported values for the factor betas and the expected returns for the two stocks.

b. You expect that in one year the prices for Stocks D and E will be $55 and $36, respectively. Also, neither stock is expected to pay a dividend over the next year. What should the price of each stock be today to be consistent with the expected return levels listed at the beginning of the problem?

c. Suppose now that the risk premium for Factor 1 that you calculated in Part a suddenly increases by 0.25% (i.e., from x% to (x +0.25)%, where x is the value established in Part a). What are the new expected returns for Stocks D and E?

d. If the increase in the Factor 1 risk premium in Part c does not cause you to change your opinion about what the stock prices will be in one year, what adjustment will be necessary in the current (i.e., today's) prices?

5. Suppose that three stocks (A, B, and C) and two common risk factors (1 and 2) have the following relationship:

E(Ra) = (1.1) X + (0.8) X E(Rb) = (0.7) X1 + (0.6) X2 E(RC) = (0.3) X1 + (0.4) X2

a. If = 4% and X2 = 2%, what are the prices expected next year for each of the stocks? Assume that all three stocks currently sell for $30 and will not pay a dividend in the next year.

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