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 premia 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: λMKT = 7.5%, λMACRO1 = –0.3%, and λMACRO2 = 0.6% . You have also estimated the following factor betas (loadings) for all three stocks with respect to each of these potential risk factors: Factor Betas Stock MKT MACRO1 MACRO2 QRS 1.24 -0.42 0.00 TUV 0.91 0.54 0.23 WXY 1.03 -0.09 0.00 (a) Calculate expected returns for the three stocks using just the MKT risk factor. Assume a risk-free rate of 4.5% (assume intercept is zero). (b) Calculate the expected returns for the three stocks using all three risk factors and the same 4.5% risk-free rate (assume intercept is zero). (c) Briefly 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 (systematic) risk factor?
4. 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 premia 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
Factor Betas
Stock MKT MACRO1 MACRO2
QRS 1.24 -0.42 0.00
TUV 0.91 0.54 0.23
WXY 1.03 -0.09 0.00
(a) Calculate expected returns for the three stocks using just the MKT risk
factor. Assume a risk-free rate of 4.5% (assume intercept is zero).
(b) Calculate the expected returns for the three stocks using all three risk factors and the same 4.5% risk-free rate (assume intercept is zero).
(c) Briefly 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 (systematic) risk factor?
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