# Question: Exhibit demonstrated how the Fama French three factor and four factor models could

Exhibit demonstrated how the Fama-French three-factor and four-factor models could be used to estimate the expected excess returns for three stocks (MSFT, CSX, and XRX). Specifically, using return data from 2005–2009, the following equations were estimated:

Three-Factor Model:

MSFT: [E(R) – RFR] = (0:966) (λM) + (−0:018) (λSMB) + (− 0:388) (λHML)

CSX: [E(R) – RFR] = (1:042) (λM) + (−0:043) (λSMB) + (0:370) (λHML)

XRX: [E(R) – RFR] = (1:178) (λM) + (0:526) (λSMB) + (0:517) (λHML)

Four-Factor Model:

MSFT: [E(R) – RFR] = (1:001)(λM) + (−0:012)(λSMB) + (−0:341)(λHML) + (0:073)(λMOM)

CSX: [E(R) – RFR] = (1:122)(λM) + (−0:031)(λSMB) + (0:478)(λHML) + (0:166)(λMOM)

XRX: [E(R) – RFR] = (1:041)(λM) + (0:505)(λSMB) + (0:335)(λHML) + (− 0:283)(λMOM)

Using the estimated factor risk premia of λM = 7.23%, λSMB = 2.00%, λHML = 4.41% and λMOM = 4.91%, it was then shown that the expected excess returns for the three stocks were 5.24%, 9.08%, and 11.86% (three-factor model) or 6.07%, 10.98%, and 8.63% (four-factor model), respectively.

a. Exhibit 9.8 also lists historical factor risk prices from two different time frames: (1) 1980–2009 (λM = 7.11%, λSMB = 1.50%, and λHML = 5.28%), and (2) 1927–2009 (λM = 7.92%, λSMB = 3.61%, and λHML = 5.02%). Calculate the expected excess returns for MSFT, CSX, and XRX using both of these alternative sets of factor risk premia in conjunction with the three-factor risk model.

b. Exhibit also lists historical estimates for the MOM risk factor: (i) λMOM = 7.99% (1980–2009), and (2) λMOM = 9.79% (1927–2009). Using this additional information, calculate the expected excess returns for MSFT, CSX, and XRX in conjunction with the four-factor risk model.

c. Do all of the expected excess returns you calculated in Part a and Part b make sense? If not, identify which ones seem inconsistent with asset pricing theory and discuss why.

d. 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.

Three-Factor Model:

MSFT: [E(R) – RFR] = (0:966) (λM) + (−0:018) (λSMB) + (− 0:388) (λHML)

CSX: [E(R) – RFR] = (1:042) (λM) + (−0:043) (λSMB) + (0:370) (λHML)

XRX: [E(R) – RFR] = (1:178) (λM) + (0:526) (λSMB) + (0:517) (λHML)

Four-Factor Model:

MSFT: [E(R) – RFR] = (1:001)(λM) + (−0:012)(λSMB) + (−0:341)(λHML) + (0:073)(λMOM)

CSX: [E(R) – RFR] = (1:122)(λM) + (−0:031)(λSMB) + (0:478)(λHML) + (0:166)(λMOM)

XRX: [E(R) – RFR] = (1:041)(λM) + (0:505)(λSMB) + (0:335)(λHML) + (− 0:283)(λMOM)

Using the estimated factor risk premia of λM = 7.23%, λSMB = 2.00%, λHML = 4.41% and λMOM = 4.91%, it was then shown that the expected excess returns for the three stocks were 5.24%, 9.08%, and 11.86% (three-factor model) or 6.07%, 10.98%, and 8.63% (four-factor model), respectively.

a. Exhibit 9.8 also lists historical factor risk prices from two different time frames: (1) 1980–2009 (λM = 7.11%, λSMB = 1.50%, and λHML = 5.28%), and (2) 1927–2009 (λM = 7.92%, λSMB = 3.61%, and λHML = 5.02%). Calculate the expected excess returns for MSFT, CSX, and XRX using both of these alternative sets of factor risk premia in conjunction with the three-factor risk model.

b. Exhibit also lists historical estimates for the MOM risk factor: (i) λMOM = 7.99% (1980–2009), and (2) λMOM = 9.79% (1927–2009). Using this additional information, calculate the expected excess returns for MSFT, CSX, and XRX in conjunction with the four-factor risk model.

c. Do all of the expected excess returns you calculated in Part a and Part b make sense? If not, identify which ones seem inconsistent with asset pricing theory and discuss why.

d. 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.

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