Based on the historical estimates of the four risk factors given the table below

Question

Based on the historical estimates of the four risk factors given the table below you are required to calculate the expected return on MSFT, CSX and XRX using the three factor and four models such as 6. Where SMB (i.e., small minus big) is the return to a portfolio of small-cap stocks less the retum to a portfolio of large-cap (growth) stocks, HML (i.e., high minus low) is the return to a portfolio of high book-to-market ratios (value) stocks less the return to a portfolio of low book-to-market ratios stocks, and MOM is another risk dimension reflecting price momentum facto, capturing the average return to a set of stocks with the best returns over the prior year minus the average return to a set of stocks with the worst returns Coefficients Factor Risk Premia Risk factor MSFT CSX XRX 1980 2009 7.1196 1.50% 5.28% HML SMB 0.9660.018 0.388 1.0420.043 0.37 1.178 0.526 0.517 MKT 1927-09 MKT | SMB HML | 7.92% 3.61% 5.02% Factor Risk Premia Coefficients 4-factor MKT SMB MSFT CSX XRX HML MOM 0.7770.655 0.186-0.074 0.593 0.123 0.084 0.042 0.496-0.158 MKT SMB HML MOM 1980- 2009 7.11% 1.50% 5.28% 7.99% 0.804 0.1 a. Calculate the expected excess returns for MSFT, CSX and XRX using both of the above alternative sets of factor risk premia in conjunction with the three-factor risk model b. Using the information about historical estimates of the four-factor model, calculate the expected excess returns for MSFT, CSX and XRX in conjunction with the four-factor model.

Explanation / Answer

1. Expected excess Return using 3 factor model for 1980-09 is as below:

a. MSFT: 0.966*MKT(fact)-0.018*SMB-0.388*HML(0.966, -0.018, 0.388 are coefficient given above)

=0.966*7.11-0.018*1.50-0.388*5.28

=4.79%

For CSX:

1.042*7.11-0.043*1.50+0.37*5.28

=9.3%

For XRX

=1.178*7.11+0.526*1.50+0.517*5.28

=11.89%

Similarly for other factor risk premia I.e. for 1927-09 we have same coefficients but different risk factors as given in the table. So we can calculate the expected excess return for the three markets as given below:

A)MSFT: 0.966*7.92+-0.018*3.61-0.381*5.02

=5.64%

B) CSK: 9.95%

C) XRX: 13.82%

Now for 4 factor model we need to consider 4 risk factors as given in table 2 and four coefficients.

Thus for each market calculating the expected excess return is:

1. MSFT: 0.77*7.11-0.655*1.50-0.186*5.28-0.074*7.99

=2.91%

2. CSX; 0.593*7.11-0.123*1.50+0.08*5.28+0.042*7.99

=4.8%

3. XRX: 0.804*7.11+0.1*1.50+0.496*5.28-0.158*7.99

=7.22%

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