Anon

58 The Basics of financial economeTrics

So, in this instance we have k = 2. The multiple linear regression to be
estimated is

y = b 0 + b 1 x 1 + b 2 x 2 + e

where y = the monthly return of an index
x 1 = the monthly change in the Treasury yield
x 2 = the monthly return on the S&P 500

In a simple linear regression involving only x 2 and y, the estimated
regression coefficient b 2 would be the beta of the asset. In the multiple linear
regression model above, b 2 is the asset beta taking into account changes in
the Treasury yield.
The regression results including the diagnostic statistics are shown in
Table 3.4. Looking first at the independent variable x 1 , we reach the same
conclusion as to its significance for all three assets as in the univariate

TAbLE 3.4 Estimation of Regression Parameters for Empirical Duration—Multiple
Linear Regression

Electric

Utility Sector

Commercial

Bank Sector

Lehman U.S. Aggregate

Bond Index

Intercept

b 0 0.3937 0.2199 0.5029

t-statistic 1.1365 0.5835 21.3885

p-value 0.2574 0.5604 0.0000

Change in the Treasury Yield

b 1 –4.3780 –1.9096 –4.0885

t-statistic –3.4143 –1.3686 –46.9711

p-value 0.0008 0.1730 0.0000

Return on the S&P 500

b 2 0.2664 1.0620 0.0304

t-statistic 3.4020 12.4631 5.7252

p-value 0.0008 0.0000 0.0000

Goodness-of-Fit

R 2 0.1260 0.4871 0.9312

F-value 12.0430 79.3060 1130.5000

p-value 0.00001 0.00000 0.00000