Table 7
Regressions of Changes in Real Yield Spreads of SCM Long-Term Corporate Bond Indices on Changes
in Selected Real Determinants -
AR-GARCH Estimation
Table 7 reports the results of the AR-GARCH estimation of regression model (4) in which the dependent
variable is the monthly change in the real yield spread. This regression model is of the following form:
∆S = β0 + β1∆ Ylt + β2(∆ Yltr )2 + β3∆Slope + β4I + ε,
where ∆S is the monthly change in the real yield spread, ∆Yl,t,r is the monthly change in the real yield on the
constant maturity long-term Government of Canada index, (∆Yltr)2 is a convexity term, ∆Slope is the
monthly change in the real spread between the constant maturity long-term Government of Canada index and
the three-month Treasury bill yield, and I is the monthly real return on the Toronto Stock Exchange 300
index. t-values are in parentheses, m gives the degree of the autoregressive process as determined by the
stepwise autoregression method, p and q are the GARCH(p,q) parameters, Norm. Test gives the p-value for
the normality test for detecting misspecification of the GARCH model, and finally LM gives the p-value for
the Lagrange multiplier test. Panel A reports the estimates for the entire sample, covering the 08:1976-
07:2001 25-year period. Data during this sample period are dominated by corporate bonds carrying a
standard call provision. Panel B outlines the results for the 01:1995-07:2001 sub-period, in which bonds
carrying the doomsday call are expected to dominate all indices.
Panel A: 09:1976-07:2001
Regression Coefficients AR and GARCH Parameters
Index |
β 0 |
β1 |
β 2 |
β 3 |
β 4 |
m |
p |
q |
Norm. Test |
R2 |
LM |
AAA |
-0.0041 (-0.55) |
0.0019 |
0.0002 |
-0.0418 (-3.06) |
-0.0005 (-0.31) |
1, 2 |
1 |
1 |
<0.0001 |
0.15 |
<.0001 |
AA |
-0.0040 (-0.71) |
-0.0178 (-1.36) |
0.0052 |
-0.0706 (-5.91) |
-0.0040 (-2.90) |
1, 2, 4 |
1 |
1 |
<.0001 |
0.19 |
0.0005 |
A |
-0.0032 (-0.52) |
0.0005 |
0.0044 |
-0.0571 (-4.28) |
-0.0034 (-2.81) |
1, 2 |
1 |
1 |
0.0012 |
0.15 |
<.0001 |
BBB |
-0.0022 (-0.15) |
-0.0029 (-0.21) |
0.0208 |
-0.0818 (-3.10) |
-0.0078 (-2.38) |
- |
1 |
1 |
<0.0001 |
0.11 |
- |
Panel |
B: 01:1995-07:2001 | ||||||||||
Regression Coefficients |
AR and GARCH Parameters |
Goodness of Fit | |||||||||
Index |
β 0 |
β1 |
β 2 |
β 3 |
β 4 |
m |
p |
q |
Norm. Test |
R2 |
LM |
AAA |
N/A | ||||||||||
AA |
-0.0180 (-1.15) |
-0.0104 (-0.29) |
0.1060 |
-0.0453 (-0.98) |
-0.0044 (-1.49) |
- |
- |
- |
- |
0.16 |
- |
A |
-0.0115 (-0.64) |
-0.0130 |
0.0927 |
-0.0503 (-1.05) |
-0.0042 (-1.45) |
- |
- |
- |
- |
0.10 |
- |
BBB |
-0.0185 (-0.68) |
0.0465 |
0.0997 |
-0.0131 (-0.18) |
-0.0122 (-2.77) |
- |
- |
- |
- |
0.13 |
- |
41