A Pure Test for the Elasticity of Yield Spreads

Table 2 are still all negative and statistically significant. In general, the coefficient c
decreases with credit quality, and is similar in magnitude to that estimated for each index for
the entire 25-year sample period. This clearly shows that Longstaff and Schwartz's (1995)
asset factor is robust.

Next, we examine the results for relative yield spreads. Panel A of Table 3 reports the
estimates for our 25-year sample, covering the 08:1976-07:2001 period. Recall that data
during this period are dominated by callable bonds, carrying a standard call provision. Like
Longstaff and Schwartz (1995), we find stronger support for the negative relation, i.e.,
higher absolute t statistics for b and regression R²’s in regression model (2).

***Insert Table 3 here***

Compared with the results reported in Table 2, the results reported in Panels A and Panel
B of Table 3 for regression model (2), indicate that the t statistics for the coefficient b are
always higher when one uses the relative spread. Also, the regression R²’s experience a
significant increase when regression model (2) is applied, which suggests that this regression
model introduces a negative structure into the data. Focusing on the economically
noncallable BBB index during the 01:1995-07:2001 period, it is interesting to note that
although we find no yield spread - riskless rate relation for absolute spreads, when relative
spreads are used instead, b becomes statistically negative.¹³

Instead of interpreting the result to be evidence in support of the negative spread-rate
relationship, we analyze the regression structure first and find that the more significant
negative relation for relative spreads is born out of a mathematical definition rather than a
reflection of economic relationship.

Let R denote relative spread, S denote the absolute spread, and Y denote the riskless rate.
Then by definition: R = YYS. We find the following relationship between the sensitivity to
interest rate of absolute spread and that of relative spread.

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