A Pure Test for the Elasticity of Yield Spreads

yield spread is defined as the difference between the yield on the relevant SCM index and
that of the constant maturity, long-term Government of Canada index. Their model for the
absolute spreads is given by:

∆S=a+b∆Y+cI+ε                   (1)

where ∆S is the monthly change in the absolute yield spreads, ∆Y is the monthly
change in the constant maturity, long-term Government of Canada yield, which proxies
changes in the riskless rate. I is the monthly return on the Toronto Stock Exchange 300 index,
which proxies firm assets’ returns.

The second model tested is the Longstaff and Schwartz (1995) model but with relative
spreads instead of absolute spreads. The relative yield spread is defined as the ratio between
the yield on the relevant SCM index and that of the constant maturity, long-term
Government of Canada index. In Table 3, we report our result for the following Longstaff
and Schwartz (1995) relative spread regression:

∆R=a+bPY+cI+ε                  (2)

where ∆R is the monthly change in relative yield spreads, and PY is the monthly
percentage change in the constant-maturity long-term Government of Canada yield, which
proxy’s changes in interest rates. I is the monthly return on the Toronto Stock Exchange 300
index, which proxies for firm asset return.

Duffee (1998) uses a regression approach different from that of Longstaff and Schwartz
(1995). He regresses spread changes on changes both in the short yield and in a term
structure slope variable. Kamara (1997) presents evidence that the slope of the riskless term
structure is positively related to expected economic growth. Harvey (1997) presents similar
results for Canada. This finding implies a negative relation between default risk and changes
in the slope of the riskless term structure. Following Duffee (1998), we estimate the
following regression model for every index:

∆S=β0+β1∆YT-bill+β2∆Slope+ε                            (3)

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