A long-term i-rated corporate bond index, i=AAA, AA, A, BBB, consists of all bonds in
SCM's i-rated corporate bond universe, with remaining terms to maturity greater than 10
years.
Our yield spreads for these long-term indices are calculated with respect to the constant
maturity, long-term Government of Canada index, reported by CANSIM. Following
Longstaff and Schwartz (1995), to proxy firm assets' returns we use the (continuously
compounded) monthly return on the Toronto Stock Exchange 300 index.9
Table 1 reports the summary statistics for the time series of absolute and relative yield
spreads stratified by credit rating. Similar to the statistics reported by Longstaff and
Schwartz (1995) for their U.S. data, the means of both absolute and relative yield spreads
monotonically increase as credit quality decreases for all indices. The same is true for the
standard deviation of both yield-spread measures.
***Insert Table 1 here**
4.2. Regression Methodology
Our focus is on testing the three regression models introduced in the first section,
namely the Longstaff and Schwartz (1995) two-factor model, Duffee’s (1998) term-structure
model and Collin-Dufresne et al.’s (2001) comprehensive model. For all the models that
follow, we estimate the coefficients by OLS and a combined autoregressive and GARCH
(1,1) model. Financial time-series are well known to exhibit volatility clustering, a time-
varying variance of the innovations. In this sense heteroskedasticity in the regression
residuals may reduce the estimation efficiency but is commonly overcome through the
GARCH (1,1) specification. Since previous research in this area uses OLS, we first run OLS
regressions for comparison reasons. Also, using the Lagrange multiplier (LM) test and the
Portmanteau Q-test to our data, we examine their properties. We find that a combined
autoregressive and GARCH (1,1) model better fits our data.
The first model tested is based on Longstaff and Schwartz (1995), where the absolute
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