A Pure Test for the Elasticity of Yield Spreads

callable and economically noncallable bonds.

6 A Direct Test for Default Risk

In the previous section we use several well-established regression models to estimate
the yield spread - riskless rate relation for Canadian data. Because in recent year’s bonds in
the Canadian BBB bonds index are not exposed to callability and tax effects, it is safe to
assume that their yield spread is mainly driven by credit risk. Moreover, BBB bonds serve as
an excellent test case for the question of whether default risk generates a negative yield
spread - riskless rate relation. This is because this risk is quite substantial for bonds of this
rating category.

We find that, when callability and tax effects are controlled for, there is no significant
yield spread - riskless rate relation. Thus, contrary to what previous studies conclude from
their tests (see for example: Longstaff and Schwartz, 1995; and Duffee, 1998), our results
cast doubt on one of the most notable predictions of structural models; that credit spreads are
negatively related to the riskless rate. Recall that risk-neutral valuation is applied in the
context of structural models. Ceteris paribus, under risk-neutral valuation an increase in the
riskless rate implies a higher expected future value for the firm's assets relative to the default
threshold, and a lower risk-neutral probability in default. This ultimately results in a negative
credit spread - riskless rate relation.

To substantiate our contention that this prediction of structural models does not hold
empirically, in this section we offer an alternative test that involves default rates. The
advantage of this test is in that default rates serve as a more direct measure of credit risk.
They are also clean of callability and tax effects. We obtain historical default rates from
Moody’s Investors Service. Moody’s historical default rates are based on the credit histories
of nearly 10,000 corporate and sovereign entities and over 80,000 individual debt securities
since 1970.

We choose to apply the following Collin-Dufresne et al.’s (2001) type regression model

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