Credit Spread

[Sunil Natarajan]

Hi David,
In Stulz it is mentioned that as time to maturity increases the credit spread for a debt with higher credit rating would widen and for a debt with lower rating the credit spread would be narrow. I thought it was the other way round.
How does credit spread narrow as interest rates rise.

Regards,
Sunil

 

[David Harper CFA FRM]

Hi Sunil,

Right, he does say that (I parrot him, like a robot, on p 13 of credit risk C screencast)

That section of Stulz Ch. 18 is, er, really confusing. The problem (pedantically, IMO) is he mixes a fundamental model (18.6) of the credit spread ("here is a model to explain spreads") with empirical citations ("rates tend to do this") which don't necessarily comport. In short, it's all over the place. It would, IMO, be safer (less controversial) to simply say: spreads tend to widen with maturity, regardless of rating.

But Stulz is saying, that if the bond is risky enough, more time gives the issuer more time to repay. Since Stulz is all about the Merton model, it is a natural finding for him because it falls out from pricing the firm's debt as the value of riskfree debt minus a put option on the firm. So, as you can get the value of an in-the-money put to actually (counter-intuitively) fall with longer term, you can get more valuable risky debt with longer term to maturity. As is so often the case in the finance, assertions can be correct within one framework (set of presuppositions) and incorrect within another and, finally, contradicted by empirical observation. If that's true, it's important to identify the framework within which Stulz asserts "credit spreads do this" And, Ch 18, if not most of the book, is anchored in a Merton approach (debt + equity = firm value)

"How does credit spread narrow as interest rates rise?"
In regard to Stulz 18, I think we can retreat to 18.6. This is a simple (unrealistic) model.
See my copy here: http://www.bionicturtle.com/premium/editgrid/2008_credit_stulz_credit_spread/
Under this, holding D,F, and T constant, if (r) increases then the spread must decrease.
Which is the same as: risky rate = riskless rate + spread. If we hold risky rate constant (i.e., debt and value same), then spread must narrow.

Of course, that's not a narrative to explain an empirical observation. We could *argue* (by which i mean, other arguments can be made) in classic terms: economic expansion/growth causes increase in demand for fund which causes interest rates (price of money) to rise, and, since companies on average are less likely to default, spreads to narrow. But it's "off the page" from Stulz as it get into a whole mess of other factors not in his simple factor model.

David