When Rates Rise, Spreads Fall: Longstaff and Schwartz on Risky Debt

There is a quiet assumption buried in the early structural credit models that almost nobody questioned: interest rates hold still.

Merton's model treats the risk-free rate as a constant. So does Black and Cox's, in its cleanest form. That is a defensible simplification when you are inventing a field from nothing, but it is a strange one for pricing bonds, because interest rate movement is the single largest driver of what a bond is worth. A credit model that ignores rates is like a weather model that ignores temperature.

Francis Longstaff and Eduardo Schwartz fixed this in 1995, and in doing so uncovered a relationship between rates and credit that ran the opposite way to most people's intuition.

The problem: two risks, modelled in separate rooms

A corporate bondholder faces two distinct dangers.

Interest rate risk. Even if the company is bulletproof, the bond loses value when rates rise, because a fixed stream of coupons is worth less when new money earns more.
Default risk. Even if rates never move, the bond loses value if the company is heading for the wall.

Practitioners knew both mattered. The models handled them one at a time. Rates people built elaborate term-structure models and assumed away default. Credit people built structural default models and assumed away rates.

That separation is not just inelegant, it is wrong, because the two risks are correlated. The state of the economy drives both. And the interaction changes the answer in ways you cannot capture by pricing each piece alone and adding them up.

The key idea via analogy: the boat and the tide

Picture the value of a company's assets as a boat, and the level of interest rates as the tide. Earlier structural models watched the boat and assumed the tide was frozen. Longstaff and Schwartz let both move, and let them move together.

Their setup keeps the first-passage logic that Black and Cox introduced: the company defaults the moment its asset value drifts down to a trip-wire threshold. But now interest rates are also wandering, following their own mean-reverting process, and the two are allowed to be correlated. If rates and asset values tend to move together, the boat and the tide are linked, and the odds of the boat scraping bottom depend on both.

They also made the model usable in the real world in a way its predecessors were not, by handling floating rate debt as well as fixed. Floating rate notes reset their coupons with the market, so they carry almost no interest rate risk, but they carry all of the credit risk. Being able to price both in one framework is exactly what a treasurer or a bank needs.

The genuinely interesting result was empirical. When they looked at actual corporate bond yield data, they found something that catches people off guard the first time they hear it: credit spreads and interest rates move in opposite directions. When the risk-free rate goes up, the extra yield demanded of risky borrowers tends to go down.

Why would that be? There is a clean story inside the model. A higher risk-free rate means, in a risk-neutral sense, that the company's assets are expected to drift upward faster. Faster upward drift means the boat is moving away from the rocks, so the chance of hitting the default barrier falls, so the compensation demanded for default risk shrinks. There is also an economic story that lines up with it: rates tend to be high when the economy is strong, and companies are less likely to fail in a strong economy.

That single insight has a large practical consequence. It means the duration of a risky bond is not the duration of a safe bond. A safe bond falls in value one-for-one with rising rates. A risky bond also gets a partial offset, because the same rate rise is compressing its credit spread. So corporate bonds are less rate-sensitive than their coupon and maturity would suggest, and the more credit-risky they are, the bigger the offset. Anyone hedging a corporate bond portfolio with Treasury futures who ignores this will be systematically over-hedged.

Why it mattered

It joined the two halves of bond risk. After this paper, "credit model" and "rates model" stopped being separate species. The idea that a corporate bond's price depends on a joint process for rates and firm value is now standard.
It fixed corporate bond duration. Treating risky debt as if it had the same rate sensitivity as a Treasury of the same maturity is a real hedging error, and this paper explained precisely why and by how much.
It gave floating rate debt a home. Bank loans, floating rate notes and a large chunk of corporate borrowing carry credit risk without much rate risk. This was the first structural framework that priced them properly.
It produced a testable, non-obvious prediction that held. The negative relationship between the level of rates and the size of credit spreads has been re-confirmed many times since, and it remains one of the more robust empirical regularities in credit markets.

The honest limitations

The spread puzzle survives. Like every structural model, this one still tends to predict smaller credit spreads than the market actually charges, especially for high-grade, short-maturity bonds. Adding interest rate risk helps, but it does not close the gap. The eventual answer, worked out by later papers, is that much of the corporate spread is not compensation for default at all.
Correlation is a weak lever. In practice the rate-asset correlation, while real, explains only a modest slice of what moves credit spreads. Bolting it on improves the model without rescuing it.
The unobservable asset problem again. You still need the value and volatility of the firm's assets. They are still not quoted anywhere.
The barrier is still a choice. The default trigger is an input, and the model's output is quite sensitive to where you put it.
Rates and spreads are not always negatively related. The relationship is a tendency, not a law. In a rate shock driven by inflation panic or a central bank losing credibility, rates and spreads can rise together, exactly the scenario in which a hedger most needs the relationship to hold.

The one-line takeaway

Longstaff and Schwartz built the first credit model that let interest rates and firm value move together, and discovered that credit spreads tend to narrow when interest rates rise, which means a corporate bond is meaningfully less sensitive to rate moves than a government bond and needs to be hedged accordingly.