On Credit Spreads and the VIX

I got a comment on my blog following my post on rates going negative, and it’s given me food for thought about other related posts.  So to that end, I’m going to talk a little about measuring spreads and looking at indicators of spreads widening or tightening.

First, a little 3-D info visualization wizardry (SAS is awesome).  Here’s a 3-D surface I created based on 5 years of daily data at the 2yr, 5yr, and 10yr durations for investment grade bond spreads over Treasuries:

Just like the Treasury yield curve, you’d expect the spread curve to be upward sloping (longer duration, more risk exposure, so you need to be paid more).  But you can see in parts of the surface where it wasn’t.  Why?  Because default and migration risk (the risk of a credit migrating to a riskier state) was higher in the nearer term than further in the future.  In the Treasury space, an inverted yield curve is usually a harbinger of an upcoming recession.  Something to pay attention to.

So I started thinking about how to estimate spreads and spread changes.  There are models and model vendors out there, for sure.  All have respective strengths, but also one universal weakness: they are abstractions of the real world.  There’s no way you can encapsulate the whole world into an equation or even into a system of equations.

But having said that, it pays to look at them because the gains you get by viewing risk in a defined, systematic way are much better – more consistent and more measurable – than trying to assess it judgmentally.  The literature talks about structural models based on the work of Merton.  I’m not going to delve into the model, but suffice it to say it relies on the interplay between a company’s equity and its debt.  The easiest way to look at this?  Stock options.

And to that end, I looked at the VIX and its relationship to credit spreads.  Because the VIX measures volatility of equity options, it seemed to be a quick easy way to shortcut/bypass all of the other work that goes into estimating spreads and it’s easily accessible data.  The document below gives you a sense of what I looked at and how.  Specifically, I ran some regressions to look at how various spreads responded to levels in the VIX over the last 5 years:

On the surface, it does a pretty good job of explaining spreads.  When I performed the first regression using a linear model, the R-squared was 0.87 – pretty high & pretty intuitive.  As the VIX rises, spreads tend to increase.

But it does have some issues.  If you look carefully, you’ll see when the VIX is very low, the model tends to overestimate where 2yr spreads will be.  As the VIX rises, the model starts to underestimate spreads and then overestimates again when volatility is at its highest.  Plus, it didn’t fit the data at the higher end of the VIX spectrum at all.  You can see there are diminishing marginal effects at work (After you get beyond a certain level of volatility, spreads don’t rise as fast as they did before).

So I re-estimated the data using a linear-log model.  Here you can think about a percentage change in the VIX corresponding to a basis point move in the 2yr spread.  I liked the fit of the line better, but looking at the scatterplot, it’s clear it follows a similar pattern as the linear model.  Overestimation of spreads when VIX is low, but then it underestimates as the VIX increases.  And it underestimates pretty consistently across the different durations and grades.  High grade spreads tended to fit better than the high yield spread I tested, but high yield companies have more idiosyncratic risks than the investment grade ones do.  Some companies are just not run well and a simple model like this is not going to pick that up.

So what have we learned from this?  While both types of models are correct in relating the relative movement between the VIX and spreads, accuracy is lacking especially at the points where we’re most concerned about spreads: when volatility is  above normal and rising.  You’ll need to rely on more than just the VIX/optionality of debt & equity in the firm’s capital structure to make an accurate assessment of spreads.

It’s a good place to start, but it’s incomplete.

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