Slopes And Recession Probabilities

I recently published the above chart, which is not a typical slope chart for fixed income commentary. The 2-/10-year slope is more popular for one important reason: it is a tradeable “instrument,” unlike the Fed Funds/5-year slope (above), as the Fed Funds leg has no duration. However, moving the short maturity leg to a tradeable instrument like the 2-year misses the important information embedded in the Fed Funds to 2-year slope. Although some people did use the 2-/10-year for recession forecasting, the tendency has been to shift to the 3-month Treasury Bill as the short maturity instrument. (The advantage of the 3-month bill is that it is a “market rate” and it exists as a time series in databases typically over the same horizon as bond yields, whereas other money market rates are based on instruments of more recent vintage or did not exist as a concept — for example, the Fed did not announce a target for the Fed Funds rate until the 1990s).

Chinn looked at variety of probit models that are meant to back out a probability of recession events based on the slope (and calibrated against historical recession dates). As I do not have a source for a model output handy (readers can click the link to see Chinn’s chart), I will just note that the level of inversion we see in recent data is similar to that around past recession events, and so the estimated recession probabilities are quite high. (Chinn lists model outputs that range from a 66.4% to 90.8%.)

Bull Versus Bear Steepening

One of the pieces of bond market jargon that showed up in the piece was “bear steepening” versus “bull steepening.” For people who read economic commentary and just look at the slope, the terms are somewhat mystifying. The reason is we need to look at the level of yields, and not just the slope (like in the above chart.) There are two axes to discuss.

• Bull/bear: whether bonds are in a bull/bond movement. Since bond prices move in the opposite direction of yields, a bear market is yields going up, while bull market is yields going down. Note that bond yields beyond the 2-year point tend to all move in the same direction, but it is technically possible that the short and long maturities move in the opposite direction. The direction of the yield change of the long maturity instrument presumably determines whether it is a “bull” or “bear” move. Since it does not happen very often, not sure how others would classify that.

• Steepening/Flattening: is the slope (long maturity yield minus the short maturity yield) going up or down.

So the slope is increasing recently (as seen in the bottom panel) while the long maturity is rising: hence, a bear steepener. Since this means that the 5-year is discounting less cuts (putting aside term premia quibbles), that is directionally bullish for the economy. However, this easy interpretation does not work for the 2-/10-year slope: if the 2-year yield is falling, that indicates a rising expectation of near-run rate cuts (or less hikes).

The bond/bear steepener/flattener distinction is also important for fixed income commentary in that it is possible to structure conditional curve trades. By using a pair of payer/receiver swaptions, one can enter a flattening/steepening trade that is only active in a bull or bear market. This is a good way to express conditional forecasts: you think that markets will behave a certain way if an event happens, but you do not have a strong view if it does not. Since the front end typically moves faster than the long end, one would be biased to enter bear flatteners or bull steepeners — but implied volatility normally prices in that behavioural bias, and so it is not enough to be correct on the direction of the change of the slope, you need to beat a hurdle level that is determined by the forwards and the implied volatility differential.

Probit Models are Great for Economists, Not So Much For Bond Investors

I have never built one these probit models on the view that I am not in the target market for the models. They are designed for economists (like those at central banks) who want to have a way of reading “what does the bond market price in for the economy?” beyond just slapping the slope chart up and pointing out that inversions tend to happen before recessions. Being able to say that the market is discounting a 90.8% or 66.4% chance of a recession makes it look like your doctorate is paying dividends.

From the perspective of a bond investor, one can attempt to invert the usual logic: do I think there is an x% chance of recession over the next year? If I think the odds of a recession are much lower than that, then I want to be bearish on bonds. Unfortunately, this is probably only useful when the probability is quite high (like now) — where you do not need a fancy model to offer the insight that bonds are expensive in the absence of a recession. If the implied probability is 20%, there is probably not a lot of useful valuation information if I think the probability only 5%. You need to look at other valuation metrics.

A larger issue is that bond market pay-offs are not given from whether the NBER committee decides there was recession, rather they are based on where yields end up relative to forwards (driven by the cost of funding). What ultimately matters is the realised path of the short rate, not the economy. The bond market correctly priced in the mini-cut cycle ahead of the pandemic, but whether the pandemic recession was truly “priced in by the bond market” is a tiresome debate.

Another thing to keep in mind with these models is that the probability estimation is not going to cope with a changing term premium. One of the common habits of finance professionals is that they want to grab as many mathematical models as possible, and are happy to quote them without worrying about their internal consistency. For example, one should not rely on probit model recession probabilities and at the same time argue slope changes are the result of changing term premia unless you adjusted the slope for your term premium estimate.

Concluding Remarks

From the perspective of someone not deeply interested in bond market pricing, probit recession odds models are neat way of summarising market pricing. However, one needs to keep in mind that this is just the weighted average of investor positions, and not some time series that pops magically out of nowhere. Investors can be wrong, and/or there can be other technical factors “distorting” yields.