The BIG event in markets that has occurred this year is the massive selloff in global bonds, accelerating since the stunning victory of Donald Trump in the US elections.

The common and widely held view, which now seems to be reflected in the bond markets, is this: (1) Fiscal stimulus will result in more bond issuance, which (2) will result in inflation and (3) more losses in the bond markets. Investors who own bonds want to know what to do now – should we buy more, sell what we own, or wait and see?

The rise in bond yields since November 8 of half a percent (50 basis points) is, for many investors, a symptom of the inflation “disease” that may grip the economy. But before we agree and panic, let us put our biases aside for just a minute and analyze this situation.

There is something utterly convincing about the notion of inflation rising and bond yields rising since they both have been so low for so long. It is just natural to expect some mean-reversion to longer term levels. The negative and very low yields that have existed in the world’s fixed income markets over the last few years just make it easier to argue the case that yields should now rise. And given that central banks artificially propped up the bond markets makes this case even stronger, since we see clearly the proximate “cause” for the low yields.

Now we know that the probability of observing a symptom (sharply rising bond yields) given the disease (that inflation is going to rise) is not the same as the probability of rising inflation (the disease) given bond yields are rising (the symptom). They are, of course, related by the famous Bayes rule, but not identical. We have to carefully evaluate causality.

As an example, suppose you discovered one morning that you had the symptoms of a very rare disease. You ask a doctor and are told that given the disease, the probability of having the symptoms is 90%. But what you want to know is not the probability of having the symptoms given the disease, but having the disease given the symptoms.

The probability of having the disease given the symptoms is proportional to the product of the conditional probability of having the symptoms given the disease and the unconditional probability of having the disease. Since the disease is very rare, let us say it has an unconditional probability of only 1%. This base rate, as it is called, decreases the probability of having the disease (given the symptoms). If we can also somehow figure just the unconditional probability of having the symptoms, we have all the information we need to compute the probability of having the disease given the symptoms.

Let us assume that the unconditional probability of having the symptoms is 5% (i.e. we can sample the whole population and estimate this number). Then using the Bayesian approach, the probability of having the disease given the symptoms is 90% times 1% divided by 5%, or about 18%. Not negligible, but much lower than the 90% probability of the symptoms given the disease. So it is clear that asking the question in the right way makes a big difference in our answer to the relevant question.

Another, visual example is in the pictures below. Do you see a hill or a crater? Are you sure?

Try flipping the image (or see next page for flipped image and an explanation). This is not an optical illusion, but actually a demonstration of how human brains are Bayesian by design, interpreting data probabilistically in the context of new information and prior conditioning, and thus vulnerable to mixing cause and effect.

So let us apply the Bayesian approach to the bond markets and inflation expectations today. One could argue that the probability of a sharp rise in inflation is 10% (assume high inflation in the US means 5% or higher over the next three years). We want to know the probability of high future inflation given that bond yields have risen.

This is equal to the product of the probability that bond yields have risen given high future inflation times the probability of high future inflation divided by the unconditional probability of bond yields rising sharply like they just did. Let us also assume that a half percent shock in the level of bond yields over a short period happens only about 20% of the time (close enough based on historical experience).

The last item we need is the probability of a sharp rise in bond yields given high future inflation. Let us say this is 90%. Multiplying everything out, we see that the probability of high future inflation given a sharp rise in bond yields is only about 45%. Still not negligible, but not something to panic about, and certainly not the almost 100% probability that the market is seemingly romancing. Perhaps something else such as technical factors, or a change in sentiment towards bonds is really the culprit? Hard to tell with certainty just yet.

So is this a buying opportunity or a selling opportunity for bonds?