## Friday, August 16, 2019 ... //

### Inverted yield curve and similar superstitions

The most recent 3% drop of the U.S. stock market indices – which had global repercussions – took place almost completely due to the fact that the main yield curve got inverted.

It's a sign of recession – in average, it comes in 22 months from now, a Swiss bank said. A Czech Canadian wrote me that the yield curve inverted and "f*gg*ts are buying stocks on that day" (the f-category surely included me).

The "bad sign of the inverted yield curve" is a similar rule-of-thumb as the technical analysis used to predict the future movements of prices of securities and other things. All these rules may be justified by heuristic arguments but none of the proofs really seems solid, ever. In most cases, these arguments act as a self-fulfilling prophesy.

The stock markets actually drop when the yield curve gets inverted – because tons of people are being trained to believe this "wisdom" which may very well be a superstition.

What I find particular amazing is the precision of the timing and the rate comparisons that is supposed to justify a 3% drop of the stock market. What did exactly happen when the "curve got inverted"? Well, the yield on 10-year U.S. government bonds which stood at 1.623% was below 1.634%, the yield on the 2-year U.S. bond.

(The yield $$Y$$ is close to the interest rate $$R$$, I suppose that $$\exp(R)=1+Y$$ where $$1\%=0.01$$).

Great. The difference between the two interest rates is some 0.01%. Just imagine that. A difference of 0.01% in the annual yield of some papers – U.S. government bonds – is claimed to justify a 3% drop of completely different securities, namely the U.S. stocks. Don't you see that it's totally disproportionate?

If the yield inversion is a gloomy news, then there should certainly be some "degree" to which the news is gloomy. The more clearly the curve gets inverted, the more likely the recession should become, or something like that. On top of that, the influence of the bond market on the stock market cannot be 100% tight. So if something, you should expect the justifiable change of the stock indices to be smaller than 0.01%. It's clear that a change by 3% on a particular day is mostly a result of a collectively believed superstition.

Well, some people may not care whether stock prices change because of rational reasons or superstitions but I do care and greatly. In general, I think that successful investors must care as well – because at this level, the trading is a zero-sum game and the flash crash caused by this rule must either be a good reason to buy or a good reason to sell. Statistically, one of the decisions is probably turning to be better in the long run, right? If there's a good way to use the rule, you should have predicted the bond market coincidence and sold the stocks before they crashed 3%, of course.

If the 2-year yield 1.63% is below the 10-year yield 1.62%, if you care about the difference, and if you assume these yields to stay fixed – and these "sufficient conditions" for my argument may be pretty much seen to be almost necessary as well – then it means that a saver is better off if he buys the 2-year bonds (than 10-year bonds), then sells them, and buys the new 2-year bonds in two years from now again, and so on. And these incentives are said to be bad news, nefarious, unnatural, whatever – a reason to panic.

Does it make any sense? First of all, the difference between 1.62% and 1.63% is utterly negligible. It affects almost no one. You can't reasonably simultaneously believe that 1) the difference between 1.62% and 1.63% is significant; and 2) the interest rates or their difference will stay the same for 2 or 10 years. It is very clear that the interest rates will change by much more than 0.01% in two years let alone ten years – and many times. The idea that a rational saver is comparing the interest rates with the accuracy of 0.01% which largely determines whether he buys 2-year bonds or 10-year bonds is laughable.

On top of that, this "strange" situation in which the 2-year bonds might look better – given the unrealistic assumptions – is self-defeating i.e. suppressed by negative feedbacks. When 2-year bonds look more attractive, more people will buy them than the 10-year bonds. It means that the price of the 2-year bonds will grow more quickly than the price of the 10-year bonds. But the signs are opposite for yields so it also means that the yields on 2-year bonds will drop faster (or grow more slowly) than the yields on the 10-year-bonds.

So the simple market forces tend to push the situation in the normal state in which the 10-year yields become higher than the 2-year yields once again.

I wanted to argue that even within the bond market, it's nothing special when the long-term rate drops below the short-term rate. The magnitude of this difference is utterly tiny and its meaning is overstated by orders of magnitude, even when it comes to bonds. The precision is overestimated by several orders of magnitude as well. Why wouldn't we try to derive some other quantities, i.e. a derived 1-year rate with a 5-year rate instead? We would almost certainly find the "critical moment" on a different day. Similarly, if there were a "theory", why wouldn't it predict that after something like a yield curve inversion, the average GDP growth in the next 3.5 years would be less than 1/2 of the inflation rate, or 1/3 of the 5-year bond rate, or anything else? The rule-of-thumb looks so arbitrary and therefore unlikely to be true in general. The rule is only meaningful if one believes very precise and subtle details of the claim that depend on tiny quantities but there's no reason why the details should work exactly in this way – and there are so many of them.

Now, the yields are bound to keep on changing, the inverted gap may deepen but we may also return to the "normal yield curve". And the Federal Reserve may affect these yields verbally or by interventions, too. So even if you look at the bond market, the part of markets where the inversion could be relevant, I think that it is irrational to make a big noise about it.

But it's even more stretched to believe that one can predict recessions in this way. Whether there will be a recession depends on many things. After all, the very fact whether there is a minor enough recession is just some irrelevant factoid as well. If the economy drops by 0.1% in a quarter or a year, do you really care? –0.1% only differs by 0.2% from +0.1%. Is that a big enough difference to justify a 3% change of the price of stocks? I don't think so. Even the "presence of a recession" is greatly overvalued because it is usually a mild one. People believe in lots of similar "qualitative switches" but the relevant quantities are universally continuous and there aren't any real "tipping points" at all. All the tipping points are clearly artificially invented superstitions!

Can you predict the recession or the drop of the stock market in the next 2 years or something like that? An interesting question. One direction to address this question is to realize that predictions of such incredibly complex questions about the future are virtually impossible in general. The GDP growth rate in the U.S. in the next year or two will depend on an extraordinary number of factors and people's decisions, on the weather which affects the agriculture in particular, and through the free will theorem of quantum mechanics, it will depend on random outcomes of quantum measurements that cannot be determined in advance, not even in principle!

So it's clearly true that with a sufficient certainty, the existence of recessions cannot be predicted at all!

But assume that it can be predicted from the yields and prices on the markets "rather well" and you want to find some of the best criteria to decide whether the recession will take place. If you care about stocks, should you really look at some 0.01% differences in yields in another, bond market? Can't you find better criteria?

Well, the stock prices themselves are determined by people's expectations about the future recessions. If the traders know that some bad economic conditions are coming, the stock prices may go down in advance, perhaps 6 months in advance. If you believe that the stock prices are a better indicator of the future economic performance than small differences in the bond market, and I do, then it's clear that you can't make helpful decisions because the probability of the future recessions etc. is already priced into the stock prices!

The texts saying that the "inverted yield curve" is a sure sign of a looming recession usually argue that the correlation worked in several examples of the recession so it must work now, too – and to be skeptical about this conclusion means to say "this time is different" which is considered stupid. That's a very subtle argument. Why?

Because, you know, there are two kinds or levels of "this time is different" argumentation. Sometimes, we use it for predictions that may be actually demonstrated by some pretty good argument. A bubble ultimately bursts, we may often say. We say it not just because it has been true in many examples in the past. We also know a pretty good proof why it was true.

But the "inverted yield curve" panic isn't understood equally well. There may be some anecdotal evidence but there isn't really a good enough argument that shows that exactly when a 2-year rate goes above the 10-year rate by some 0.01%, it means a binary signal about some looming trouble. Because of the reasons above, it seems utterly implausible that any such a proof, if completed enough, would look convincing. As I said, the choice of the 2-year and 10-year variables seems arbitrary – and the conclusion depends on this choice, anyway. Also, the difference 0.01% that mattered this time seems tiny relatively to all other differences in yields and returns-on-investment that actually matter in the investors' decisions.

If it looks like a superstition and quacks like a superstition, it is probably a superstition.

Now, I am not saying that I am certain that there won't be a recession. There are many good reasons to expect one, like the trade war. But even though some people will deny this claim, even if this correlation between the inverted yield curve and a coming recession worked correctly one more time, it would still not prove that it is more than a coincidence. It would just marginally strengthen the anecdotal evidence in favor of this hypothesis.

There are lots of similar rules-of-thumb that are used by traders. Like the technical analysis. Some of these patterns may be pretty good rules because they estimate whether something is overbought or oversold. They try to extract some underlying trend from some noise – assuming that the noise is caused by the accidental temporary surplus of buyers or sellers. That's nice and it can work if the assumptions are right but they are not always right. The changes of the price often have very good reasons – something has changed about the rational expectations in the future profits of a company. These "real price changes" should be the actual main reasons that change the prices of stocks and bond yields in nearly perfect markets!

And many "technical analysis" are all about the complete denial of the rational reasons for something's price! In this sense, these arguments are almost totally inadequate for nearly perfect markets. They are more suited for markets that have almost no underlying fundamentals, like the Bitcoin price. But to predict the Bitcoin price still seems almost impossible. There are no fixed magnitudes of the fluctuations, of the autocorrelation coefficients, of time scales at which the Bitcoin price may change by 50%. Not only there are no rational, stable enough laws determining the Bitcoin price. There are even no good "statistical laws". Everything is uncertain, including the degree of uncertainty.

Then you have many special prices and points of reversal such as those determined from the golden mean ratio. Those are mathematically cute rules-of-thumb because the golden mean may be defined by the condition $$1+x = 1/x$$ which gives $$x\approx 0.618034$$. The equation says that the ratio of $$1+x$$ and $$1$$ is the same as the ratio of $$1$$ and $$x$$, so in some sense, it doesn't matter whether you subtract the original price, you may see the same ratio of the two moves of the price.

But is there something that would prefer a price reversal at that price? If I think about the actual messy Einsteinian-Brownian-motion-like rules for the movements of the prices, I can't imagine that they would care about some proximity to such golden mean. For the golden mean to matter, you also need to compare some previous points of reversal. And if you believe that those matter now, you are also saying that the system – the market – must have quite some detailed memory. Although the golden mean is cute mathematically, I find this memory implausible (at least whenever the special phenomena are said to occur at a new level – so that you can't explain the resistance etc. by some leftover of buying or selling orders), so I don't think that something special happens at the golden-mean points.

They may be a good convention to distinguish "small changes of the price" from "significant ones". If the price increases closer to 161.8% than 100%, you might say that it's no longer OK to call it a small random fluctuation and you should treat it as some qualitative change instead.

There's one way how the golden mean rules could be right – as I mentioned at the beginning, such rules may be true because of self-fulfilling prophesies. If many people learn to "sell" when a condition is met, then you will see dropping prices when the condition is met. We surely got it two days ago because of the inverted yield curve.

But I think that even with this self-fulfilling prophesy argument, the algorithms don't really work. Why? Imagine that some stock price is predicted – by these golden mean rules – to reach $1.618 and then drop again. Will it actually happen? Well, if the traders are really mindless stupid sheep, it might. All of them are trained to sell when the price reaches$1.618 so the sales will be sparked at a precise moment.

However, if there are many traders with basic intelligence among them, they know that at the moment of reaching $1.618, the price collapses quickly because of the trained sheep from the previous paragraph. And if it is so, it will be too late to sell very quickly – because the price may collapse very quickly due to this "$1.618 is the golden predicted reversal" rule. So these people know that they should better sell a bit before the maximum is reached and they may choose to sell already at the price $1.617 – before the selling pressure kicks in. But if it's so and if you imagine that the percentage of the smart money goes up, these smart people will compete against each other. The level$1.618 will never be reached because of these people and the drop of the price starts earlier. How earlier? It depends on the amount of smart people or their stocks that must be pumped to the market – and on their expectations about what the other smart people are doing and how much they're willing to sacrifice from the idealized, golden mean maximum price.

At any rate, the presence of intelligent traders on top of the mindless traders acts against the self-fulfilling prophesy. The maximum price that will be reached will probably be very different from $1.618, anyway. Needless to say, with some different mental state of the smart traders, the price may also keep on growing above$1.618. Why? For example, I can figure out that the sheep are the only major bunch of sellers that is going to push the price down. I can have reasons to think that the volume they dump to the market will be limited, I (plus similar people) may easily buy everything, and when we do so, there will be no sellers left on the market which is why the price will have to go up above $1.618. So depending on some detailed conditions and assumptions, a smart trader may either sell below$1.618 or he may wait for reaching $1.618 and then start to buy. I can't say which thing will happen in general but it's almost guaranteed that one of these things will be important in the presence of intelligent traders. The self-fulfilling prophesy will only produce an accurate$1.618 maximum price if all the traders are mindless sheep! And that's very unrealistic, I think, even in the market with Tesla (where the intelligent bears are the key price makers because they sell and buy according to the data etc., although they still play with the price that is vastly above the fair one – they play with a price increased by the religious Musk premium).

To summarize, I think that none of these rules-of-thumb really works reliably enough and they're not primary for anyone whom I would consider an intelligent investor. An intelligent (short-term) trader may be a different issue but I think that the actual rules that are promising in this occupation are more complex, too, simply because even the short-term game is close to a zero-sum game and the winners simply have to defeat those who know at least the basic simple rules of the short-term trading.

So yes, I doubt the usefulness of these simple rules-of-thumb in the short-term trading, too. And I believe that the sophisticated people who teach you about these matters earn more money by selling their books about these rules – than by applying them. ;-)