Probability

The Cockeyed Business of Prediction A Systematic Inability To Frame

Sanjeev

Sanjeev

The current Chinese Coronavirus 2019-nCoV allows us to understand how we handle Uncertainty. One of the big contributors to Uncertainty is Unpredictability, which is nothing but the presence of Probability Density Functions (pdf) in the various possible scenarios that pepper a futuristic landscape. Now, while unpredictable must be unpredictable, there are surprisingly intelligent ways to think about it.

Declaimer: This article was originally in February 2020, and some data points may be outdated

 

True Positive False Positive
False Negative True Negative

Now consider the above table. If we predicted something, say, rain tomorrow, and it happened, we have a True (it happened) Positive (we predicted Rain). But if we predicted Rain, but it didn’t happen, we would have a False Positive.

Conversely, if we predicted NO RAIN, and it DIDN’T happen, we have a True (we were correct) Negative (i.e. we predicted that something WOULD NOT happen. But if we predicted NO RAIN, but it then rained, we would have a False Negative, i.e. we predicted something would not happen, but it happened.

So to get a complete understanding of the skills of a Prediction ‘Expert’, our understanding is incomplete unless we know his track record across the entire table, especially the parts we often miss out on, the False Positive/ Negatives. You’re not an expert on the Rain Predictions unless you get BOTH the Positives/Negatives right and the False Positives/Negatives under control.

That’s why sensible forecasters don’t project timelines for something to happen. You know the difference between an astrologer and a forecaster, based on who crosses his boundaries, and pretends to know what he does not. In stocks, particularly, a person who sets timelines is a person who does not know his boundaries/ limitations.

And you know a bad client when he asks you the wrong question, i.e., when will I get my profit? He is very likely to get trapped in the wrong mode of thinking.

Symmetric Uncertainty

 Symmetric Uncertainty happens when the possibility of Estimation Errors is a bell curve, i.e. you can over or under-estimate the result. So if you’re trying to predict the weight of an ox, you could both go over or under the actual weight. Or of a stock price, at the end of the month.

Symmetric Uncertainty does not always have to be perfectly symmetric, it just has to be a Bell Curve, but with Skewness/ Kurtosis, which is a bias to one way or the other. In the two charts below, we have two extremes: the first, is a perfect Bell Curve (which is the simplistic assumption of the Black & Scholes Model, in the absence of any real insight into how stock prices will move. The second extreme could be your own Probability Distribution of how stock prices will move if you’re confident in predicting the future. Reality is somewhere in between.

So there’s nothing wrong with being at an extreme, and then being wrong. But there’s something wrong with getting a Nobel Prize for a non-insight like this……i.e. when you don’t know, you put it somewhere in the middle.

So let’s consider how the Coronavirus is being reported. The dead are probably dead (True Positive), it’s unlikely that they’re not dead (False Positive). But how did we come to predict the number of Infected (True Positive)? Did we consider:

  • That someone may be infected but has not reported in sick yet.
  • Someone has not been infected but has reported himself sick (maybe because of some other viral infection). Okay, let’s not take this too far, this guy would have been soundly thrashed by the now thoroughly irritated Chinese authorities. But how about other scenarios?
  • What if some province has under-reported the infections, especially since you’re now sacking officials for non-performance? This was one statistic where they did not want you to maximize, you just got it wrong….
  • But you get the picture, it’s very unlikely that the estimates can be taken as gospel, just as we believe the Option Chain to be carrying some great insight about future stock prices.

So we know the total number of actually infected cases. Now consider:

  • How many are suspected of having caught the virus and have been quarantined? Let’s say, 2000…
  • How many people came in contact with the infected, BEFORE they were infected? Let’s say they were 5 times the number declared infected. So if the number of people declared infected is 10,000, we can expect that number to be 50,000.
  • And how many are outside both circles (we don’t know what we don’t know). For example, how many other wet flesh markets are there in China, where the said virus is still to break out? Or other kinds of virus? You get the picture……?!
So let’s now ascribe Probabilities to the above populations:
  • The quarantined population would have a 90% probability, 90% of 2000 = 1800
  • The persons who came in contact might have a 20% chance of being infected, so 20% of 50,000 = 10,000
  • The ‘ambient’ probability that there are other such markets like Wuhan and other such outbreaks, would include the entire population of Asia, which might sound ludicrous to you. So we’ll ignore it for the time being (this is what creates the Black Swan that Nassim Taleb was talking about).

But do you understand now? Against an initial estimate of 10,000 infections, we already have another 11,800 infections, not counting the Tail Risk (of other ambient infections spread across Asia or the world). So the Estimation Error is at least 100% in this case.

We spend all our time in the real world, making estimates of future probabilities, from trying to predict rain to trying to predict the prices of stocks at the end of the month. We should be conscious of asymmetric and symmetric error, and when one is passed off for the other. It would help us to listen to ‘experts’ who make their money off the predictions, not on the probability of them being right. A doctor gets paid when he prescribes the medicine, not when it is effective. You’re the one whose life is hanging on the probability of the ‘expert’ being right…..

The errors, as I have shown you above, can be extremely large. Sometimes they can be lethal for your physical or financial health. Remember, after multiple cycles of such estimations, you will get a distribution of errors in the predictions themselves, which should tell you about the quality of the predictions and the quality of the predictor itself.

But the big point here is Asymmetric Errors and an awareness of their existence. This itself would put you ahead of the amateurs, any further understanding of the distribution of errors would make you Jim Simons. There are some behavioral dimensions to this, and each such problem would have its peculiar reactions to how human beings handle Uncertainty:

  • When it’s bad news, people will not highlight estimates, they will only report Confirmed Deaths. Those in the ICU will still be reported as alive, those maimed or disabled forever (brain damage) will similarly be reported as alive, even cured. This understates the actual situation.
  • If you’re researching sex or some private issue, you will get another distortion. If it’s women, those who’re doing it MAY report it, but those who’re not doing it will not report it (the opposite is true for men). This applies to ‘good traders’, who claim to have made money all their lives. They tend to ‘remember’ selectively, and hence, good trading track records tend to get over-reported.

I call it Umbra Thinking. The mind tends to listen only to explicit numbers, not the ‘missing’ numbers (hidden in the penumbra). This is particularly true of amateurs/laymen, who don’t watch their thinking. The Chinese aren’t even trying to estimate the number of deaths, they only want to ‘confirm’ the number of deaths. Like in war, you only count the number of bodies you come across, not locate the ‘missing in action’ (MIA). The same in stocks, where we conveniently forget to recount ‘the one that got away’. So even though these figures are misleading, people WANT to be misled by such figures. Which is why TV has a business.

This is where the idea of a Margin of Safety becomes important. The Skewness of the Estimation Errors has to be provided for, and that’s paid for, by the Margins of Safety that we set in our Rule Book.

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