Category: Using Statistics

A Black swan

This is a term commonly used – but I struggle to understand what people mean by it.

Types of probabilistic events?

In Taleb’s book of the same name, “Black Swan” appears to be used in a variety of ways:

  1. For a well-defined outcome with a low probability
    for example: selling lottery tickets or buying CDOs in 2006/7.
    (perhaps the people buying such CDOs did not understand that they were selling lottery tickets but they should have!)
  2. For general uncertainty
    We all know it is possible to have a currency crisis in the UK in the next 5 years but it is not very sensible to put a single number on it. This is concept of “uncertainty” from Knight and Keynes and many macro issues fit into this category. A frequentist approach to probability works for rolling dice but often not for rare events.
  3. For “fat tail” events
    Extreme events occur in reality more commonly than a normal distribution would suggest.
  4. For when the distribution is just unknown
    It is possible that it will be known at a later stage, but currently there is insufficient information.
  5. For an unknown, possible outcome
    This seems to be the new, popular meaning.

Numbers 1 through 4 are well-known and have perfectly good ways to describe them. I think that only number 5 really makes sense as a potential separate meaning for “Black Swan”.

Does number 5 actually exist?

This is also the meaning I have most problem with as I struggle to find real-world examples of it. There are many examples where people did not consider the possibility of a given outcome, but at the same time you can find many people who did and even had decent reasons to expect it to happen. At the individual level it makes some sense as being imaginative can be hard work! However, if some people are not surprised at the occurrence, then how can it be something which “is not even imagined as a possibility prior to its occurrence” unless as you say it is entirely subjective and individual.

It may have been unimaginable to Cheney that the Iraqi people did not embrace US troops as liberators in 2003. Does that mean it was a Black Swan as it was not conceived possible and was clearly important? Or does it just mean Cheney was wrong?

Common usage

Let’s consider what many see as the great Black Swan of 2008:

This is what I think people mean:

· 2008 was a massive drop in markets

· A great deal of common practice in managing risk was terrible

· They didn’t see it coming because it was unforeseeable

Therefore

· I should not feel bad about not predicting it

· Black Swans are very rare, so we should not expect it to happen again

· We should carry on pretty much as before

 

Why it annoys me

This version of events is just an excuse for being wrong, for not learning from it or changing behavior. It should be obvious that I find the term annoying in this way of excusing poor decision making and avoiding responsibility.

Alan Greenspan indeed said that the financial crisis was “unforeseeable”.

 

On Epistemology

Another confusion I had about the theory of the “Black swan” laid out in the book, is the way it sits at odds with the philosophy of science and specifically Popper. Popper, in fact, gets no mention in Taleb’s book, even though Popper’s key concept of falsifiability has long been linked and explained via the original example of black swans.

Quick aside on jargon

  • A conjecture – is an unproven proposition which appears correct
  • A hypothesis – is a testable statement

To illustrate Popper’s concept:
If your hypothesis is that all swans are white.
It would be disproved if you find a black swan.

Given its falsifiability, this is compatible with scientific enquiry

It is clear in this example, to be testable, you have to have considered what events would falsify it.

If we now put Taleb into similar language:

  • Taleb
    a Black Swan is an unimagined event for certain people which disproves their conjecture
  • Popper
    a Black Swan is a defined event which would falsify a hypothesis

Written this way, I think it show the two meanings are incompatible. Popper’s version makes sense and is useful. It is therefore such a shame that Taleb’s popularisation of the term “Black Swan” has taken something important and meaningful and turned it into nonsense.

Games 7 Is trading gambling?

My story of the racetrack (https://appliedmacro.com/2017/07/12/desire-the-fatal-flaw/) is how many people, from outside finance, see my world of traders and hedge fund managers. A bunch of gamblers who, at the mercy of their desires, love the thrill with the outcome largely down to luck.

This is invariably intended to be an insult. While I do not enjoy being insulted, I also find it interesting that it is so poorly directed. As with many insults, there is an element of truth but it says more about the speaker than the target.

Using the previous framework on games, they are suggesting that trading is:

  1. High volatility
  2. Low skill
  3. Motivated by desire for excitement

This is probably a fair representation of how a non-professional might engage in it. It is a very fair description of how I play poker with friends. This is why I think it says a lot about the speaker.

In contrast, I would describe professional trading in the game framework as:

  1. High volatility
  2. High skill
  3. Desire for consistent profits and to minimise excitement

This is also a good description of how a professional poker player would view their play.

For both trading and poker, the experience and motivations of amateurs and professionals are very different.

For a non-participant, the most common error is to assume that high volatility games are low skill ones – which we have already seen is certainly not the case. It is also easy to generalise from the few lucky cases that make a good story, and then mistakenly think that luck is all that matters.

Conclusion

Trading and poker have a lot in common. To some, they can be games with a high degree of randomness, where the motivation for playing is the fun that comes from experiencing the volatility. Or they can be games played by professionals, who want to reduce the volatility as much as possible to focus on the non-random positive earnings they can obtain from it.

Games 6 Why do people gamble?

In my previous post, I discussed how the common use of the word “gambling” mixes up volatility with randomness, and frequently leads to incorrect assumptions about skill.

Another perspective on gambling is examine people’s motivation.

Why do they do it?

There are four main motivations I can think of why people gamble

  1. For the excitement, the drama of winning and losing
  2. To add some interest to an activity
  3. To deliberately add volatility to an outcome
  4. To make money consistently


Volatility and expected value

Here is a framework with two dimensions “Expected Value” and “Volatility”.

Positive expected value is when you expect on average to make a profit
Negative expected value might be called “against the odds”.

High volatility means that the short-term outcome is highly uncertain
Low volatility means the outcomes are far more tightly distributed.

a. Excitement e.g. playing in a casino

This is the activity that most often comes to mind when we think of gambling: playing roulette in the casino, betting on horse racing. The desire to induce a feeling of vertigo is the primary purpose. https://www.youtube.com/watch?v=TAaSJcIIruI

A key element to this form of gambling is that it has a negative expected value i.e. you lose on average. It is well known that casinos design their games to produce exactly this i.e. the house advantage. The player gets the excitement coming from high volatility; they will lose on average but they might win big tonight!

These games tend to be low skill. There may be a skill in minimising losses but this tends to reduce the volatility or “fun” element. For example, playing Blackjack with Basic Strategy, not difficult to learn, but extremely boring to play as every decision is pre-determined.

This motivation is very common but although I understand it, I do not really enjoy it myself. A low skill game, in which I expect to lose on average, sounds dreadful.

b. Adding interest e.g. betting on a football match you are watching

This is the form of gambling that I think of when I am engaged in an activity, and people say to me they want to “make it interesting”. We might be watching a football match, or playing golf together. There is an underlying activity but it can make it more fun if a monetary aspect is added.

Some people really like this and I think it’s because they really enjoy the gambling aspect i.e. they get to combine an activity they enjoy with gambling which they also enjoy (much like a. above). It could also be that they find the underlying activity a bit dull and want to add something to it to make it worthwhile. They want to experience the feeling of vertigo and having some “skin in the game” will induce or magnify that feeling.

But perhaps the important idea is that it means spectators have a reason to personally care. They are not just watching other people play a game, they have something that means that the outcome directly affects them.

c. Add volatility

This is an interesting category to me. This is where it is important to add volatility to a result and the impact on the immediate expected value is not so important.
Some example may help to clarify what I mean:

i) You owe a loan shark £10k and if you do not pay up in full tomorrow you will be killed. You only have £5k. A good plan is to walk into a casino and put £5k on black (or red). The fact that the bet itself is slightly negative expected value is irrelevant in the broader context.

ii) You are playing chess and are doing badly, perhaps simply down a pawn or two. If you carry on as you are playing sensible moves you will very likely lose. A good strategy here may be to embrace complexity; adding complexity to the board increases the chance of a mistake from either side and may outweigh the initial advantage. Conversely if you are winning, then the simplest route to victory is best i.e. a clear technical win rather than a beautiful attack.

iii) It is the end of a movie and to defeat the monster/get the guy (or girl) /win the game etc the hero acts in a way which is highly likely to fail, but if it succeeds will end in triumph.

What is interesting about this form of “gambling” is that it is highly rational, but only applies in specific situations. If these situations were to repeat, then the expected value and volatility would be highly damaging. Unless of course you are in a Fast and Furious sequel.

d. Make consistent profits

Professional poker players or expert traders/investors fall into this category. They expect to win on average, but accept in the short term they might not. They would prefer to minimise volatility, as they are not engaging in the activity for the excitement and drama, but to make a profit. The volatility is just a price to pay for the longer-term profits.

An aspect of this that is really interesting to appreciate is the extent to which a person who is primarily motivated by winning is usually trying to minimise the feelings of excitement and vertigo. Top sports people train themselves with exercises such as breathing techniques and mental training to disengage their emotional brain as it generally leads to worse performance. Just think about golfers under stress missing short putts or footballers missing penalties in a shootout. It is the same for poker players. The amateur loves the drama but the professional is doing a job.

It is debatable whether this category of wanting to make consistent profits should be even classified as gambling.
Different people have given me clear and differing views. My view is that calling it gambling is very misleading.

This category is exactly the OPPOSITE to the first one in the grid.

  • A pure gambler plays games with NEGATIVE expected value because he WANTS volatility and wants to MAXIMISE the feeling of vertigo
  • A professional plays games with POSITIVE expected value, DISLIKES volatility and wants to MINIMISE the feeling of vertigo.

Matching motivation to the activity

All four motivations make sense. But the motivation should true up to the activity. If you are not being honest about this, it will end badly for you.

a. Excitement
You should look for a game in which you minimise your negative expected value. Then you will be able to play for longer. The dangers of gambling addiction are a massive negative impact on your life.

b. Adding interest

If you like doing it, it seems easy to self-manage. The mistake would be to pretend this is your motivation but, if you are honest, it’s more the excitement of a. This could be a gambling problem in disguise and you need to ensure you do not gamble more than you can afford.

c. Adding volatility

It is a useful skill to recognise how and when you should add volatility to what you are doing. Sometimes in a limited sense it looks risky but when you see the bigger picture it is a very logical approach.

d. Making a profit
People who enjoy playing games of skill and are emotionally able to handle short-term volatility, will enjoy and may excel at.

It is possible that with this motivation you could be seen playing high stakes poker against better players. Your motivation however must be to learn, improve and develop your skill level so that your long-term expected value becomes positive. Other motivations such as you think you are going to win, are likely to be become expensive losses to you.

I described earlier how people commonly think that excitement a. motivates the people in my profession. I also meet plenty of students who love gambling and so want to become a trader. But people like this do not succeed as this is the wrong objective.

For trading and investing, the objective is positive expected value and you want to minimise excitement (volatility). In addition, your desires will likely overwhelm your ability to make profitable decisions.

Conclusion

People engage in activities with uncertain outcomes for very different reasons. If you assume that other people are doing them for the same reasons you are you may be making a big mistake. You need to make sure that your motivations match well with the games you are playing.

Games 5 What is gambling?

I have been writing about games recently: what they are, why we play them and common confusions from not understanding the importance of volatility. A category of game that is worth further investigation are those that falling under gambling.

Definition

Gambling:

  1. Playing games of chance for money / Betting on an uncertain outcome
    “gambling on a toss of the dice”
  2. Take risky action in the hope of a desired result / taking a chance (often) recklessly
    “If you don’t back up your data, that’s gambling”
    “I’m gambling that the new store will be a success.”

I find these two main dictionary definitions to be confusing enough by themselves, but the fact they both have very different meanings can lead to even more confusion.

Is money intrinsic to the game?

If money is not intrinsic to the game, then I would say you are gambling on the game rather than the game itself being gambling e.g. betting on the result of a football match or the number of goals. Football itself is not gambling. If you play golf for money, you are gambling on the game, but golf is not gambling.

In contrast for poker, betting is intrinsic to the game. Attempt to play poker without chips and the game is reduced in skill, becoming like snakes and ladders. Chips are to poker, what goals are to football. Poker tends to be called gambling while golf does not, mainly because the monetary aspect is intrinsic to the game. Here lies an obvious confusion in the definition of the word.

Game of chance

If we go back to the games categorisation, we can observe an important issue.

Volatility?

The first thing to note is that gambling is associated with high volatility. Few people would call playing chess gambling and no-one engages in low skill low volatility games.

Does high volatility imply gambling? It is not that simple. We saw above that it is the addition of money that is critical.

Skill?

Neither definition specifies whether the game or “risky” action involves skill. I think this looseness of definition illuminating. I would say that gambling commonly implies a game of low skill and random outcome. We have seen before how high volatility often leads to the incorrect conclusion that the game is random and low skill (Game 3) We now see a similar issue with games described as “gambling”.

Let’s compare two games:

Both games are referred to as “gambling” but bear crucial differences. Poker has high volatility, but I would not call it a “game of chance” so does not even fit the original definition. However, poker is commonly described as gambling or a gambling game.

Risky vs reckless

In the above definition, both risk and reckless appear and, in common usage, can be used similarly.
However, they are very different concepts.

Let’s take a golfing example. You were the last to play on the last day of the Masters, now standing on the 15th fairway, 192 yards from the flag. Your playing partner is 2 shots ahead of you. You go for the pin.[1]

Risky? Sure
He had not managed an eagle in his previous 450 holes at Augusta

Reckless? Not at all
He needed that eagle to make the payoff which he subsequently won for his first major.

Conclusion

The problem in the definition of gambling is that it does not differentiate between an act of random chance and something which involves a great deal of skill i.e. a non-deterministic outcome with a monetary consequence.

Again we see that this uncertainly in the outcome is misinterpreted is random (logic error) and therefore there is limited skill involved (logic error) and that risk is in fact often reckless (logic error). These confusions are similar to what we have seen in games generally, but still makes them hard to spot.

 

[1] http://www.golf.com/tour-news/2017/04/09/watch-sergio-garcias-eagle-15th-masters