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09 / 09 / 2022

The High Risk, High Reward Fallacy

The Bad Beat Story. If you are a regular in casinos or card rooms, you will know exactly how the story goes. You are all in, every single one of your chips are in play and you are holding the best hand you can possibly have, a pair of Aces. The bullets. Your bet is called by the gentleman directly opposite you then he shows you a pair of Jacks. You are flying high, seeing yourself with towers of chips ready to take to battle in the next hand. Then comes the flop, the turn and then the river…. a Jack. Your opponent has made Three of a Kind which beats your Pair of Aces. You have lost all your chips, you are incandescent, don’t believe how unlucky you have been. Again. You feel compelled to tell everyone around how unlucky you’ve been, that once again you’ve been the victim of a Bad Beat.

To put this into context as to how unlikely this is for those who don’t know the poker maths, the probability of losing in this situation is 20% or 1 in 5 times. Which all in all is actually not that unlikely at all! It’s more likely than rolling any given number on a six sided dice, and anyone who has played a board game before will have a sense of how likely that is. Why in such cases do we have an underlying sense that these events that aren’t in fact particularly rare are so remote and why when they occur do they affect us so?

Very Superstitious

As human beings we are terrible at properly gauging probabilities, in particular when it comes to repeated events. We are hard wired to follow patterns and behave accordingly. You grow up learning by trial and error, you touch a hot frying pan, you hurt yourself and you learn to never touch a hot pan again. Seeing trends and behaving accordingly is key to how we evolved and survived, however this trend-following in fact distracts us in many cases to what is truly going on. We are inherently biased.

To return back to a gambling analogy, roulette is a game most people would have played or at least heard of, but simply put a wheel is spun and it will land on a single number between 0 and 36 and you can bet on the outcome. If you get the outcome correct you win money, if you don’t then you lose your bet. Additionally you can bet on if the number will be odd or even and other outcomes. Suppose you come to a roulette table and you see the number 25 has appeared 5 spins in a row. What is your reaction? Your inherent instinctive feeling (despite what you might be determined to say it is) will be in one of two camps:

  • You believe that this is a trend and as such it is highly probable the next spin will more likely be 25 again;

  • You believe that 25 has now come up too often, so to even things out the next spin is much less likely to be 25.

In fact both of these thoughts would be entirely wrong, the next spin being the number 25 has the same likelihood to occur as it always has.

This is a simple example, but this bias is seen in all manner of situations, and defines how we go about our daily lives and influences all our decision making.

What is Risk?

Over the years working in finance and asset management, I have seen risk defined and quantified in many different ways, though risk in itself applies to all sorts of situations in life and beyond.

Whether you are crossing the road, trading cryptocurrency or choosing your next holiday destination you are assessing the chances of an adverse event affecting your desired outcome when you make each decision. When you make that decision you make a judgement on: the positive value to you of the desired outcome coming true and the negative value associated to the desired outcome not occurring as you would like. Then you compare these values of the various likelihoods of each outcome, and if the likelihood of success is high enough compared to the positive outcome (and similarly the equivalent is true that the likelihood of the event not going in your favour being low and the negative value associated with it) then you make that decision.

In my opinion, risk should be defined by both the likelihood of a negative value event occurring as the result of a decision but also how negative that event might be to you. This might seem obvious, however hopefully by the end of my article it will be clear why I am highlighting both the likelihood and the quantum of negative value effect.

Most approaches to risk will only analyse the potential loss and not the likelihood. Why is that? It is much easier to gauge and measure the loss, whether monetary or not. You have a pretty good idea of the consequences say if a very negative outcome occurs when you board a plane!

As I have said in the previous section we not only have a terrible grasp intuitively of the likelihood of events, but most of the time events happen singularly. They are not repeatable. As such there is no “experiment” which could be carried out to work out the exact probabilities. Very few real outcomes can we determine the chances exactly, beyond very simplistic gambling examples. For example, when you hire someone for a role, you can’t know with exact probability the chance that they will be a good hire. As such, most simple risk analysis approaches focus only on the potential loss.

In finance and economics more broadly, you often carry out stress testing to see what would happen to a company or a portfolio. You calculate what the loss would be in that scenario without a full appreciation of the likelihood of that stress test.

The High Risk, High Reward Fallacy

A quick trip on Twitter or Instagram you will see plenty aspiring to be the next most successful entrepreneur, and that is fantastic. There is nothing wrong with ambition. What do you do see a lot though, are these motivational multi-step guides to success. One phrase which comes up repeatedly is “High Risk, High Reward”. People’s misunderstanding of this phrase is evident. People take this in many multiple ways, that if you take high levels of risk you will get high rewards, or that the only way to success is via taking high risk. Both of these are incorrect. In fact the truth is, in a sense you will make the same reward regardless of the risk you choose to take. Let me explain.

Let me take a basic example, I give you the chance to bet on 1 million coin flips or 1 million dice rolls. You wager the same each time. If a coin flip is a success you double your money, if you get the correct roll of the dice you get six times your bet. If you want to maximise your earnings what do you choose? In the long run, the expected outcome is exactly the same. This is despite each dice roll being both higher risk and higher reward than the coin flip. But that’s exactly the point, you are being rewarded exactly the amount for the given risk, thus in the long run in this repeatable example it makes no difference because you will lose enough coin flips or dice rolls to make up for the amount you are winning.

Throughout your life, you will make innumerable decisions, all of which will add together, and as such in the end everyone should have the same outcome, since the rewards will even out the losses as above. We all know that this isn’t true, some people are much more successful that others. So why is this? In the above example you are rewarded exactly the amount equivalent to the risk you take, this is simply not the case in real life. As previously discussed, we don’t know what the likelihood of different events are and even how to quantify eventual rewards, not only is this difficult to measure but humans are inherently bad on the whole at understanding risk because of underlying biases.

All the time you see situations where people take significant risks in their lives and careers and they fail, the risks were very high and the rewards were simply not there. People putting all their savings into their business idea, which in the end was always going to fail because the business plan was not correctly thought out.

Taking high levels of risk does not always come with potential high rewards. It is about identifying the likelihoods and whether the potential rewards make up for that risk. This is why risk management is key.

Understanding clearly the probabilities and gauging the risk-reward profile of every decision is the route to correct decision making. Success doesn’t come from taking high risk, it come from taking decisions which appear higher risk, that are in fact lower risk and you can reap the benefits of the higher rewards.

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