Today I will continue the review of Daniel Kahneman’s “Thinking, Fast and Slow” with the third article of the series (the first two can be found here – 1, 2). After talking about overcoming overconfidence and understanding extreme events today I would like to address arguably the most important aspect of Kahneman’s work – namely Risk Aversion and how we can get a hold of our fear of the unknown.
Entering this topic we are getting into the domain of Prospect Theory – a body of works deemed so important for the field of economics that Kahneman was awarded the Nobel Prize in Economic Sciences for his contribution to it. Prospect Theory is central to the concept of behavioural economics and deals with the ways we approach losses and gains and our attitudes towards uncertainty. We will look into how we can best employ Prospect Theory to improve our betting and how to reduce the logical fallacies we are committing when dealing with risky situations.
Dealing with Risk Aversion
Patience pays out – don’t cash out
In a chapter about the benefits of patience the author tells a story of an experiment, where a four-year old child is offered either a cookie now, or two cookies in 15 minutes if the child manages to sit on a table for those 15 minutes without eating the first offered cookie lying in front of it. Some children endured the 15 minutes and some not, but the interesting part of the experiment comes many years later when the same kids were tested again on various measures for cognitive control. It turned out that the four-year olds, who managed to wait for 15 minutes in order to get two cookies, scored higher on intelligence tests, were less likely to take drugs and were in general better at allocating their attention according to their choosing.
There is something to take out here not only for your betting activities, but also in general – patience seems to pay out. As a punter you should always think in numbers and avoid your urges to act fast on anything if the payoff is not worth it. As an example, if you have a bet that is going well but the event has not closed yet, the bookie will often offer you a cash-out option. The cash-out price will be unfavourable, but many punters would rather take it in order to secure the winnings instead of taking a risk and letting it run. This is just one of the many examples in betting where a lack of patience would cost you money. Train yourself to think in averages and not to obsess over single bets and your wallet would thank you later.
Losses loom larger than gains – insurance is costly
In the early stages of Kahneman’s research in the field of behaviourial economics, he and his partner Tversky have discovered one very obvious violation of the rules a rational economic agent is supposed to obey – apparently, we humans regret losses more than we enjoy winnings of the same or similar magnitude. That is why we are ready to pay extra in order to insure ourselves. Furthermore, Kahneman claims, the less you have, the more you are inclined to pay for an insurance premium, since having no “backup money” makes it next to impossible for you to recover from a big loss.
Experiments show that most people tend to avoid a gamble even when it has a positive expected value. Just ask yourself what price would you pay to participate in a coin toss with a 50% chance to win $100 – if your answer is anything less than 50$ you are clearly more of a risk-avoider, as most people are. Expected value should be approached with caution as the St. Petersburg paradox shows, but in most situations it is still supposed to be a pretty good indicator for the fair price of a bet. Nevertheless most people are not even ready to pay anything near that “fair price”. Clearly, we punters are somewhat different in that respect and have somewhat higher tolerance for risk. Yet we too sometimes fall into the trap of paying an insurance premium, which is ultimately causing us to lose money.
It is often said that you should bet only what you can afford to lose. If breaking your bank would be a life-changing event for you, you probably shouldn’t play at all. The financial reasons for this are clear and have often been discussed, the behavioural – not so much.
It is not only about being at the mercy of lady Fortune. Not being able to afford a loss would obscure your judgment and force you to make financially unsound decisions. Next to cashing out (the drawbacks of which I have explained above) there are further ways of hedging your exposure to a bet. You would most often place the opposite bet at another bookmaker, which would allow you to insure yourself at the best available price on the market instead of restricting yourself to the price offered by the original bookie. This will normally be less expensive than a cash-out, but would still cost you something. The optimal course of action if you want to maximize your return would be to take the bet with an edge and not cover it anywhere. The price you will need to pay for maximising your expected return would be that you would have to live with the risk – which in betting tends to be very high, at least in the short term. If you cannot afford to take the risk you would be reducing your edge and if you have to do that – you probably should not be betting in the first place.
Prospect Theory – Risk-averse in the profits, risk-seeking in the losses
Prospect Theory is arguably the pinnacle of Kahneman’s work in behavioural economics. It is the alternative he and his research partner Amos Tversky suggested to the Utility Theory, which is by now well-established in economics. Prospect Theory suggests that people threat profits and losses differently and that changes in people’s utility are caused by changes of wealth rather than by states of wealth. To illustrate the point, consider the following two problems:
Problem 1: Which do you choose?
Get $900 for sure or 90% chance to get $1000
Problem 2: Which do you choose?
Lose $900 for sure or 90% chance to lose $1000
If you are like most people you would have picked the sure win in Problem 1 and you would have gambled to avoid the loss in Problem 2. Classical Utility theory has no explanation for this choice, but Prospect theory does have one. You can have a look at the utility from certain changes of wealth as suggested by the utility curve of Prospect Theory. On the vertical axis you have the utility a person is receiving from winning/losing certain amount of money. That basically means how happy/unhappy you are from a certain outcome. On the horizontal axis you have the different amounts.
Notice that the curve in the lower left quadrant is steeper then the one on the upper right, referring to the fact that we normally are more disappointed from losing certain amount than we are satisfied for winning the same amount. However, the “loss” line in the lower left is more curved, referring to the observation that after a certain amount we become indifferent to the size of the loss faster than it is the case for gains – risk-seeking in the losses, risk-avoiding in the gains. While this might seem a little too theoretical at a first glance, it might actually have profound implications for the world of betting.
When betting on the favourite in a football game you essentially take on a small chance for a large loss and a large chance for a small profit (see Problem 1). This is a risk you are biologically programmed to dislike and a situation in which you would be risk-averse and tend to avoid this gamble. On the contrary, when betting on the outsider you take on a large chance for a small loss and a small chance for a large profit. This turns out to be a situation we are programmed to like better.
It might have to do with the fact that we tend to underestimate large probabilities and to overestimate small probabilities. If it weren’t so, a whole industry of lottery ticket selling probably wouldn’t exist. Or it might be that in early human societies large losses could have cost you not only your money, but your life as well. On the other hand if your life was already at stake your survival instinct would dictate you to try to achieve the impossible, even if the probability for success is slim. You certainly don’t think about risk aversion when fighting for your life.
Whatever the reason, it has been proven numerous times in experimental setting that most of us treat risk in losses differently than risk in profits. Kahneman provides summary of our attitude towards different situations with the Fourfold Pattern. The picture below refers to the chance of winning a court trial and the attitude towards an offered settlement in any of the given cases, however it can easily be applied to any other area.
We are ready to accept an unfavourable price if we are faced with a small chance of a large loss. Conversely, enjoy a lottery-ticket type of gamble and are unwilling to give it up even when offered a favourable price. All this leads to a clear preference for backing an outsider as opposed to backing a favourite in a betting context. The favourite-longshot bias is a well-known and long-lasting phenomenon in the betting markets and the above might be just another one of the reasons behind it. Therefore, all else equal, a strategy backing the favourite is more likely to be a profitable one as the base rate there is more favourable to the punter. I would even argue it is usually the best starting point for any betting strategy. However, a punter would need to overcome his inclination to lottery-ticket bets and learn to live with the large losses that a favourite-backing strategy will deliver every now and then.
The Certainty Effect
It has been already mentioned above that according to prospect theory people tend to overestimate low probabilities and underestimate high probabilities. It turns out that this effect is especially profound when it comes to extremely high and extremely low probabilities. Consider the following problems:
Problem 1: 61% chance to win $520,000 OR 63% chance to win $500,000
Problem 2: 98% chance to win $520,000 OR 100% chance to win $500,000
What is your preference in the two cases? When asked, most people would prefer the left hand option in the first problem and the right hand option in the second one. However, if you think about it more carefully, such choice does not make a lot of sense. The second problem, compared to the first one, adds 37% chance to win $520,000 in the first option and the same 37% chance to win $500,000 in the second one. Since the first amount is higher in absolute terms, the expected value added to the first option in Problem 2 is strictly higher than the expected value added to the second one. Therefore, if you choose the first option in the first problem you must choose it in the second one too. This is not what happens in reality. This set of problems has been labelled the Allais paradox, named after Maurice Allais, a French economist who presented it to a circle of the most esteemed economists of his time. The majority of them committed the same logical mistake that most people do when faced with these two problems.
The problem most people are having with the 98% chance is that it is just 2% short of the sure thing. This is where we tend to take our risk aversion level to the extreme. We seem to prefer the sure thing – that preference is being labeled by Kahneman the “Certainty Effect”. A two percent chance not to get what we want causes us a disproportional amount of stress – a stress we are ready to pay dearly to get rid of. This very simple fact is at the core of the multi-billion insurance industry, but is also something that could be used in betting. Placing a bet on an almost sure outcome is something most punters wouldn’t do, since the profit from it is minuscule but the chance to lose it all is still there. If most punters tend to avoid it, there might be some value there. Therefore, designing your betting strategies with the experiment above in mind might bring you some benefit.
The endowment effect refers to our preference to things that are currently ours compared to things that are not. In general we favour the status quo – perhaps because even if we don’t like it, at least we know it well, whereas we fear the uncertainty that comes with the alternative.
In classic economic theory such preference should not exist – the value of goods should not be dependent on who is in possession of them. However we frequently add a premium when selling our belongings and pay less when we acquire a similar item from someone else. Kahneman recalls an acquaintance of him collecting wine bottles, who was ready to give a maximum of $30 on an auction for a bottle of wine he liked. When asked for how much would he part with a bottle he already owned, he suddenly increased the price to $100.
This does not make much sense in the context of classic utility theory, however it is a behaviour observed in humans time and time again. We tend to exhibit preference for things that we consider ours – be it a betting strategy that we have formulated or one that we have purchased from someone else. However, we should not forget that regardless of whether we are following that strategy or just saw it on the Internet a few minutes ago, it is not “ours” any more than any alternative strategy and should answer to the same set of standards as any other.
In that context, risk aversion might actually be the dominant strategy. It is recommended that you define certain objective rules (profitability, volatility, availability of bets, cost of discovery of eligible bets, etc) and put any strategy you follow or consider following to the test in regular intervals. In that way you would filter out any subjective and irrational preference you have towards any of your betting strategies.
That was it for today’s article and the third part of my review of Daniel Kahneman’s “Thinking, Fast and Slow”. Stay tuned for the fourth and final article of the series dealing with the topic of Successful Habits and Policies. Good luck and till the next time!