![]() You can confirm this yourself using three glasses of water, one hot, one cold and the other with a temperature in between.įor a minute or so, leave your left hand in the hot glass and your right hand in the cold, before immersing both simultaneously into the one in between. Via evolution our neural circuits have become finely tuned to detect relative changes in stimuli rather than absolute values. Since we represent the winners in the line of evolution (we are here after all), it necessarily implies that loss aversion is a preferentially selected adaptation according to natural selection. As Kahneman has explained, living things that evaluate threats more urgently than opportunities have a better chance of surviving and reproducing. How high would the win probability have to be before you’d consider changing your mind? 60%? 70%? 95%? Higher?Īn evolutionary explanation for loss aversionįrom an evolutionary perceptive, it’s unsurprising that losses motivate us more the gains. Would you accept a fair even-money bet that could grow your bankroll by a third if it won, but shrink it by a third if it lost? If you wouldn’t, like I suspect most of us, then you are demonstrating loss aversion. And in terms of the utility of gains and losses, we dislike losing more than we like winning. Kahneman proposes that, since few of us pay much attention to these reference points, our attitudes to gains and losses are not derived from our evaluation of absolute states of wealth, but rather relative ones. In A it was existing wealth + $1,000 in B it was existing wealth + $2,000. The explanation is that problems A and B have different starting or reference points. Since in this example they don’t, respondents were obviously not behaving rationally. When Kahneman and his colleague Amos Tversky experimented with this teaser they found that the majority of respondents preferred risk aversion (and took the sure thing) when faced with the gain in A and risk seeking (and took the gamble) when faced with a loss in B.Įquivalent statements of the same decision-making problem should yield identical choices. If you choose to gamble, you will end up with either $2,000 or $1,000, depending on the outcome. If you choose the sure thing in either A or B you will end up with $1,500 (in addition to your existing wealth). In terms of absolute wealth, the outcomes for problems A and B are identical. You are now asked to choose one of two options: You are now asked to choose one of two options:ī) You have been given $2,000 in addition to your existing wealth. In his book Thinking, Fast and Slow, Daniel Kahneman explains how with a simple thought experiment.Ī) You have been given $1,000 in addition to your existing wealth. Understandably, this is not the sort of drawdown that most bettors can tolerate, even if there are other opportunities available to grow the bank by a similar magnitude.įor most people, even risk-seeking people, losses of this magnitude hurt significantly more than gains of a similar magnitude. PSG’s match against Caen ended in a draw and nearly a third of a Kelly bankroll would have been wiped out in a single bet. After accounting for the margin, this implied an expected advantage of 11.5% (assuming the Pinnacle market is wisest) and a Kelly stake percentage of 32.8%. A rival bookmaker priced PSG at 1.35 to beat Caen, whilst Pinnacle had 1.20. If we remind ourselves how a Kelly stake size is calculated (edge – 1 / odds – 1), sudden and large drawdowns will arise where a short price bet, which we believe holds significant positive expectation, loses.Ī Ligue 1 match from this month provides us with an example of the above. In other words, the evolution of the bankroll is volatile. It is frequently commented that a big problem with Kelly is that bankroll growth will be erratic, with profits interrupted by sometimes significant losses. In this follow up I investigate what we can do to reduce those variance risks and what impact that will have on expected profitability. uninvestably high” in his analysis of the Kelly Criterion. However, it was still clear that Joe Peta had a point when he wrote: “no matter what you calculate your expected return to be, your variance will be ridiculously. Rather surprisingly, I found that Kelly was able to accommodate the risks of not knowing precisely your advantage so long as you are accurate on average. ![]() To recall, Kelly advocates staking in proportion to the probability of winning and your perceived advantage you hold over the bookmaker’s odds. In my article last month I revisited the Kelly Criterion as a means of money management.
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