“What would you do if you were invited to play a game where you were given $25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60 per cent of the time?”
So begins a research paper* by Richard Haghani, founder and chief executive of Elm Partners, and Richard Dewey, from bond fund manager Pimco. It shouldn’t surprise you that quite a few people were willing to play. Haghani and Dewey limited their experiment to 61 participants playing an online version of the game (with real monetary rewards).
It also shouldn’t surprise you to know that, while they knew that the odds were in their favour, most people didn’t know the optimal strategy for maximising their profit over the 30 minutes available. That’s because, outside the professional gambling fraternity, few people have heard of the Kelly Criteria.
This mathematical formula, published by John Kelly in 1955, optimises profit in games of chance where the odds are skewed towards the player. We won’t go into the details here (Matt wrote a Kelly Criteria blog post a few years back) but, given the game described by Haghani and Dewey, a profit maximising participant should bet 20 per cent of their available funds on each flip of the coin. Bet any more than that and the inevitable run of bad luck is going to be ruinous. Bet less and you are leaving too much profit behind. The concepts coming out of Kelly’s formula are useful additions to an investor’s tool kit. For an entertaining introduction to its use in practice, try William Poundstone’s book Fortune’s Formula. But it is impossible to apply his profit maximising mathematics directly to the stockmarket, where the probabilities and payoffs are unknowable and often interdependent.
What is most fascinating is how many participants in the experiment managed to make a complete mess of the wonderful opportunity presented to them. The 61 subjects were university-aged finance and economics students and young professionals at leading asset management firms. Yet one-third ended up with less money than they started with. And an astonishing 28 per cent lost more than 90 per cent of their initial $25. To put this into context, a strategy as simple as having 25 bets of $1 would result in only 15 per cent of participants losing money. It is hard to imagine how so many people got it so wrong. Until, that is, you think about the strategies employed by those who lost money and how common these are in the real world.
Human biases bring us unstuck
The authors interviewed subjects after the experiment and found out that they were, not surprisingly, all too human.
“Without a Kelly-like framework to rely upon, we found that our subjects exhibited a menu of widely documented behavioral biases, such as illusion of control, anchoring, over-betting, sunk-cost bias, and gambler’s fallacy”.
The latter was probably the most common. Gambler’s fallacy is the mistaken belief that because something has happened more frequently in the recent past, it is less likely to happen in future. If three heads come out in a row, for example, most of us intuitively feel that the next flip is more likely to be a tail. Almost half (48 per cent) of the experiment participants bet on tails more than five times, despite it being the lower probability outcome.
There is a vast amount of data about stock prices and movements and you can find almost any pattern you are looking for in the historical numbers. Our propensity to extrapolate these random patterns into the future has sold many an expensive charting program and spawned pages of industry sayings, like “Sell in May and go away, come back on St Ledger’s day.” Most are useless. Some can be extremely costly.
Avoid the desire to double down
Perhaps the most useful general principle from Kelly’s criteria is that you should bet a constant percentage of your available funds. So, if your first bet is $5 (20 per cent) on heads and it loses, you should bet only $4 out of the remaining $20 on the next round. If you win your first bet, your next bet should be $6 out of the $30 of available funds. Reducing bets as the portfolio shrinks dramatically reduces the damage from a run of bad luck.
In practice, we tend to do the opposite.
At best, we tend to invest the same $5 on every bet, irrespective of the size of the portfolio. At worst, we increase our bets, assuming that the run of bad luck must come to an end.
How often have you felt this same desire to dig yourself out of a hole in the stockmarket? Our propensity to double down, imagine we are “due a win” and to try and win back losses often has disastrous consequences.
The odds may not be well defined for every stock you buy, but they are certainly in your favour. Over more than 100 years, simply owning the Australian sharemarket has returned roughly 10 per cent a year. Yet many investors manage to lose money despite that. The reasons why can be seen in a simple game of coin flip.
*Rational Decision-Making Under Uncertainty: Observed Betting Patterns on a Biased Coin. Victor Haghani and Richard Dewey. Working Draft October 19, 2016
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