The Kelly Criterion – Effective risk management technique
You bet on the flip of a coin for 30 minutes.
Coin is biased with a 60% probability of coming up heads
You can bet as much as you like on each flip
You will be given a cheque for however much is left in your account at the end of your 30 minutes
The results of the above experiment highlight an apparently gaping hole in the quantitative knowledge of ‘financially trained’ individuals when Wall Street is fiercely debating the worth of active management.
That’s because the best betting strategy for this experiment is dictated by mathematics – specifically the work of John Larry Kelly, Jr.
The Kelly Criterion – to maximise profits through the optimal investment of a fraction of their bankroll. Mathematician Ed Tharp seized on Kelly’s work for fleecing casinos and then price options – correctly. *
The success of the Kelly Criterion relies on its ability to smooth earnings and losses – enabling gamblers to bet in larger amounts as their wealth grows and vice-versa.
In the above experiment the Kelly Criterion would tell the subject to bet 20% of his account on heads on each flip.
Bet 1 – $5 (20% of $25)
if he won he’d then
Bet 2 – $6 (60%)(20% of $30)
or if he lost he’d bet
Bet 2 – $4 (40%)(20% of $20)
and so on.
Only 20% of the 61 participants reached the maximum payout of $250, well below the 95% that should have hit maximum pay dirt by simply deploying a ‘simple constant percentage’ betting strategy. 33% of participants lost money and 28% went bust.
Without a Kelly-like framework subjects exhibited behavioural biases such as illusion of control, anchoring, over- betting, sunk-cost bias and gambler’s fallacy. Gamblers fallacy is the mistaken belief because something has happened more frequently in the recent past; it is less likely to happen in the future.
The ability of portfolio managers to justify their commissions has become a major point of contention for it has allowed cheaper passive investment managers to seize market share. There is a gaping divide between the passive managers and the complex quantitatively driven LTCM founded in 1988 but later bailed out because of huge losses.
‘If a high fraction of quantitatively sophisticated financially trained individuals have so much trouble playing a simple game with a ‘biased’ coin, what should we expect when it comes to the more complex and long-term task of investing ones savings?’
Even though the odds were in their favour most people didn’t know the optimal strategy for maximising their profit. Few people have heard of the Kelly Criterion.
Constant proportion betting.
The most useful general principle from Kelly’s Criterion is that you should bet a constant percentage of your available funds. Reducing the bets as the portfolio shrinks, dramatically reduces the damage for a run of bad luck. In practice we tend to do the opposite. How often have you felt the desire to dig yourself out of a hole in the stock market?
Money management plays a key role in defence and attack. Liken it to war if you like but the disciplined deployment of a well thought out strategy that balances defence with attack in the stock market is more likely to bring you success than a ‘flying blind’ approach. It is still amazing how many investors and financially trained investors still don’t grasp this concept.
*Ed Tharp books – A Man for all Markets and Beat the Market
Attribution: Based on a research paper By Richard Haghani, founder and chief executive of Elm Partners and Richard Dewey, bond fund manager of Pimco
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