Money Management: The Kelly Formula
Oct 19, 2011 at 11:50 am in Risk Management by
Money Management: The Kelly Formula
I’d like to continue my current theme of ‘money management’ by telling you about the Kelly Formula for optimising your bet sizes.
Who’s Kelly and What’s His Formula?
John Larry Kelly Jr. was a scientist who worked at Bell labs and who in the 1950s devised a formula — also known as the “Kelly Criterion” — for optimising the sizes of stakes that you place on a series of bets.
When playing any gambling game, if you know the probability of a win, the probability of a loss, and the odds you are being offered, you can calculate what percentage of funds you should stake on any one ‘turn’ using the formula:
Stake % = ((odds offered * win probability) – loss probability) / odds offered
Taking the simplest of games, let’s suppose a casino offers you odds of 2-to-1 on a coin toss, so they will pay you twice as much if you guess right than you will lose if you guess wrong. The calculation would be:
((2 * 0.5) – 0.5) / 2 = 0.25
So in this case you should bet 25% of your available funds at each turn.
Now suppose the casino is stupid enough to offer you the same odds to throw your biased coin that gives you a 70/30 chance of guessing correctly. The calculation would be:
((2 * 0.7) – 0.3) / 2 = 0.55
So in this case you should bet 55% of your available funds at each turn.
Who can us the Kelly Formula?
While the formula is applicable to any “betting game” including casino games and sports betting as well as financial spread betting, it is not a panacea in the sense of guaranteeing success. It is designed merely to keep you in the game long enough to realise your edge if you have one.
For example: although it will get you thrown out of the casino (or worse) the practice of ‘card counting’ gives you an edge in the game of Blackjack, but this edge will not be realised at all (unless you are very lucky) if you bet the farm on the first game that is dealt.
This formula prevents you from betting the farm, and since it recommends a ‘percentage of available funds’ to bet at each turn, the actual amount staked at each turn will fall and rise as your available funds are depleted through losses and replenished through wins. In this respect, it’s anti-Martingale – and that’s good!
Relevance to Financial Spread Betting
The Kelly formula can be problematic for financial traders who are trading deep-value high-risk stocks, because sometimes the formula suggests much higher bet sizes that the trader is (or should be) comfortable with. So some traders prefer to stake a consistent fraction of the suggested ‘Kelly bet’. When the formula suggests staking 50%, maybe you should stake 5% instead.
Some financial traders regard it is as nigh-on impossible to calculate the true probabilities of success and failure, so the result of the Kelly formula will be meaningless. They keep it simple by avoiding the calculation altogether and merely betting a fixed 1% of available funds on any one trade.
Tony Loton is a private trader, and author of the book “Stop Orders” published by Harriman House