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In the world of gambling and trading, Ed Thorpe is a legend. He is the man who essentially perfected card counting and managed to beat a roulette table with the help of the first handheld computer ever invented. Then he moved on to Wall Street starting one of the earliest quant funds in the business and pioneering fields like convertible arbitrage.
He wrote several books, including Beat the Dealer all of which are worth reading for their entertainment value alone. But his greatest contribution to the world of trading is popularizing the Kelly Criterion which is essentially a formula for optimal bet size.
The mathematics for the Kelly Criterion along with a deep discussion of its various permutations can be found here http://www.elem.com/~btilly/kelly-criterion/. But if your eyes glaze over the moment you see a Greek letter, don’t worry, the key thing to take away from the Kelly Criterion principle is the idea of proportional betting.
The two cardinal sins of all traders are 1. Betting too large. 2. Increasing size when you have lost money. The Kelly Criterion deals with the first issue by calculating optimal opening size and deals with the second issue by betting only a fixed percentage of equity each time. This way when equity declines, the trader naturally trades smaller and when it rises the trader naturally increases size. This creates a disciplined structure to your trading without any conscious effort on your part.
But while the fundamental idea of proportional betting is truly one of the best practices in trading, the Kelly formula in its original form is full of problems. First of all, Kelly was designed for games with fixed outcomes and is, therefore, an imperfect fit for the open-ended world of trading where nothing is fixed and odds are perpetually shifting. People generally adjust for this reality by relying on the law of large numbers, but that idea assumes that you as a trader must survive ten’s of thousands of trades in order for the Kelly math to bear fruit. As Yogi Berra once said “In theory, there is no difference between practice and theory. In practice, there is.”
In trading, therefore, Kelley grossly overestimates the odds and makes trading bets too large, leading to a risk of ruin albeit it a proportionally slower rate than the normal “have-a-hunch-bet-a-bunch” approach most of us use. Many traders like to degrade the Kelly number by half or even by three quarters to establish a more realistic basis for trade size and that’s a good start but I prefer to look at the whole problem of trade size from the other end. Kelley, after all, deals with maximizing reward. In essence, it can be renamed the “Greed Formula”. I, on the other hand, believe that as traders we should always focus on the “Fear Factor”. Wins take care of themselves. It’s controlling losses that requires true skill in trading. So to that end, I’ve come up with my own proportional betting approach that makes sense for me.
Let’s assume the following things. I have a $10,000 account. I make 10 trades each day. Each trade has a risk of 85 pips (or 85 basis points). I set my daily loss limit to 1% or $100. I trade a very high probability set up that is 80-90% accurate, but let’s assume on my worst days it will be only 50% accurate ( Note this is not the WORST assumption I can make, but I am comfortable with the risk-reward implications of my approach. At very worst, if I was totally wrong I would wind up losing 2.5% of my account on any given day which is very much a survivable event.)
Let me show you why. Using my original settings I would bet 0.03 lots on any given trade. That means that if I lost 5 trades in a row I would lose $125.00 or just a bit more than 1% of my account. At that scale, if I lost 10 trades in a row I would lose $250 or 2.5% of my account – hardly a blow up in the world of FX. Once I made 10% on my account (equity grew to $11,000) to keep the proportionality in place I would increase my bet size by 0.01 lots to 0.04. Conversely, if my account declined by 10% to $9,000 I would decrease my bet size to 0.02 lots until I could rebuild the equity.
Now, this is hardly the classic Kelly approach, but it does stay true to the idea that you should bet proportionately. It also, I believe, is a more realistic approach to how we all actually trade on a day by day basis. If nothing else, the Kelly Criterion shows us that in trading, bet size is the single most important decision you can make and yet most of us – including yours truly – have been cavalier about choices for far too long.