I’m sure some people know about Efficient Frontier, but I guess there are fewer investors who know about Kelly Criterion. So what is Kelly Criterion and who is Kelly? Kelly worked at AT&T and published his original article in 1956. His mathematics is quite involved with communication and information theory, mainly in relation to probabilities. However, behind all the math, there is an astonishing result: by placing bet amounts according to the Kelly Criterion (originally applied to the game of horse racing), one can maximize returns in the long run. Here is the betting formula that has been adapted to stock trading:

K% = ((b + 1) * p – 1) / b = (b * p – (1-p)) / b

Probability of winning (p): The probability that any trade you make will return a positive amount.

Profit / Loss Ratio (b) or Odds: The total positive trade amounts divided by the total negative trade amounts.

If you think of b as the odds of ba-1, payout of b when betting 1 unit of money, the numerator is simply the average value of the expected payout, or the so-called “advantage.” Therefore, K% can be expressed as edge / odd. For an obvious reason, you don’t want to bet on any game where the expected payout is 0 or negative.

If the Kelly Criterion is so good, why isn’t it being heard or used very often in the investment world? There are a couple of reasons that prevent it from being used in a practical way:

1. The volatility of strictly using the Kelly criterion is quite large. Although in the long run, probabilistically speaking, your portfolio will perform as highly as possible, the ups and downs are too great for most people to take in. Therefore, people talk about using “half Kelly” or half the bet amount calculated from the Kelly Criterion in an attempt to reduce portfolio volatility.
2. To use the Kelly Criterion, you need to know how well you trade stocks (in p & b terms). Obviously, if you don’t know exactly what your “edge” is, Kelly’s bet amount will likely be out of the correct amount. Estimating and knowing your edge will be a much more difficult task than calculating Kelly’s bet amount.

Despite the mathematical correctness of the Kelly criterion, it is much more difficult to reverse it in practice. Is there nothing we can get away from such an excellent investment formula? In fact, there is. This is what I personally learned after investing in stocks for almost 10 years. The riskier the stocks or entry point, the less you will need to invest; The safer the stock or entry point, the more you must invest. This is exactly the spirit of the Kelly Criterion that the bet should be proportional to your edge or your supposed edge. I have been burned by stupid bets so many times that I finally learned to carefully measure each of my stock trades. In fact, the size of your transaction is just as important, if not more so, than the stocks you choose. While most of the investing world talks about what to buy, much less attention is paid to how much to buy. But for each transaction, it always consists of the following elements: what (shares) to buy / sell, when to buy / sell, and how much to buy / sell. For a successful investment, all three elements must be chosen carefully. And Kelly Criterion helps you decide the last item: how much.

For more related articles, you can refer to investopedia article. Tom Weideman also has an excellent article that uses simple calculus to derive the Kelly Criterion with less mathematics from information theory. You can find Kelly’s original article here.