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## Kelly Criterion for Stock Trading Size

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 paper in 1956. His mathematics is quite involved in communication and information theory, dealing primarily with probability. However, behind all the calculations there is an astonishing result: by placing bet amounts according to the Kelly criterion (originally applied to games of chance on horse racing), one can maximize long-term returns. . Here is the betting formula that has been adapted to stock trading:

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

*Win Probability (p): The probability that a given trade you make will earn a positive amount.*

*Win/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 b against 1, the payout of b when you bet 1 unit of money, the numerator is simply the average value of the expected payout, or what is called “the edge”. Therefore, K% can be expressed as edge/odd. For obvious reason, you don’t want to bet in a game where the expected payout is 0 or negative.

If Kelly Criterion is so great, why isn’t it heard or used very often in the investment world. There are a few reasons that prevent it from being used practically:

- The volatility of strictly using the Kelly criterion is quite large. Despite the fact that over the long term your portfolio is likely to have the maximum return possible, the ups and downs are too big for most people to digest. Therefore, people talk about using “half Kelly” or half of the amount of the bet calculated from the Kelly criterion to try to reduce portfolio volatility.
- To use the Kelly Criterion, you need to know how much you trade in stocks (in terms of p&b). Obviously, if you don’t know exactly how much your “edge” is, the Kelly bet amount will likely be different from the correct amount. Estimating and knowing your edge will be a much more difficult task than calculating the Kelly bet amount.

Despite the mathematical accuracy of the Kelly criterion, it is much more difficult to invest in practice. Is there nothing we can get away from with such a great investment formula? Indeed, there are. Here’s what I’ve personally learned after investing in stocks for almost 10 years now. **The riskier the stock/or entry point, the less you need to invest; the safer the stock/or entry point, the more you need to invest.** This is exactly the spirit of Kelly Criterion that the bet should be proportional to your advantage or supposed advantage. I’ve been burned by stupid bets so many times that I’ve finally learned to carefully size each of my stock trades. In fact, your trade size is just as important, if not more so, than the stocks you choose. While most people in the investment world talk 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 (stock) to buy/sell, when to buy/sell and how much to buy/sell. To invest successfully, all three elements must be chosen carefully. And Kelly Criterion helps you decide on the final element: how much.

For more related articles, one can check out the investopedia article. Tom Weideman also has a great paper using a simple calculus to derive Kelly’s criterion with less math from information theory. You can find Kelly’s original article here.

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