# Kelly Criterion for Stock Trading Size

Im sure some people know about Efficient Frontier, but Im guessing that there are less investors that know about Kelly Criterion. So what is Kelly Criterion and who is Kelly? Kelly worked at AT&T, and published his original paper back in 1956. Its math is quite involved with communication and information theory, mostly dealing with probabilities. However, behind all the maths, there lies an astonishing consequence: by placing bet amounts according to Kelly Criterion (originally applied to horse-race gambling), one can maximize the returns in the long term. Here is the betting formula which has been tailored to stock trading:

K% = ( (b+1) * p – 1) / b = ( b~p – (1-p) ) / b
Win probability (p): The probability that any given trade you make will return 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-to-1, payout of b when betting 1 unit of money, the numerator is simply the average value of expected payout, or the so-called edge. consequently, K% can be expressed as edge/strange. For obvious reason, you dont want to bet in any game where the expected payout is 0 or negative.

If Kelly Criterion is so great, why is that this is not heard or used very often in the investing world. There are a associate of reasons that prevent it to be used nearly:
For more related articles, one can check out the article from investopedia. Tom Weideman also has an excellent article using simple calculus for deriving Kelly Criterion with less math from information theory. You can find the original Kellys paper here.

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