# What Does Negative Mean In Math latest 2023

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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:

1. 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.
2. 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.

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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