Money Management Strategy : Kelly Criterion

RiskManagement

Due to the overwhelming interest from yesterday’s posting on ‘Keys to Correct Trading Attitude: Are you Trading or Gambling?‘, I am glad to receive questions from readers on the type of money management strategies that are applied by professional traders and portfolio managers within their own private fund or proprietary fund.

We often hear about the importance of diversifying. ‘How much money do we risk in each stock?’ ‘What is the optimal risk size?’ This questions can be easily answered by a defining money management system. Here we look at Kelly Criterion, one of the many techniques that could be used to manage your risk effectively in the financial market, or even casino.

The Kelly Criterion is the the % of capital to risk, to achieve the maximum compounded growth of equity over a quantity of trade size (no. of trades). It defines the trade size to produce the greatest expected growth rate in the long run (based on no. of trades). Even when there is an edge, beyond some threshold, larger bets will result in lower compounded return because of the adverse impact of volatility. The Kelly Criterion defines this threshold.

Formula as follows:

F = Pw – (Pl/ W)

where

F = Kelly Criterion fraction of capital to bet

W = Dollars won per dollar risked (eg. win size divided by loss size)

Pw = Probability of Winning

Pl = Probability of Losing

Example 1 : A trader loses $1,000 on losing trades and gains $1,000 on winning trades, and 60% of all trades are winning trades, the Kelly Criterion indicates an optimal trade size equal to 20% of capital (0.60 – (0.40/1) = 0.20).

Example 2: A trader wins $2,000 on winning trades and loses $1,000 on losing trades, and the probability of winning and losing are both equal to 50%, the Kelly Criterion indicates an optimal trade size equal to 25% of capital (0.50 – (0.50/2)=0.25).

Kelly Criterion could mathematically demonstrate a cumulative return higher than any other strategy for determining trading size, over a large quantity of trade samples.

However, this formula assumes that the probability of winning and the ratio of the profit to loss per trade are precisely known, which is typically impossible as win/loss rate probability is often an estimate at best. The formula requires a strong application on the Law of Large Numbers (larger trade sample size increases the calculation of proficiency on every individual trader’s ability) Therefore, if the precise probabilities of win/loss are not known, then the best trade size should be significantly smaller than the full Kelly Criterion result.

On this note, if you believe your can roughly estimate your probability of winning and average win/loss ratio, then the Kelly Criterion formula can be extremely useful in defining the appropriate risk size per trade. Even in this instance, it is recommended to use 1/2 or lower Kelly for most people, for the sake of risk mitigation and capital preservation.

Jeffsun
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