The Kelly Criterion - Money Management 101

[Emmanuel Lovski Ijeawele Maduagwuna]

There are several money management systems to get ahead in this challenging business where only scholars and principled traders reign supreme.

Today we briefly re-visit the Kelly Criterion.

The Kelly Criterion (or Kelly Formula) helps an investor specify the allocation required to ensure  long-term portfolio performance given an investment’s probability of winning compared to the amount won or lost.  It is a formula for bet sizing that leads to practical portfolio growth compared to any other strategy over a sufficient period of time, and is the optimal strategy for money management in games betting.

Mathematically, it is expressed as : f% = S –[1 - S]/R where:

* f% = Percentage or fraction of capital risked per trade, 

* S = Historical Winning Percentage of a Trading System.

* R = Historical Average Reward/Risk Ratio.

[Sergey Golubev]

Money Management Revisited - MT4 article

This is the so-called Kelly criterion. Its idea is quite simple. If you have a ТS with the win probability exceeding 0.5, while profit and loss values are equal, then you need to use the funds share calculated using equation (19) when placing a bet. For example, p=0.55, in this case, f*=0.55-0.45=0.10. It means that you need to use one tenth of the funds when placing a bet in order to make the funds grow efficiently.

[Sergey Golubev]

Risk Evaluation in the Sequence of Deals with One Asset - MT5 article

In this article, we will draw on the idea of Ralph Vince on managing position volumes (in this connection, it will be useful to recall the Kelly formula as well). This is also known as the optimal f. In this theory, f is the fraction of funds that is at risk in every deal. According to Vince, f is chosen depending on the conditions of optimization (maximization) of profit. There are two problems arising when using this theory in trading. They are:

1. Too large account drawdown.
2. f is known only on the history of deals.

An attempt to solve these problems is only one of the aims of this article. Another problem is yet another attempt to introduce the theory of probability and mathematical statistics into the analysis of trading systems. This will cause occasional deviation from the main topic. I will refrain from expounding the basics. If the necessity arises, the reader can refer to the book "The Mathematics of Technical Analysis: Applying Statistics to Trading Stocks, Options and Futures".

This article features examples. They are just an illustration of the theory considered in the article, therefore, they are not recommended to be used in real trading.

[Sergey Golubev]

Optimal F for MQL5 (per Ralph Vince) - library for MetaTrader 5 (CodeBase)

I couldn't find MQL5 code for the Kelly Criterion, so I decided to write it myself; but it turned out that the Kelly Criterion only works for Bernoulli Distributions. This means it works only for fixed profits and losses, i.e. fixed SL and TP, but I rarely do.

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