Kelly Criterion and other common position-sizing methods

20 sept. 2023

What is position sizing & why is it important?

Position size refers to the amount of risk - money, contracts, equity, etc. - that a trader uses when entering a position on the financial market.

We assume, for ease, that traders expect a 100% profit or loss as a result of the profit lost.

Common ways to size positions are:

• Using a set amount of capital per trade. A trader enters with $100 for example, every time. This means that no matter what the position is, the maximum risk of it will be that set capital.
  
  It is the most straight-forward way to size positions, and it aims at producing linear growth in their portfolio.
  
  
• Using a set amount of contracts per trade. A trader enters with 1 contract of the given asset per trade. When trading Bitcoin, for example, this would mean 1 contract is equal to 1 Bitcoin.
  
  This approach can be tricky to backtest and analyse, since the contract’s dollar value changes over time. A trade that has been placed at a given time when the dollar price is high may show as a bigger win or loss, and a trade at a time when the dollar price of the contract is less, can be shown as a smaller win or loss.
  
  
• Percentage of total equity - this method is used by traders who decide to enter with a given percentage of their total equity on each position.
  
  It is commonly used in an attempt to achieve ‘exponential growth’ of the portfolio size.
  However, the following fictional scenario will show how luck plays a major role in the outcome of such a sizing method.
  
  Let’s assume that the trader has chosen to enter with 50% of their total capital per position.
  
  This would mean that with an equity of $1000, a trader would enter with $500 the first time.
  
  This could lead to two situations for the first trade:
  - The position is profitable, and the total equity now is $1500
  - The position is losing, and the total equity now is $500.
  
  When we look at these two cases, we can then go deeper into the trading process, looking at the second and third positions they enter.
  
  If the first trade is losing, and we assume that the second two are winning:
  a) 500 * 0.5 = 250 entry, total capital when profitable is 750
  b) 750 * 0.5 = 375 entry, total capital when profitable is $1125
  
  On the other hand, If the first trade is winning, and we assume that the second two are winning too:
  a) 1500 * 0.5 = 750 entry, total capital when profitable is $2250
  b) 2250 * 0.5 = 1125 entry, total capital when profitable is $3375
  
  Let’s recap: The trader enters with 50% of the capital and, based on the outcome of the first trade, even if the following two trades are profitable, the difference between the final equity is:
  
  a) First trade lost: $1125
  b) First trade won: $3375
  
  This extreme difference of $2250 comes from the single first trade, and whether it’s profitable or not. This goes to show that luck is extremely important when trading with percentage of equity, since that first trade can go any way.
  
  https://www.tradingview.com/x/qHhX6jyo/Traders often do not take into account the luck factor that they need to have to reach exponential growth. This leads to very unrealistic expectations of performance of their trading strategy.
  

What is the Kelly Criterion?

The percentage of equity strategy, as we saw, is dependent on luck and is very tricky. The Kelly Criterion builds on top of that method, however it takes into account factors of the trader’s strategy and historical performance to create a new way of sizing positions.

This mathematical formula is employed by investors seeking to enhance their capital growth objectives. It presupposes that investors are willing to reinvest their profits and expose them to potential risks in subsequent trades. The primary aim of this formula is to ascertain the optimal allocation of capital for each individual trade.

The Kelly criterion encompasses two pivotal components:

*Winning Probability Factor (W): This factor represents the likelihood of a trade yielding a positive return. In the context of TradingView strategies, this refers to the Percent Profitable.

*Win/Loss Ratio (R): This ratio is calculated by the maximum winning potential divided by the maximum loss potential. It could be taken as the Take Profit / Stop-Loss ratio. It can also be taken as the Largest Winning Trade / Largest Losing Trade ratio from the backtesting tab.

The outcome of this formula furnishes investors with guidance on the proportion of their total capital to allocate to each investment endeavour.
Commonly referred to as the Kelly strategy, Kelly formula, or Kelly bet, the formula can be expressed as follows:

Kelly % = W - (1 - W) / R

Where:
Kelly % = Percent of equity that the trader should put in a single trade
W = Winning Probability Factor
R = Win/Loss Ratio

This Kelly % is the suggested percentage of equity a trader should put into their position, based on this sizing formula. With the change of Winning Probability and Win/Loss ratio, traders are able to re-apply the formula to adjust their position size.

Let’s see an example of this formula.

Let’s assume our Win/Loss Ration (R) is the Ratio Avg Win / Avg Loss from the TradingView backtesting statistics. Let’s say the Win/Loss ratio is 0.965.

Also, let’s assume that the Winning Probability Factor is the Percent Profitable statistics from TradingView’s backtesting window. Let’s assume that it is 70%.

With this data, our Kelly % would be:

Kelly % = 0.7 - (1 - 0.7) / 0.965 = 0.38912 = 38.9%

Therefore, based on this fictional example, the trader should allocate around 38.9% of their equity and not more, in order to have an optimal position size according to the Kelly Criterion.

The Kelly formula, in essence, aims to answer the question of “What percent of my equity should I use in a trade, so that it will be optimal”. While any method it is not perfect, it is widely used in the industry as a way to more accurately size positions that use percent of equity for entries.


Caution disclaimer
Although adherents of the Kelly Criterion may choose to apply the formula in its conventional manner, it is essential to acknowledge the potential downsides associated with allocating an excessively substantial portion of one's portfolio into a solitary asset. In the pursuit of diversification, investors would be prudent to exercise caution when considering investments that surpass 20% of their overall equity, even if the Kelly Criterion advocates a more substantial allocation.


Source about information on Kelly Criterion
https://www.investopedia.com/terms/k/kellycriterion.asp