What is the Impossible Trinity of Position Sizing
When we think about the number of lots to trade (position sizing), we may face an interesting situation called the Impossible Trinity of Sizing. The Impossible Trinity of Sizing is a trilemma which states that it is impossible for us to control over all 3 of the following at the same time:
- Stop Loss Size
- Risk per Trade
- Leverage Used
The Impossible Trinity of Sizing states that we can only control at most two of the three factors - Stop Loss Size, Risk per Trade and Leverage Used.
This trilemma exists when we use an account risk position sizing method. To recall, the account risk method calculates our trade size according to the percentage of our account balance that we are willing to risk. Hence, if we have a $100,000 account and we plan to risk 2% per trade, we need to trade a certain quantity such that we lose $2,000 in one trade.
Quantity per Trade (in $) = (Risk per Trade * Account Balance) / Stop Loss Size
Quantity per Trade (in Lot) = (Risk per Trade * Account Balance) / (Stop Loss Size * Contract Size)
Application to Trading
Let us examine what happens when we try to control all three factors. Here’s our setup:
- Trading EURUSD
- Account balance of 100,000USD
- Risk 2% per Trade (Determined by us)
- Stop Loss Size of 100 pips (Determined by us)
- Leverage Used (Undetermined)
Based on the above formula, we trade 2 lots. Leverage Used is 2 to 1 (Trading 2 lots requires $200,000). We decided to control Risk per Trade and Stop Loss Size in this example and Leverage Used was decided for us.
We can see that it is not possible to control Leverage Used in this situation. If we want to control our leverage, we need to modify the values of Risk per Trade or Stop Loss Size to ensure our Sizing Algorithm functions accurately.
Selecting Two Corners
The million dollar question is: Which two factors should we control?
Scenario 1: Controlling Stop Loss Size and Sizing
Stop Levels and Sizing should be strategy-dependent. Thus, our first choice is to control Stop Loss Size and Sizing.
Problems arises when our broker does not give us enough leverage for our trades. In this case, we need to decide if we want to give up control on Stop Loss Size or Sizing. In order to decide this, we must understand which factor is more important for our robot’s performance.
Scenario 2: Controlling Stop Loss Size and Leverage Used
Giving up control over sizing is synonymous to leaving your money management strategy to your broker. Fortunately, this may decrease your upside but will not increase your downside per trade.
Let us assume that our broker gives us a maximum leverage of 1.5 to 1. In our previous example, we need a leverage of 2 to 1. If we fix our Leverage Used to the maximum amount (1.5 to 1), our Risk per Trade drops to 1.5%.
If our broker gives us a maximum leverage of more than 2 to 1, our Risk per Trade will stay at 2%. Our broker cannot force us to increase our Risk per Trade by increasing maximum leverage. Hence, the amount we risk (downside) will not increase.
Scenario 3: Controlling Sizing and Leverage Used
At AlgoTrading101, we believe that Stop Loss Size is a tool to buffer market noise. Hence, giving up control of Stop Loss Size is usually a bad idea. However, there are times when retaining control of Sizing is more important than Stop Loss Size.
For example, strategies such as martingale betting (not recommended) require a specific sizing structure to work. When faced with such strategies and leverage limitations, we opt to give up control of Stop Loss Size.
This article serves to explore the effects of leverage limitations. Traders need to be aware of the impact these constraints have on a robot’s architecture in order to design long term profitable strategies.
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Lucas has been designing and building algorithmic trading robots since 2010. He worked at a proprietary trading firm and taught programming for financial applications to Government of Singapore Investment Corporation (GIC), one of the largest sovereign wealth funds in the world. He runs this blog and the AlgoTrading101 course.