The optimal capital allocation in trading is most likely not very well understood by most traders. The balance between attack and defense is often a thin line. Most of us are optimists and we rarely watch out below. It’s human nature – pessimists never won any wars! What is the optimal capital allocation in trading?
You can calculate the optimal capital allocation in trading by using two very simple formulas: the Kelly Criterion and a formula provided by Wolf von Rönik.
They are both theoretical values, of course, but they provide you with estimates but foremost an understanding of how you can better balance attack and defense in trading.
Before we go on to calculate the optimal capital allocation in trading, let’s briefly discuss the most important factors in trading:
What is most important in trading?
The most important thing in trading is having a trading edge. In a former article, we asked the following: is focusing on psychology overrated in trading? We still believe it is and the assumption is correct. However, trading is mainly about three things:
- Having a trading edge.
- Know yourself and your limit. You need a trader’s mindset.
- You need proper risk management.
The first bullet point is by far the most important one, but this article is mainly about the third point. Avoiding big drawdowns and the risk of ruin in trading is very important. To balance that you need to have some ideas of what is the best allocation of your capital.
First, let’s define what we mean by risk in trading.
What is risk in trading?
We define risk as the chances or probability that you will suffer losses that force you to stop or be unable to recover from a financial loss. It doesn’t necessarily mean that you lose “everything”.
Our experience is that very few traders and investors have what it takes to go through a severe drawdown in trading. When the drawdown exceeds 20% many simply stop trading or make substantial changes to their strategies.
They start fiddling with their strategies and in reality abandon them. What looks so easy in backtesting is not as easy in the midst of a drawdown.
Why do you want to minimize risk in trading?
If you lose 50% of your capital you need to make 100% to recover. If you lose 75% you need to make 400%. The math makes it pretty easy to see why you want to avoid any substantial losses.
With that in mind let’s go on to look at the optimal capital allocation in trading:
What Is The Optimal Capital Allocation In Trading?
Let’s start by explaining the Kelly Criterion:
What is the Kelly Criterion?
The mathematician John Kelly made a formula in 1956 that looked at the optimal betting size when the expected returns are known.
The whole idea with the Kelly Criterion is that you need to understand the difference between arithmetic and geometric averages. The Kelly Criterion is based on the expected geometric return and not the arithmetic average. It maximizes the expected value by considering the risk of ruin and losses. To better understand the Kelly Criterion we also recommend one of our older articles about linear vs logarithmic charts and scale.
A typical log scale of the Kelly Criterion looks like this (taken from Mark Spitznagel’s Safe Haven Investing):
How to calculate the optimal betting size by using the Kelly Criterion
The Kelly Criterion is straightforward: it’s only dependent on two inputs.
- The win/loss ratio – the win percentage of your trading strategy (R) (dividing the total gains of the winning trades by the total loss of the losing trades)
- The win ratio of the trading strategy (W) (the number of trades that showed a profit divided by the number of trades that made a loss)
The variables need to be put into this formula:
Kelly % = W – [(1 – W) / R]
Let’s make up a trading strategy that has passed the out-of-sample backtest. The strategy has these numbers:
- Total gains of the winning trades: 10 000 000
- Total loss of the losing trades: 3 500 000
- (The win/loss ratio is thus 2.86)
- The win ratio is 71% (thus 29% of the trades showed a loss)
Let’s put the numbers into the formula:
Kelly % = 0.71 – [(1 – 0.71) / 2.86] = 0.6086
This means the optimal betting size according to the Kelly Criterion is 0.6086 of your equity.
The Kelly Criterion is a theoretical value. A backtest is a theoretical estimation and is, of course, no guarantee that it will resemble the future. There are many disadvantages of backtesting. Because of this, we always recommend trading a smaller size than you’d like.
The Kelly Criterion and the win-ratio
Take notice of one very important aspect of the formula: a low win ratio increases the probability of ruin and losses. We have previously written about why we regard the win ratio as one of the most important factors in trading. It’s important because of four factors:
- The chances of many consecutive losers increase the lower the win ratio.
- Many consecutive losers make you do behavioral mistakes.
- Big drawdowns are often a result of a low win ratio.
- Ultimately a low win ratio increases the risk of ruin.
Optimal capital allocation in trading needs to balance the expected profits and losses
To better show the importance of the win ratio in trading, we make some further mathematical calculations to show how the win ratio influences how much you can allocate to each trade or strategy to balance profits and losses.
If you trade one strategy, what is the optimal allocation of capital per trade?
In July 2001 Wolf von Rönik had a good article in Technical Analysis of Stocks And Commodities about risk and ruin. Rönik provided a formula that calculates the optimal capital allocation based on the win ratio and the expected gain per trade.
The formula is like this:
A = Profit/loss ratio
P = The win ratio
The profit/loss ratio is the average gain for the winning trades divided by the average loss for the losing trades.
Let’s assume we have the following data for a trading strategy:
The win ratio is 65%, the average gain is 2% for the winning trades, and the average loss for the losing trades is also 2.1% (the profit/loss ratio is thus 0.952). This returns the following optimal allocation of capital:
(((0.952+1)*0.6)-1)/1 = 0.1712
This means an optimal capital allocation of 17.12% to each trade or each strategy.
Let’s make a twist and change the parameters:
The average winner is twice the size of the average loser, but the win ratio drops to a modest 40%. This might be a typical trend-following strategy.
This returns the following optimal allocation of capital:
(((2+1)*0.4)-1)/2 = 0.1
You need to reduce the capital allocation to 10%.
The win ratio is lower and this needs to be offset by a lower allocation per trade. This is the margin of safety to avoid ruin or loss!
Let’s make a final test: The average loser is 2.5% and bigger than the average winner of 2%, but the win ratio is a big 75%.
Put into the formula we get the following optimal capital allocation:
(((.8+1)*0.75)-1)/0.8 = 0.4375
The win ratio is higher and thus we can risk more per trade without risking ruin: 43.75%
What Is The Optimal Capital Allocation In Trading- conclusion
This article has provided you with some theoretical values of how you can determine the optimal capital allocation in trading.
However, we always advise erring on the safe side to allow for a margin of safety. Always trade smaller than you’d like. By all means, go ahead and calculate your optimal betting sizes, but allow for some margin of safety. In trading and investing, it’s always better to be safe than sorry!