Focusing on Position Sizing

Rather than searching for the perfect strategy, the level of exposure to risk is a more important ingredient to successful investing.


Every trading edge is going to be naturally constrained by the arbitrage activity of all market participants – extraordinary profit opportunities will be temporary at best. Asset classes, investment strategies (eg. value & momentum strategies) and trading strategies (eg. short volatility, carry and trend-following strategies) with a positive return expectancy have the tendency to find an equilibrium at a similar long-term level of risk-adjusted return. The market is quite risk efficient overall, but maybe risk-adjusted returns tend to be a bit lower the more mainstream the investment is. For example, asset class returns congregate at a Sharpe Ratio of 0,3-0,4; factor returns around 0,5-0,6 and good alternative strategies around 0,7-0,8.
A diversified portfolio of different assets and strategies has historically topped out at a Sharpe Ratio of about 1 for very successful money managers – this is the general target of the portfolio, as I describe it in this blog.


In this article I want to zoom in all the way to look at risk at the individual position level. This is a major topic in short-term trading, but is as important for long-term strategies.


Position sizing is the most important factor to balance the risk and return of an investment / trading strategy within its performance parameters. It can make the difference between good returns, mediocre returns and blowing up your account with the exact same strategy.
Market beating return will usually come hand in hand with uncomfortably high volatility as risk and return are closely intertwined and the possibilities to optimize for low risk paired with high returns are limited. It basically comes down to diversification not only between assets and asset classes, but also between strategies with uncorrelated return characteristics and across time.


When looking at the performance of investment strategies and trading systems it is vitally important to take into account the position sizing methodology used – especially with more complex strategies that trade across multiple positions and markets.


Leverage
Investment strategies by default usually invest 100% of the available capital forming a portfolio of assets. It would be a rare coincidence, if this were the optimal level of exposure to the strategy for your risk / return goals. It pays to look beyond the default allocation and consider leveraging up or down from a 100% allocation. Addressing this is very uncommon in the description of investment strategies (except for more sophisticated ideas like risk parity or long-short strategies) as leverage is often thought to be synonymous with being risky and expensive. In reality leverage is a useful tool, that scales return and risk equally and there are ways to access it inexpensively.


Sizing positions according to volatility
For each strategy it makes sense to use a volatility-based position sizing algorithm, if you expect a similar risk-adjusted return across assets and strategies. Each position risks a set percentage of your equity per trade and the volatility contribution of each position to the portfolio is equal by taking diverse and dynamic market volatilities into account.
Each position should cause the same daily portfolio fluctuation on average.


Position Sizing Methods
  • Constant percentage of equity at risk depending on a stop loss: a stop loss at a predetermined logical position can determine the size of the position. Risking 1% to 2% of capital per position are commonly suggested levels, but across multiple positions this can quickly become too high and I often use levels closer to 0,25% to 0,5% across my different portfolio strategies. As this method can lead to vastly different contributions to daily portfolio volatility for each position, I usually prefer to include a volatility measurement when sizing positions.
  • Margin to equity: In my trend-following managed futures strategy, for example, 50% of the required margin for a position at Interactive Brokers approximately equals the strategy’s average loss. Some contracts have higher margin requirements than others (eg. VIX or Bitcoin futures), but it is a good method to double check risk levels at a glance across all instruments (IB shows the margin required for buying and selling stocks, ETF, futures, options etc. whenever you place an order). Overall margin level is also a good method to judge the exposure of the entire portfolio.
  • Realized Volatility can be used to calculate position sizes.
  • In a similar way, I use the Average True Range ATR of an instrument (the average daily movement), which gives a volatility adjusted position size with a simple calculation:
For a long-term position in an ETF, as an example, you could risk 1% of your capital (NAV) and set a trailing stop loss at a distance of 5 ATR:
1% NAV : 5 ATR(50) = number of ETF
This would lead to a portfolio of about 5 to 10 ETF (depending on the volatility of the underlying markets) with your capital fully invested.
A second example is the position sizing algorithm I use in my trend-following managed futures strategy, which has to take the multipliers for different futures contracts into account:
(0,33% NAV) : (1 ATR(20) x contract multiplier) = number of contracts
This formula leads to an average of around 0,3%-0,5% of capital at risk per position in a short- to medium-term trend strategy – in this case this also equals the average daily fluctuation in value you can expect for each position.


It is easy to find examples for position sizing and money management in books and strategy descriptions, but it pays to look closely at the return and volatility these rules might cause in real-life trading – especially when combining several positions across strategies into a portfolio.


Trend Following with the Turtle Strategy
A good example for an extreme position sizing methodology is a trend trading system with similarities to my own trend strategy – the famous 1980´s Turtle Trend Strategy, which has publicly available rule sets including a simple yet efficient volatility-based position sizing method based on ATR. Find the complete description here.
The strategy uses a simple 20-day breakout trend signal as an entry combined with a 10-day breakout as an exit signal across 21 markets. I will postulate that it has the edge of a classic trend strategy that can be constructed in many different ways.
Such strategies have a historic Sharpe Ratio around 0,8, which would translate into an average annual 10% return at 12% volatility – in recent years classic trend-strategies in the short- to medium-term spectrum have shown deteriorating returns, though.


Let´s analyze the position sizing as stated in the paper – it is quite complex as it pyramids aggressively into profitable positions and restricts maximum position sizes on several levels:


  • Basic position sizing calculation:
1 Unit = 1% of account equity at risk : (20-day exponential moving average of the True Range (N) x Dollars per Point movement of futures contract) – (this is equivalent to my own formula above, but 1 Unit would be 3 times my basic position size)
  • Stop Loss: 2% of account equity per position (including pyramiding)
  • Pyramiding into positions: After an initial position of 1 Unit an additional Unit is added every 1/2 N (half an average day’s movement) that the position moved into your favor – that is very rapid and the initial stop loss of 2 ATR distance quickly moves closer as the position grows to ensure a maximum loss of 2% of capital.
  • Position size restrictions:
Single Markets – A maximum of four Units per market.
Closely Correlated Markets – A maximum of 6 Units in one particular direction.
Loosely Correlated Markets – A maximum of 10 Units in one particular direction.
Single Direction – The maximum number of total Units in one direction long or short was 12 Units.


Implications
If you try this out in practice, you will quickly find out that you are taking on a lot of risk. I would say the risk level is unsustainable and almost certain to lead to a blow-up of your account sooner or later. At the very least it will trade at the very limit of a position size aimed at maximum growth of capital, that you can calculate with the Kelly Criterion and likely lead to severe drawdowns way beyond -50%.


Here is where I see concrete danger:
  • Extremely high position sizes: 1 Turtle Unit would be 3 times the basic position size of my own trend strategy that trades a similar time frame. Pyramiding would raise this to 12 times (4 Units) and in real trading even my smaller position sizing has led to uncomfortably large fluctuations in portfolio value for me, when the volatility regime changed very quickly in February 2018.
    Correlated choppiness and whipsaws across most markets would likely have wiped out the Turtle Strategy during the first half of 2018. For example, if 10 open positions witness a moderately adverse day simultaneously a 20% daily loss is easily possible! With the maximum 4 units per single market the average daily fluctuation for each profitable position is 4% of portfolio value – talk about nerve racking!
  • Low percentage of profitable trades: even in the 70´s and 80´s  the tight stop loss would cause a very large percentage of positions to be stopped out by random noise – only 2 to 3 trades would generate all the profits in a year. In today’s choppier markets this would lead to an unprofitable strategy – the edge is lost as few trends are caught successfully.
  • Turtle lore: original turtle trader Jerry Parker, who is still a successful CTA, said he had a 60% loss in a single day in his early days (in an interview on the “chat with traders” podcast).


Why did that work out for the Turtles?
The original Turtles weren’t actually trading off a real capital base, but were assigned a notional account value backed up by the capital of the entire firm. This notional value was scaled down over-proportionally in a drawdown (for each 10% loss their capital would be reduced by 20%) and not raised in line with gains, but dependent on a yearly performance review.
In theory this makes drawdowns over 100% possible – something which is unrealistic for the individual trader, unless he has easy access to additional capital in case of a severe drawdown.


Conclusion
It is essential to align position sizing with your risk tolerance and return goals – it is the direct connector between your strategy´s performance parameters and the realized return and volatility. On a position level this is a simple process, but the money management of a portfolio quickly becomes complex and difficult. This has recently caused problems for me, when many positions across strategies suddenly began to show close correlations (especially when they went against me!) over extended periods of time in the first half of 2018 – causing outsized strings of profitable as well as losing periods.




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