Risk-Based Position Sizing

Let’s start with a thought experiment. Let’s say we have two traders who are each given identical trading systems to execute on the SPDR S&P 500 ETF (SPY).  Because both systems are identical copies of an automated trading system, both trading systems generate the same buy/sell signals, use identical stop loss and trailing stop parameters. These two trades are also going to start trading on the same day, with the same starting account size.  In essence let’s pretend we have two traders that have identical trading circumstances. At the end of the trading period, we would expect them to have the same account balance, right? But at the end of the trading period, reality has made fools of us. One trader generated nearly twice as much net profit. How can this be? Reviewing the trading results for both traders you can see both traders took the same signals. Both traders have the same win/loss ratio and even the same number of stop-out trades. But there is one difference. One trader used a simple mathematical formula to determine how many shares to buy. This formula utilized a risk-based metric to calculate the number of shares thus, help to protect the trader from risk. His account grow at a much faster rate.

Position sizing is an integral part of both system trading and discretionary trading alike. It answers the question, how many shares or contracts should I buy? Too often this question is answered by nothing more than an educated guess. Too many traders position size their trades by not accounting for risk in determining the number of units to buy. In doing so you could be sabotaging your results, your system and maybe your career as a system trader! By tying your trade size to a risk metric you are acting defensively in the face of a dynamic market. Managing risk should be a top priority of any good trader. Thus, using a risk-based metric to help you mathematically determine how to size your trade is vitally important.

For most people they simply use a fixed number of shares or dedicate a fixed dollar amount for a trade. Let’s think about this for a moment. When a trading system generates a new buy signal you could risk all of your cash on that one signal. If you win you might double your money very quickly. Yet if you lose, your account it at zero. It’s probably not a good idea to bet all your account on a single trade, right?  Most people understand this extreme example and thus, will not bet their entire trading equity on a single trade. It’s way too foolish. So, how much do you bet? Maybe 90% of your account? Or maybe you decide 100 shares is about right. What many system developers fail to see is how their trade size affects the risk and reward of the given trade. As you risk more, the payoff can be greater. However, risk too much and you can be quickly wiped out by a string of losing trades. There exists a theoretical optimal balance between the risk and reward based upon the given trading system. Your job is to find a near optimal level that is comfortable for you as a trader.

While talking about the nuances on finding an optimal position sizing method for a given trading system is well beyond this article, I’m going to demonstrate the difference between using a risked-based position sizing algorithm vs. simply buying a fixed number of shares. Buying the fixed number of shares will represent what most people do (not taking into account a risked based metric to properly size their trades for the given market conditions).  Does using a risk based really help? Let’s find out.

Our Trading System

We will be using a simple strategy model for our demonstration on position sizing algorithms. I chose a simple RSI based system since most strategy traders have experience with this type of setup. I based our testing on daily SPDR S&P 500 ETF (SPY) data going back to 2/1/1993. Trades are executed on a daily bar and all trades are long only. Calculations are performed at the end of the trading day and orders are placed at the open of the next trading day. In all cases, we assumed a starting capital of $50,000. $20 for commission and $.02 per share for slippage was accounted for each round trip.

Go Long When:
2-Period RSI is below 10
Exit When:
2-Period RSI > 70
Below is an example of the strategy trading on the daily chart of SPY over the past couple of months.
Trade_Size_Examples

Method 1 Fixed Shares


The fixed-share method is a non-risk-based method. In this case we simply buy the same number of shares (200) for each signal.
Shares To Buy = 200

Method 2 Fixed Dollar

The fixed-dollar method is a non-risked based method. In this case we simply dedicate the same dollar amount for each signal. In this case we are going to use 50% of our starting equity to each signal which comes out to be $25,000 per trade.
Shares To Buy = $25,000 / Current Price

Method 3 Percent Risk

The percent-risk method is a risked based method. In this case we determine a fixed percentage of our equity (2%) to risk on each signal. This dollar amount is then divided by the dollar amount you are willing to risk on a individual trade. If our trading system had a known stop value we would use this value in our calculation. However, since our demo trading system has no stop value we are simply going to estimate a dollar number based upon the security’s price. Let’s use 5% of ETF price as the amount to risk. For example, let’s say SPY is trading at $100 and we are willing to risk five percent. Thus, we are risking $5 ($100 * .05 = $5 ). As the amount we risk climbs, we reduce the number of shares to purchase.

Shares To Buy  = (2% of Total Equity) / ( 5% of  Current Price)

Method 4 Percent Volatility

The percent-volatility method is a risked based method. In this case we determine a fixed percentage of our equity to risk on each signal. For our example we are going to risk 2%. We then take this dollar amount and divide it by a multiple of the security’s 10-day average true range. In our case we are using 3 times the 10-day average true range. In other words, we are dividing our risk capital by the average amount the security moves within 3 days. As volatility increases we reduce the number of shares to purchase.

Shares To Buy  = (2% of Total Equity) / 3*(10-Day Average True Range)

Conclusion

TradeSizeResults

In this article I wanted to demonstrate the difference between non-risked based position sizing methods (Fixed Shares and Fixed Dollar) and risk-based methods (Percent Risk and Percent Volatility). As you can see our demo trading system generates improved trading performance with the risk-based positions sizing methods. You can see this with the increase with the Profit Factor scores as well as the increased profit per trade. Most traders simply use the non-risk based methods or guess the number of shares. Such a strategy may not be optimal for your trading system. It will be important to test different position sizing methods to find out what works best. 

While this is far from an in-depth look at position sizing and how it can be used to improve your trading, this should highlight the impact a position sizing model can have on your system. 

About the Author Jeff Swanson

Jeff is the founder of System Trader Success – a website and mission to empowering the retail trader with the proper knowledge and tools to become a profitable trader the world of quantitative/automated trading.

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