Tuesday, August 05, 2008

Drama Creates Trauma: Position Sizing and Risk Management in Trading

I recently received an email from a trader who was going through difficult emotional swings as a result of swings in his portfolio. He assured me that he was a knowledgeable, experienced trader and that he limited his risk to 5% per trade.

I didn't need to read any further to know the problem.

So let's return to Henry Carstens' P&L Forecaster to see what's gone wrong.

In the top chart above, we're looking at forecasted returns for a $100,000 portfolio in which the standard deviation of returns per trade is 1% or $1000 and the trader has entered a period of flat performance (average zero return per trade). That might represent the scenario in which a trader risks 1% of portfolio per trade with moderate discipline. Over the course of 100 trades, that trader shows an equity peak of about $9000 (up 9%) and trough about -$3000 (down 3%), for a peak-to-trough drawdown of 12%.

In the world of professional money management, such a swing would merit the attention of risk managers. I don't know too many portfolio managers who would feel good about going from up 9% on the year to down 3% within the span of 100 trades. It wouldn't be a catastrophe, but it would be a concern.

Now, in the bottom chart, let's take a look at the performance of the trader who ramps up risk to a 5% standard deviation per trade, like our correspondent. That again might represent a scenario of risking 5% of the portfolio per trade with moderate discipline. Over the course of 100 trades, that trader displays an equity peak of about $15,000 (up 15%) and trough of almost -$30,000 (down 30%) for a gut-wrenching peak-to-trough drawdown of 45%.

In the world of professional money management, that would be wholly unacceptable.

We all hit periods of flat performance; during those times, note how risk levels affect *psychological stress*. In one scenario, we swing from 9% up to 3% down. Raising the risk per trade by a factor of five swings up from 15% up to 30% down. Note that the order of the gains and losses could just as easily have been reversed: in the first scenario, we could have first gone from 9% down to 3% up; in the second scenario, we could have gone from 30% up to 15% down.

It's the swings that are important--and the effect of those swings on the psyche.

When we trade size that is too large for our account size, we subject ourselves to drastic swings in P/L, and that subjects us to drastic swings in mood. In turn, we then make trading mistakes that bring a negative expectancy to each trade, and the size eventually blows us up.

My advice to the gentleman? Think of the charts above as measuring risk per day instead of risk per trade, so that the equity curves represent 100 days of trading. You can see that a 1% standard deviation of returns still generates peak-to-trough drawdowns of over 10%. I would cut risk below that level--risking less than 1% per day, and thus significantly less than 1% per trade--for at least a month of consistent, disciplined trading before considering a *modest* rise in size (which, in turn, would need to be accompanied by a full month of consistent, disciplined trading).

Only such a sustained period of trading without large swings will counteract the emotional fallout created by the large equity swings. In trading, if you create drama in your returns, you'll create trauma--and that's how trading careers end. The links below explain this in detail.


The Psychology of Risk and Return

Risk Management and Human Biology

Inside the Trader's Brain