Thursday, July 10, 2008

Small Edges, Consistent Returns

Today we're going back to Henry Carstens' P&L Forecaster to take a look at how small edges in trading result in meaningful differences in long-term outcomes.

I ran the Forecaster 10 times under different scenarios to generate a variety of forecasts. Let's imagine a small trader with a $20,000 portfolio whose average win size per day is $100, or 50 basis points. Imagine that this trader's average win size and loss size are equal, but that he has different win percentages: 48%, 50%, and 52% over a period of 100 days.

Here are the outcomes I generated for the 48% scenario: -442.9, -534.0, -250.1, -351.2, -332.0, -137.2, -373.9, -324.0, -432.5, and -211.8. As you can see, the trader with a ratio of 48% winners and 52% losers ends up losing over 1% of his portfolio on average during the 100-day period. There is no scenario in which he makes money.

Here are the outcomes for the 50% scenario: -73.8, 23.6, -96.8, 10.0, 244.3, -50.0, 87.6, -3.2, -95.5, and 114.5. Now, with 50% winners and 50% losers, the trader neither consistently makes or loses money, as we'd expect.

Finally, let's look at the outcomes for the 52% scenario: 240.3, 26.9, 370.2, 322.2, 394.5, 385.7, 393.5, 441.3, 333.4, and 552.9. Here, with 52% winners, the trader makes over 1% during the 100-day period and makes money across all scenarios.

My findings were very similar if we assume that the trader has 50% winners and 50% losers, but vary the ratio of win size to loss size from .90 to 1.0 to 1.1. Under the .90 scenario, all outcomes were losers, with the trader losing well over 1% over the 100-day period. Under the 1.1 scenario, all outcomes were winners and the trader made well over 1%.

Here are the outcomes for the trader who has 48% winners, with the ratio of win size to loss size at .90: -904.2, -727.4, -718.5, -763.5, -786.1, -551.0, -518.9, -610.5, -760.5, and -812.6. The trader loses over 3% of his portfolio before expenses over a 100-day period.

When the trader has 52% winners and win size to loss size is 1.1, the outcomes are: 769.9, 667.5, 614.7, 783.8, 528.7, 830.4, 933.0, 500.7, 791.5, and 884.2. Here the trader makes over 3% during the 100-day period.

What this tells us is that even small edges in the market generate consistent returns if they are consistently acted upon. This is the message of Henry's Axiom of the Small Edge: you don't need a huge edge to make good money; you need to act consistently on the edge that you have.

Our little exercise also shows you how fragile these things are. Just a dip in win percentage from 52% to 48% matters quite a bit over time. Changes in market conditions, changes in our psyche: it doesn't take much of a nudge to make us profitable or unprofitable.

Finally, note the scenario in the chart above with 52% winners and win size to loss size of 1.1. Even in these situations, drawdowns are common. Traders with an established edge can still undergo extended periods of flat performance or drawdown merely by chance. If they are not resilient and change what they're doing out of a lack of confidence, there goes their edge. It's a vivid demonstration of why, psychologically, it is so difficult to maintain profitability even when you are a trader with profitable methods. That conclusion will be important for my next post, when we look at risk and return in these scenarios.


The Psychology of Risk and Return