FX Quant > Evidence of Profitability

Figure 1. A very important feature of Fx Quant's system is the stationarity, or mean-reversion, of the leverage used. We define the leverage as a ratio between the total long currency exposure (all long portfolio components, USD denominated) and nominal account value. Numerical experiments show that the leverage oscillates around its long term average of 3.2 and tends to revert to it. This helps us determine the optimal moment to start trading (or the moment NOT to start). The system either 1.) makes a new profit (the leverage decreases), or 2.) the leverage increases (the equity curve retraces).

As time passes, the leverage oscillates around its mean, BUT the return makes a new high - see the diagram above.

Figure 2. There is a very strong negative correlation between the monthly rate of return (ROR) and the month-to-month leverage change. A positive monthly leverage change, however, produces not as sharp drop in monthly ROR. The opposite also holds true: a positive monthly ROR does not decrease the leverage as much (see the graph below).

Figure 3. The correlation between the monthly ROR and leverage change can mathematically be described as:

Monthly ROR = 1.822 - 0.645 x (Leverage Change x 10)

Let us sum the above formula across all months of the testing interval. The leverage changes will cancel each other, i.e. their sum will be zero (remember the leverage change has a zero mean) and we come to conclusion that

Cumulative ROR = Sum(Monthly RORs) = N x 1.822 (where N is the number of months in the testing interval), or the average monthly ROR = 1.822% (look at the intercept on the Monthly ROR axis). This correlation was persistent and the intercept was always positive, regardless the choice of system parameters. This brings us to a conclusion that, in long run, the system should be profitable, if a reasonably large leverage is to be used. Using too large a leverage can deplete the trading account, despite the long term system profitability.

You can open this Excel table and click on the Fx10d-Compounded and Regression tabs to see calculations.

Detailed performance reports can be found in the Performance section of our web site.