Hypothetical equity curves with perfect negative correlation

Days

Figure 6.5 Hypothetical equity curves that are perfectly negatively correlated;

combining them reduces the SE to zero in this contrived example, because the resultant equity curve is a perfect straight line.

We can extend the linear regression-based analysis to calculate the risk-reward ratio of a particular system by taking the ratio of the slope to the standard error. This is a quick and reliable way to compare different systems tested over the same data sets. This calculation assumes we are using daily data and looking at system paper profits.

RRR (risk reward ratio) = slope / standard error.

In the three hypothetical cases, the RRR approaches infinity for the first system because its SE is equal to zero. For the second system it would be 1.21 (100/82) and for the third 0.31 (100/318). There is little doubt we would all prefer the first system if one ever existed. You can use a spreadsheet such as Microsoft Excel for linear regression calcula­tions. For example, in Excel you can use the built-in tools to find all relevant regression data by just filling out a template (pick Tools, then Data Analysis, then Regression, and fill out the template). Otherwise,

186 Equity Curve Analysis

you could use one of the many easily available packages for statistical analysis.

In the following sections we use SE to measure equity curve smoothness. Remember that increasing the slope does not automatically increase smoothness (that is, reduce SE). We will examine how different system designs affect portfolio level equity curves.