Hypothetical data with lines one standard error above and below the best fit line

Days

Figure 6.4 The same data as in Figure 6.3 with lines on either side of the best-fit line one standard error away.

in Figure 6.3, the combined equity curve is a perfect straight line with zero standard error (see Figure 6.5).

Lowering SE is one of the arguments for diversification, usually in­terpreted as trading many markets within a single portfolio. If the mar­kets are negatively correlated at least some of the time, then the joint eq­uity curve of the combined portfolio will be smoother. Note that the slope of the joint equity curve will be just the algebraic sum of the slopes of the individual equity curves. This simply means that the slope of the line through the origin will change to accommodate all profits made over a given period.

You can expand the diversification theme to include different sys­tems on the same market. Again, the equity curve will be smoother only if the systems are negatively correlated. If the systems have positive co-variance, then the overall standard error will increase. Of course, if all systems are profitable then the slope will increase as well. Remember that slope and roughness are independent. Thus, increasing the slope does not translate into a smoother equity curve.

Measuring the "Smoothness" of the Equity Curve 185