By Thomas J. Dorsey, Tammy F. DeRosier, Paul L. Keeton, Susan L. Morrison, Joshua B. Parker
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If the sine function is written: yt = sin(t) then the popcorn function may be similarly written: yt = It sin(t) where It is an indicator function taking values 1 or −1 signaling a peak or a trough move. The math is not important here; the insight from the description and graphical depiction of the process is: Exploiting the popcorn process is not efficiently accomplished using the turtle trade. 5, panel (b), the turtle trade rule identifies a single trade with profit $2. The popcorn process suggests a rule that signals to exit a trade when the spread returns to the mean, rather than assuming it will continue beyond the mean to an extreme on the opposite side from which the trade was entered.
Chapter 5 demonstrates these points in a discussion of reversion in price series. With so many potentially costly errors attached to the use of sample moments (mean and standard deviation) why is the range so readily abandoned? What has been gained by the sophistry? In addition to the aforesaid (almost unconscious) action on the part of many, there is the conscious action on the part of many others that is driven by mathematical tractability of models. Extreme values (and functions thereof) are difficult to work with analytically, whereas standard deviations are generally much easier.
Forecasts, unlike foresight, do not come with a guarantee of the outcome. There is risk in acting on forecasts. A single pair spread expected to ‘‘revert to its local mean’’ may continue to increase beyond the point at which stop loss limits force exit from the position. This new element, risk, complicates the goal, which now becomes twofold: Maximize expected return and maintain the risk of achieving that return below a certain tolerance. So far so good. Going from foresight to forecast we exchange certainty for uncertainty; we move from guaranteed optimization to constrained optimization of a best guess.