A 'Lag-Lead' method of trading and analysis

1 A ‘Lag-Lead’ method of trading and analysis Adolf Cusmariu [email protected] Price volatility in equities is partly caused by variable ownership intervals among investors; these may vary from minutes, to hours, days, and so on, not all obviously in action concurrently. An averaging window moving through price histories should show fluctuations caused by these variations. Residuals off moving averages magnify these movements; two control parameters are available here: data interval width and mean placement; and placements can ‘lag’, ‘lead’, or be ‘centered’; see graphic below. Let’s look at Apple (AAPL) stock as an example (in blue, top panel) - 1981 though early 2025 - in log-scale; the ‘center’ estimate (overlayed in red) tracks the data (in blue) as expected; interval width here was 20 trading days. The lower panel shows the residuals off log-scales; kurtosis is 9.5451, a super-gaussian distribution. The ‘lag-lead’ strategy of the title is best explained by the images below; the strategy was applied to a section of the log-scaled AAPL stock from 1999-2002 using a 30-day window. window lag lead center 2 Legend Blue: AAPL Price data in log-scale Black: Lag estimate Red: Lead estimate Magenta: Sign(Lag - Lead) shifted to fit in the plot (scaled and shifted elsewhere) Periods of growth clearly coincided with the Lag dominating the Lead; so a trading strategy has emerged. The first-difference of the estimate Sign(Lag - Lead) is overlayed on the data stream to serve as Buy-Sell markers; see image below. The Sell markers could, of course, be ‘sell short’ signals until the Buy signal comes up; and window lengths are at the investor’s discretion. S BB B B B SS S S 3 Let’s next examine the ‘lag-lead’ method in action on the DOW average (again in log-scale), around three calamitous events; the 1929 crash, the 1987 crash, and the 2077-2009 ‘subprime’ financial crisis; see below. First, the 1929 crash, a global catastrophe worsened by actions of the US Federal Reserve. The lag-to-lead cross-over occurred well before the disastrous events towards the end of 1929; although some courageous investors got back in briefly after 1930, the action until mid-1932 appeared mostly a pure ‘short-sell’; more detail below. 4 It is unclear why such an unsustainable level of growth beginning mid-1928 continued for more than a year; perhaps a method similar to ‘lag-lead’ was in play; if so, it eventually put an end to ‘irrational exuberance’, with calamitous consequences. An amusing (rotated) graphic of the zig-zag behavior around the crash shows the log-scaled average bouncing diametrically inside a circle as if obeying some law-of-reflection! 5 Next, let’s examine events around the crash of 1987, one of considerably shorter duration; the crossover occurred again well before the event (see below); the upward trend resumed quickly as if nothing had happened, albeit at a slower pace. Finally, the ‘sell’ crossovers prior to the down-turn in this 2008 crisis were not unique using a 30-day averaging window; however, the crossover at up-turn did coincide with the very bottom the average.