If you’ve ever invested in stocks, you’ve probably heard the term “reversion to the mean” thrown around like a pigskin on the beach. However, what you might not understand is the forethought that goes into drawing such a conclusion. For centuries, scientist, mathematicians, philosophers, and now, traders, have been trying to discern determinism vs statistical processes. Brownian motion vs. ODEs. Kalman Filters vs. Lyapunov functions. The big question is: Does something that seems so “random” at heart, exemplify a set pattern (albeit predictable or not) that can be ascribed to a deterministic algorithm or do we appropriate the words of Socrates when he states that “all [we] know is that [we] know nothing.”
Most investors are too risk averse to subscribe to deterministic behavior and thus have coined the term “student of the market” due to the humble pie served to so many from Benjamin Graham’s, oh so famous, Mr. Market. Thus, whether using fundamental analysis, which uses statistical tests based upon ratios and historical data to confidently predict future values to some statistical significance; or using technical analysis, to which momentum bands, statistical oscillators and volatility measurements are tools used to trend the market direction, its extremely difficult to find anyone who would disregard stochastic processes as a necessity (and dare I say, the sole way to trade the market).
So we’re done right? The sample mean, based upon the central limit theorem, will approximate the population mean as the sample size gets large, and thus, barring any change in the underlying stochastic parameters, we can go home early and call it a day.
Well, not so fast…There is one main sect, if you will, within technical analysis that believes almost solely in trading off of deterministic functions…a so called…karma of investing. It’s called Elliott Wave Theory, which is based off of Charles Dow’s Theory that the stock market moves in waves. At the bare bones basics of Elliott Wave Theory, they believe that there are essentially 5 waves that create a cycle. Waves 1, 3, and 5 create the momentum upwards and 2 and 4 are the correction patterns. You can have waves within waves (supercycles, cycles, etc) but they usually follow closely to this 5 wave patterns. The level at which wave 1 turns into wave 2 (upward momentum changes to correction or downward direction) can be determined in many different ways. Fibonacci sequences, pivot points, etc are all useful in predicting levels at which these changes occur within any cycle.
This deterministic analysis isn’t so much based upon market data, but actually, instead, on psychological and behavioral data (as is a good portion of technical analysis). Almost like a “set formula”, people react to certain types of information a certain way. Thus, this deterministic process states that people will fear that an uptrend has gone up too far and should retrace, or vice versa. For example, if a stock is uptrending to, say, 61.8% price level from the all-time high (based on Fibonacci sequence analysis), it might re-trace back down to around the 50% price level. People will have some sort of uncertainty at the 50% price level and if it breaks below that level, then it will head to the 38.2% price level. From there, it might head back up which would become the next leg up in the uptrend.