Sunday, February 14, 2016

The Deviation Moving Average

In a previous article, the concept of the equilibrium price was discussed with reference to supply and demand dynamics upon which most mathematical economists agree. Analysts and pundits who throw rough numbers around in news articles and reports are trying to find that magic number that prices may converge. The value could be based on a calculation or a suave observation of historical price movement that suggests a certain number. Often times, these technical and fundamental projections guess at what a "fair price" would look like. A "fair price" meaning that the value reflects what the investor is paying for and how much it may benefit that individual in the future. Any trader knows, though, that actual market price and the "fair price" are dramatically different things, so many analysts turn out to be wrong.

The discussion of what the difference between a fair price and the market price is divided into two viewpoints that see the price mechanism differently. The efficient market hypothesis is the mantra of fundamental heavy analysts and investors that believe all information is reflected in the market price of an asset. The idea is hinged on the belief that information is symmetric and all players have access to the same information while making their decisions. In that way, a price will always converge to a fair value because most if not all investors are rationally buying and selling the asset based on its integrity. Th antithesis of the efficient market hypothesis is best explained by Burton Malkiel's A Random Walk Down Wall Street. His book argues that idiosyncratic trading leads to under- and over-valuation of securities leading to the taking of profits through arbitrage. Technical traders believe that these irrational prices develop through patterns and are lead by various signals. Therefore, this school looks to trade assets based on their perceived price that is communicated through the market price. The fair price has little to no value in a technical approach.

So in reality, what is the best way to predict prices? I believe a mixture of the two may be the best way to forecast prices. Using historical price trends, the Deviation Moving Average indicator may be able to paint a picture of where the actual, market price is relative to an estimation of what the "fair price" looks like. The truth is intraday fluctuations that are heavily impacted by shifts in trading mentality rarely ever trade at a fair price. Instead, assets consistently deviate from a reasonable price that can be constructed by a moving average. Traders often look at these moving averages when trying to establish a base trend that estimates the fair price given by the herd of investors that manipulate the asset's value through constant buying and selling. Those moving averages aren't actually what investors and analysts say are efficient projections; they use the trendline as a way to generate signals based on the deviation (or lack of deviation) shown in the market price. The deviation moving average takes the idea of deviation and applies it to a model that can produce buy and sell signals and an algorithm that generates a rough forecast for price.

The chart above shows the spot price for WTI contracts sold out of Cushing, Oklahoma with the deviation moving average calculated using a 50-day price moving average and a 10-day deviation moving average. The blue line tracks the daily movement of the contract over 2015 up to the beginning of this year. The orange line shows the indicator's movement over that time. The calculation used to produce this line is based on the idea that market price will always deviate from a rough estimation of the fundamental price. While the day-to-day deviations are relatively different, a moving average of those values shows a suggestion of what traders thought a reasonable deviation was. When the blue line crosses over the orange line, as seen in late February and early March, investors start to value the asset closer to the 50-day average. Crossover points in the other direction, such as movement in early May, shows that traders are enlarging the current deviation between the market price and the rough estimation of the fair price. As the scales are shown to be far apart, this indicator would be unsuccessful at developing insights about short-term trends. Instead, the short-term trends themselves drive the accuracy of the long-term accuracy.

Fluctuations above and below the orange line are inevitable and act as a sort of momentum indicator. The farther the blue line moves in one direction, the more likely that it will snap back towards the deviation moving average. In the graph above, it is noticed that the largest spikes in difference between the indicator and actual price (or just the deviation) are followed by a slope towards a difference closer to zero. The spike in February shows this property as well as those in July and September. A trader looking at this indicator will always know that prices will return to the calculated deviation moving average because that trendline does not follow the overall moving average of the price but the overall moving average of the deviation which can play a larger part when trying to find signals of over-bought or over-purchased securities.

Using this indicator as a tool for rooting out possibilities of a reversal is tricky because a trend in deviation could easily be reversed and deemed illegitimate soon after. For this reason, major reversals should be confirmed using other tools that measured different technical and fundamental aspects of the security. A reversal signal may also be unclear because of the volatile movement of the calculated price in an intermediate range. On the first chart, a crossover point above the blue line might be associated with a reversal upward until a possible peak (where the sell signal would occur). In place of a peak materializing, the price and the deviation moving average moved up with each other until another crossover point downward occurred at a price almost $10 higher. A combination of the two charts above along with an analysis of their patterns may be more helpful in discerning between viable signals and the phony signals.

Earlier in the article, it was mentioned that the indicator uses both fundamental and technical analysis to come to its conclusions, and some explanations referenced the plain "50-day moving average" as the part of the calculation that brought in a fair, fundamental price. This can be pointed out as an idiosyncrasy because the 50-day moving average actually never references fundamental data inherently. Indirectly, though, a 50-day moving average taps into the hundreds, thousands, and maybe even millions and billions of trades that occur in those sessions, Like the efficient market hypothesis says, those trades hold thousands of hours of research from millions of investors, and because those opinions and information are being averaged out, the price slowly approaches an approximate fair price which is developed by the perception of fundamental data. This indicator works relatively well at communicating that fair price, but alone, it neglects the clear evidence of irrational trading that causes the deviation. In these ways, the deviation moving average marries the ideas represented the efficient market hypothesis and behavioral finance, rationality and irrationality, and finally, fundamental analysis and technical analysis.

After further analysis, there's no doubt that there's more to this indicator than meets the eye. A second look at the chart of the differences reveals a patter in the deviations of daily prices from the calculated price. The fluctuations resembled a trigonometric function that shows harmonic motion and the cyclicality of the asset pricing mechanism of which investors know and love. Stock prices appear chaotic on a chart, and in reality, their movements are too volatile for accurate predictions to be developed from simple averages. A smaller moving average may appear to do the trick, but shrinking it too small reduces its ability to extrapolate. The deviation moving average model does not seek to predict prices using past prices but constructs projections based on the deviations from those averages. Finding a model that predicts an approximate deviation for a certain day can then allow an extrapolation for price as the projected deviation from the moving average. The model tracks the movements in the current trends using the 10-day moving average of the daily deviation so that large sentiment shifts are accounted for.

Projections for the next five trading days will be listed on a page linked to the blog, but here are the first few numbers that the model has spit out.

Next 5 WTI closing prices

The model predicts a peak in WTI price to occur on Monday with a reversal in that trend and movement towards $20 a barrel by Friday. Please remember, these are not predictions that I came up with, rather they are extrapolations from a model that I developed. Thank you and have a good weekend.


  1. Besides /co what underlying do you trade: uso, oih, xle ?