## Binary and Polynary Trading Strategies

Mon, Apr 27, 2009 | Jared Woodard

Strategy

Define a binary strategy as a set of conditions that takes one of two possible values,* typically a long or short position in the asset being analyzed.** Define a polynary strategy as one that takes at least four possible values, with the maximal value limited only by the precision of the analysis, depth and liquidity of the market, and prudence.  So where a binary strategy may regard a given data point and return a 1, -1, or possibly 0, the same strategy using a polynary approach may return any value between 1 and -1, like 0.8768, -0.9122, or 0.0001.

The advantage of the polynary approach should be clear. It permits the strategy to be more precise.  I have a habit of describing financial products as a means of expressing financial propositions; let’s regard the output of a trading strategy as the proposition to be expressed.  A binary strategy that merely produces buy and sell signals is not very expressive at all: it voices full confidence or complete doubt about the asset every time it speaks.  That’s like going out on a series of dates and, each morning, looking into your partner’s eyes with either abject hatred or utter rapture.  Life admits of more subtlety.  And if a given strategy really does track some worthwhile edge, chances are that that edge will be better expressed in degrees.

For example, most overbought/oversold indicators are designed to signal when they cross some discrete threshold: the 2-period Relative Strength Index (RSI(2)) is usually set at 10/90, 20/80, or some variant thereof.  But is it really helpful to have no position at all when RSI(2) is at 89, and then a full position at 90?  It’s far more intuitive to scale into a position as the reading gets more extreme.

One rebuttal to this line of thinking is that techniques like position sizing, pyramiding, and the use of complex stops already do much of the work.  There’s some truth to that: imagine a binary strategy that is applied with the option of entering multiple open trades in the same direction (pyramiding), allocating larger amounts of capital to each successive trade (position sizing), and using some Average True Range trailing stop for an exit.  That’s better than a simple all-or-nothing version, but as a financial proposition, it’s still rather guttural and halting: “I love this stock….I really love this stock….I REALLY REALLY LOVE THIS STOCK….Oh, now I hate it, get me out.”  What’s particularly puzzling about the issue of stops is that traders will often give little or no thought to the means by which they enter a position, but develop ever-more-arcane methods for determining the appropriate time to exit.  In many cases, those methods for exiting have nothing to do with the indicator or relationship that signaled the entry, which is strange: whether a strategy is momentum- or mean reversion-based, it seems right that if the gradual intensification of a relationship warrants an entry, the relaxation of that relationship will warrant an exit.

There are multiple ways to make a strategy or indicator polynary. Nearly any mean reversion-based strategy will already define a range in which a position should be held; it is a relatively simple matter to translate that range of -1 or 1 readings into something more gradual.  Likewise, momentum-based strategies can be described so that exposure is correlated with the strength or weakness of the trend measurement that justifies having a position at all.  One advanced application of this idea would be to track the probability that an increase in the strength of a signal will be followed by more strength: options traders could use that information to get long or short gamma in addition to the directional (delta) bias of the strategy.

One additional benefit may be that polynary requirement may help filter out uninformative strategies.  Following David Aronson, I endorse the view that if some piece of technical analysis can’t be formalized and tested empirically, it is most probably bunk.  We might add the further condition that if a strategy can’t be expressed in a polynary format, whatever edge it claims to have might be due to data mining or some other bias.

The key idea here is that designing trading strategies is a process of understanding some important tendency or overlooked relationship in the market and  expressing that tendency in a pragmatic way.  To extend the communication metaphor: whereas the binary approach demands of the strategy either complete silence or booming proclamations, the polynary approach recognizes that behind the overzealous facade will be a smaller, less dogmatic strategy with far more nuanced things to say.

* Include strategies that allow for a neutral or “flat” third value in the binary group; so a binary strategy may have values of {-1, 1} or {-1, 0, 1}.  I include such strategies here because a strategy that issues signals very infrequently – and is otherwise flat – still falls prey to the lack of precision that a polynary approach remedies.

** It would be remiss not to cite Michael over at Marketsci, who has written helpfully on this topic in the past. This post is particularly indebted to his Transactional vs Confidence-based Trading Strategies.

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