Constants, from James Sogi

January 12, 2009 |

 There are mathematical constants such as the ratio of a circle to its radius we all know as pi, the relationship of a line u and a segment such that u/u+v=u/v or the golden mean, and lim x -> 0+, (1+x)^ 1/x Seattle Phil's favorite constant, "e" a valuable computational tool allowing additive solutions. "e" allows doing complex calculations with relative ease, by replacing multiplications with additions. Pi is used in statistical computations involving the Gaussian distribution. They don't really know who discovered e. Archimedes discovered pi. Such ideas had commercial application in practical things as determining whether the coins were fake, or the volume of the King's golden crown. The curious thing about each is that no computer can state the number since some are irrational or transcendental. Each is critical to whole fields of prediction. Identification of market constants might uncover some regularities otherwise hidden and allow calculations and solutions. Some say market moves often follow the golden mean. I have been pondering what other important but unused constants might exist in the markets. Time, of course, is a constant. The vig is another. The use of the normal distribution might be viewed as a constant for computational ease and allow use of constant ratios such as standard deviation, mean, median. In the past, gold or the dollar might have been a constant but globalization and floating currencies stopped that one. The ratios are important still. What other constants might be in the markets?

Sushil Kedia writes:

I am visualizing two broad categories of market constants. The first category that is a list of constants for all participants and the later one which contains transitory constants for individual participants and varying values of the same constant for different types of participants at a given point in time.

The first variety of constants are relating to the sense/measure of time, of the variety:

1) Minimum Tick Size for each contract / market
2) The weekend
3) Market opening & closing time
4) National & other regular Holidays
6) Occurrence of earnings announcement seasons
7) Presidential Elections (every four years)
8) Options & Futures expiration cycles
… so on and so forth

The second classification of constants comes from a less easy to describe and more amenable to visualize variety that most of us are more often interested in are the price related constants. I would surmise that given any particular state of a trader the amount a particular trader is willing to risk on the next trade is a constant in the near vicinity of his recent wealth / income / consumption matrix. Thus, it may be useful to visualize a +/-2 Standard deviation price move in a day/week/month measured over the same units of time say at 20, 50 and 100 day/week/month span could be that constant threshold which evokes sense of pain/gain for say traders, speculators and investors. Variable constant for different types of participants varying for each over their journeys inside markets and varying across different participants at any given point in time is what makes the market a self sustaining, self perpetuating contest.

If one assumes that a disciplined trader is making repetitive constant sized bets (the search for that "optimal F") and Value at Risk is changing due to changes in volatility at a chosen time horizon then eventually this class of individual state dependent constants are again connecting back to the individual sense of time.

The search for thoughts on market constants is thus taking one back in a loop of figuring out if there is an inner market time.


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