HighFrequency Trading Inspires a Formula
Jan 11th, 2012  Filed under: Algorithmic and highfrequency trading, Alpha Strategies, Today's Post  By: cfaille 

In a new working paper, Godfrey Cadogan, of Toronto’s Ryerson University, offers a stockprice formula designed to capture the “empirical regularities of high frequency trading.”
As is often the case, though, the discussion can leave those of us outside the quant world confused: does the rendering of facts as a formula make them clearer, or does it just create a potentially misleading patina of precision?
Given Cadogan’s ambitioussounding program, linking HFT, bubbles, and crashes all into one formula, one remarkable feature of the result is his formula’s extreme simplicity or, as Cadogan puts it, its “parsimony.” I was reminded of the warnings in Emanuel Derman’s recent book, Models.Behaving.Badly, that the “simple models” of finance economists have failed “to reflect the complex reality of the world around them,”
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Author Bio:
Christopher Faille is a Jamesian pragmatist. William James has taught him, for example, that "you can say of a line that it runs east, or you can say that it runs west, and the line per se accepts both descriptions without rebelling at the inconsistency."
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The following is the text of a memorandum I forwarded to Mr. Christopher Faille in response to the skeptics:
Renown physicist Stephen Hawkins, writing in A Brief History of Time stated “A theory is a good theory if it satisfies two requirements: It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.” By that standard, the recent stock price formula for high frequency trading I introduced is a resounding success. In plain English, the formula says:
log (end of period stock price [index])=log(begin period stock price [index]) + sum over period (volatility of stock [index] futures x exposure to stock [index] futures x news about stock [index] futures)
where ‘x” means “times”. What some analysts call “news about stock [index] futures” is really “mispricing of stock [index] futures”. A positive value means the asset is underpriced, whereas a negative value means its overpriced. When combined with textbook cost of carry models, that formula shows that HFT capital gains depends almost exclusively on the difference between short term interest rates and dividend yield on stock [index], and volatility of the stock futures [index] and stock price volatility. For a popular hedge factor like the Emini, and its volatility, the formula not only predicts high frequency stock price behavior, it plainly shows how traders profit from and why they generate stock market volatility. Your article is quite correct to warn about the limitations of financial models by invoking Emanuel Derman’s recent book Models Behaving Badly. Ironically, Derman praises BlackScholes option pricing formula, based on some of the underlying assumptions in my formula, as an example of a successful formula.
A little history about the formula. It is a spin off of another paper on alpha strategy representation recently published by the American Statistical Association. In fact, the formula is a by product of a paper written to rebut Prof. Robert Jarrow (Cornell) paper which alleges that positive alpha is illusionary. So one can argue that Jarrow’s paper was a catalyst for the formula. I have been thinking about such a formula since my days in graduate school when renown Prof. Jan Kmenta, admonished me for paying attention to data analysis results, produced by Prof. Robert Engle and his students, without understanding the theory driving those results.
In passing, the subject formula is different from Easley, De Prado and O’Hara formula which deals with market microstructure issues arising from toxicity of order flow.
Again, thanks for taking the time to write about the formula. If you have any questions, please do not hesitate to contact me via email: godfrey.cadogan@ryerson.ca, gocadog@gmail.com (preferred) or call 7863295489.
Hi Eric,
While this is not appropriate for the comment section of AllAboutAlpha.com, we do take advertising in limited quantities. If you are interested, please contact me at kfox@allaboutalpha.com.
Kind regards,
Kristin Fox