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Daily Speculations The Web Site of Victor Niederhoffer & Laurel Kenner Dedicated to the scientific method, free markets, deflating ballyhoo, creating value, and laughter; a forum for us to use our meager abilities to make the world of specinvestments a better place. |
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6/13/2005
Fractals, by Phil McDonnell
In Paul H. Cootner's book The Random Character of Stock Market Prices (1964), there is a paper by Benoit Mandelbrot. The paper discussed the important question of how long is the coast of England? In what may be the only worthwhile result to come out of fractal mathematics, Mandelbrot argued that it depends upon the scale at which you analyze the question. At the very largest scale the length of the coast is the shortest because we are using only a few straight lines to characterize the shape. At increasingly fine granularity we use more lines and thus the total path length must increase. One could argue the coast of England is infinitely long.
The same idea holds for trading. As we increase the granularity from monthly to weekly to day and tick data the path length must necessarily increase. For market makers that is a good thing. They have near zero transaction costs - primarily bookkeeping. They even profit from the spread rather than pay it. For most others high frequency trading involves more commissions, paying the spread and sometimes information lag costs which are difficult to estimate e.g. price quotes might be 1 minute old or even 15-20 minutes delayed for some traders.
So the idea that increasing the frequency of trading will increase the profit potential is true but there is an important tradeoff because it will also increase trading costs as well. There is a third variable which is also important - what timeframe is predictable for you. For a fundamental investor relying on quarterly updates his time frame probably should be on the order of quarters or longer. For some quantitative strategies the time frame is in days or weeks. For other strategies, the anomaly they exploit may only last minutes or hours. The overall best time frame is a tradeoff between frequency, costs and your trading methodology.