Check out my earlier post on Fractals as a primer: http://myselfmeandyou.blogspot.com/2010/03/mathematics-rightly-viewed-possesses.html
My sudden interest in Fractals led me to read about different applications of it. Atmospheric sciences,forestry,astronomy,quantum physics and to my biggest surprise risk management and Finance.Having been a Risk Management Analyst at AON Corporation I had a fair understanding of portfolio management theory.I was surprised to find application of fractal theory in portfolio risk management.
Anyone familiar with portfolio risk assessment knows that for a given set of quantifiable risk in a portfolio, the aim is to maximize the profits.The risk reducing formulas behind portfolio theory has highly demanding assumptions.Firstly they suggest that price changes are statistically independent,ie.today's price change has no influence on tomorrows'. As a result predictions of future market scenarios become complex.Secondly all price changes conform to the standard bell curve(as measured by its sigma,or standard deviation).The width of the bell shape depicts the deviation from mean.
Do real time price changes conform to these? Definitely not ! If they would have then Investment Banks and risk consultancy firms wouldn't be hunting for the brightest minds on earth.
So where does Fractal theory come into picture.Have a look at the figure below.Does it strike any chords?
On a practical level, a fractal generator can be developed based on historical market data. The actual model used does not simply inspect what the market did yesterday or last week. It is in fact a more realistic depiction of market fluctuations, called fractional Brownian motion in multifractal trading time. The charts created from the generators produced by this model can simulate alternative scenarios based on previous market activity.
Further mathematical explanation on how the fractals are generated and how it can be interpolated and so on are right now beyond my grasp.Will update it as soon as I get a firm gripping about Fractal Theory:)
2 comments:
interesting article.. didnt know that fractals had applications in marketing also.so does that mean that if you observe data over a large scale sampled with a less sampling rate,then you can use fractal theories to get the exact data at any time.I mean once you get the first graph in the figure,will you be able derive the remaining graphs by just extrapolating?
@vipin : There are cyclical and seasonal trends that affect risk portfolios which can be analysed well using fractals.They form a recursive pattern.
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