Saturday, April 4, 2015

Why Kemel Density Analysis for Financial Markets

In my MBA course work from Stern School of Business, one of the courses I am currently taking is New Venture Financing by Professor Alexander Ljungqvist. His professional biography is listed here:
Briefly, Professor Ljungqvist is world renowned and he has previously taught at Harvard Business School, Oxford University (where he held the Bankers Trust Fellowship), Cambridge University (where he held the Sir Evelyn de Rothschild Fellowship), and London Business School. 
One of the topics he covered in the class was about using kemel density to analyze market and return performance of Mutual Funds versus Hedge Funds versus VC Fund versus Buyout Fund - in terms of relative fund risk. 
This prompted me to learn more about kemel density and its significance for analyzing risk in financial markets. 
The use of kemel density estimates in discriminant analysis is quite well known among scientists and engineers interested in statistical pattern recognition. Using kemel density estimate involves properly selecting the scale of smoothing, which is significant for minimization of misclassification errors. In the kemel density theory this is known as the "bandwidth parameter". Kemel density befits both single scale as well as multi scale dimensional analysis. In practice, it serves well to look at results for different scales of smoothing for the kemel density estimates. There has been extensive scientific research done to apply sub-classification when the scales are disparate. These characteristics make applying the kemel density particularly favorable when looking at performance of funds in the financial markets that we are interested in comparing for 'risk versus return' given that the funds themselves are fairly dispersed in their respective models. 

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