### On the Nature of Outliers: Quant Vs. Fundie Analysis

I've been thinking a lot about the implications of one of my prior posts, "Useful Applications for Quantitative Ability with Fundamental Analysis." I think there are a few things worth mentioning about the nature of residuals versus outliers, and how that plays into this whole schema I've written about god knows how many times.

The bottom line:

Sure, I could de-noise my time series prior to calculating rolling correlations of every stock on every other stock, and sure I could calculate the correlations of the wavelet spectra, but while that may be more technically precise, it first of all dramatically increases the computational time. But even assuming computational time wasn't an issue, it's not really hitting at the point.

Traditional correlation and the correlation of wavelet spectra are not orthogonal concepts. They are generally jabbing in the same direction. If that is true, then turn to what the goal of analytics are in a deep value setting, and what deep value investors are attempting to do. They are attempting to find situations which are completely out of the ordinary, and are content on sitting on their hands until they are able to find such a situation.

If I am looking for a situation that is truly out of the ordinary, then statistics and hardcore mathematics will not help me 99% of the time, because we aren't trading

I know that a lot of times, a good investment comes as a result of many small oddities lumped on top of eachother. In this sort of situation it does help to have the additional precision. But the driving notion is to keep in mind the nature of the diminishing returns due to precision in a value framework.

The bottom line:

- Quants may toss outliers to denoise their data so that they can properly estimate the "true" relationship between two variables. Once they have established the "truth," they can simply trade the noise. That is the game of tons of prop trading shops, and it does make some sense. I have done it myself while at a big bank. And we traded a ton of bonds.
- Fundamental analysts ('FA's') actively seek those same outliers which were thrown out. Rather than trade continuously, they sit on their hands in waiting most of the time. And when those outliers surface themselves, the FA's put on their positions in size. This also makes sense.

Sure, I could de-noise my time series prior to calculating rolling correlations of every stock on every other stock, and sure I could calculate the correlations of the wavelet spectra, but while that may be more technically precise, it first of all dramatically increases the computational time. But even assuming computational time wasn't an issue, it's not really hitting at the point.

Traditional correlation and the correlation of wavelet spectra are not orthogonal concepts. They are generally jabbing in the same direction. If that is true, then turn to what the goal of analytics are in a deep value setting, and what deep value investors are attempting to do. They are attempting to find situations which are completely out of the ordinary, and are content on sitting on their hands until they are able to find such a situation.

If I am looking for a situation that is truly out of the ordinary, then statistics and hardcore mathematics will not help me 99% of the time, because we aren't trading

*noise*, we are trading*outliers*. Whatever intuitive concept I am trying to pick up with statistics would have to be so extraordinary that at that point, any statistic generally pointing in a similar direction should be flashing red lights!I know that a lot of times, a good investment comes as a result of many small oddities lumped on top of eachother. In this sort of situation it does help to have the additional precision. But the driving notion is to keep in mind the nature of the diminishing returns due to precision in a value framework.

## 3 Comments:

Dan,

I am a little confused about your reference/s to wavelet spectra. I tried to lookup some resources on their applicability in finance. Can you share some?

Thanks.

By Anonymous, at 10:49 AM

I gotta admit that I'm no expert (my friend is though). However I've read a few papers on some of its applications.

A little background on the wavelet transform: I would be inclined to think of the wavelet transform as a bigger brother to the Fourier transform. Both are used to "decompose" a signal into its component parts. So instead of looking some process which is an odd function of its location, one can reduce that function to a bunch of numbers on an xy-plot representing the "frequency domain" with Fourier. With wavelets, one can do similar things to time series; however wavelets are much more flexible than Fourier could ever be. (To be technical in the case of Fourier, for example, one goes about doing this by creating a "basis" in the frequency domain consisting of a bunch of sines and cosines that are orthogonal to one another; one transforms whatever function you happen to be looking at from normal space to s-space and solves the resulting differential equation).

Because wavelets model time series in a very flexible way, they can be very helpful in finance-- not only for modeling but for de-noising. The reason is that what you'll end up with is a bunch of coefficients of varying frequency; the lower frequency coefficients is more likely than not to be signal, and the higher frequency coefficients are more likely than not to be noise. Below is a simple ppt which helps explain some of the benefits of wavelets:

http://faculty.kfupm.edu.sa/math/mgebeily/Wavelet%20SC/Introduction.pps

Wavelets can be useful when trying to detect correlation because one can simply compare the wavelet coefficients of the two signals with one another. This can be much more powerful than normal correlation because it is a cinch to remove the noise- just throw out the high frequency crap.

By Dan McCarthy, at 11:48 AM

As far as reading more into wavelets, your best bet might be with some of the primers that are now out in book format. There are bunch that can be found online. I would emphasize the use of wavelets as statistical tools before going into the finance applications. Finance-specific books tend to gloss over what really matters at times.

As soon as possible though I would recommend actually trying out the bad boys, for example in R (which is free). Here is a link to a list of contributed packages; there are a few wavelet packages in here: http://cran.r-project.org/src/contrib/PACKAGES.html. This in conjunction with a decent primer and you should be well on your way to a more intuitive understanding of their value.

By Dan McCarthy, at 11:56 AM

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