Beta in the tails

Every form of strength is also a form of weakness*. I love statistics, but I focus to much on methodology, which is not for everyone. Some people (right or wrong) question: “wonderful sir, but what can I do with it?”.

A new paper titled “Beta in the tails” is a showcase application for why we should focus on correlation structure rather than on average correlation. They discuss the question: Do hedge funds hedge? The reply: No, they don’t!

The paper “Beta in the tails” was published in the Journal of Econometrics but you can find a link to a working paper version below. We start with a figure replicated from the paper, go through the meaning and interpretation of it, and explain the methods used thereafter.

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How flexible neural networks really are?


A distinctive power of neural networks (neural nets from here on) is their ability to flex themselves in order to capture complex underlying data structure. This post shows that the expressive power of neural networks can be quite swiftly taken to the extreme, in a bad way.

What does it mean? A paper from 1989 (universal approximation theorem, reference below) shows that any reasonable function can be approximated arbitrarily well by fairly a shallow neural net.

Speaking freely, if one wants to abuse the data, to overfit it like there is no tomorrow, then neural nets is the way to go; with neural nets you can perfectly map your fitted values to any data shape. Let’s code an example and explain the meaning of this.

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Correlation and correlation structure (5) – a new coefficient of correlation

This is the fifth post which is concerned with quantifying the dependence between variables. When talking correlations one usually thinks about linear correlation, aka Pearson’s correlation. One serious limitation of linear correlation is that it’s, well.. linear. By construction it’s not useful for detecting non-monotonic relation between variables. Here I share some recent academic research, a new way to detect associations that are not monotonic.

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Correlation and correlation structure (4) – asymmetric correlations of equity portfolios

Here I share a refreshing idea from the paper “Asymmetric correlations of equity portfolios” which was published in the Journal of financial Economics, a top tier journal in this field. The question is how much the observed conditional correlation on the downside (say) differs from the conditional correlation you would expect from a symmetrical distribution. You can find here an explanation for the H-statistic developed in the aforementioned paper and some code for illustration.

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Adaptive Huber Regression

Many years ago, when I was still trying to beat the market, I used to pair-trade. In principle it is quite straightforward to estimate the correlation between two stocks. The estimator for beta is very important since it determines how much you should long the one and how much you should short the other, in order to remain market-neutral. In practice it is indeed very easy to estimate, but I remember I never felt genuinely comfortable with the results. Not only because of instability over time, but also because the Ordinary Least Squares (OLS from here on) estimator is theoretically justified based on few text-book assumptions, most of which are improper in practice. In addition, the OLS estimator it is very sensitive to outliers. There are other good alternatives. I have described couple of alternatives here and here. Here below is another alternative, provoked by a recent paper titled Adaptive Huber Regression.

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Day of the week and the cross-section of returns

I just finished reading an interesting paper by Justin Birru titled: “Day of the week and the cross-section of returns” (reference below). The story is much too simple to be true, but it looks to be so. In fact, I would probably altogether skip it without the highly ranked Journal of Financial Economics stamp of approval. However, by the end of the paper I was as convinced as one can be without actually running the analysis.

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Create own Recession Indicator using Mixture Models


Broadly speaking, we can classify financial markets conditions into two categories: Bull and Bear. The first is a “todo bien” market, tranquil and generally upward sloping. The second describes a market with a downturn trend, usually more volatile. It is thought that those bull\bear terms originate from the way those animals supposedly attack. Bull thrusts its horns up while a bear swipe its paws down. At any given moment, we can only guess the state in which we are in, there is no way of telling really; simply because those two states don’t have a uniformly exact definitions. So basically we never actually observe a membership of an observation. In this post we are going to use (finite) mixture models to try and assign daily equity returns to their bull\bear subgroups. It is essentially an unsupervised clustering exercise. We will create our own recession indicator to help us quantify if the equity market is contracting or not. We use minimal inputs, nothing but equity return data. Starting with a short description of Finite Mixture Models and moving on to give a hands-on practical example.

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Price Movement Prediction – another paper

Just finished reading the paper Stock Market’s Price Movement Prediction With LSTM Neural Networks. The abstract attractively reads: “The results that were obtained are promising, getting up to an average of 55.9% of accuracy when predicting if the price of a particular stock is going to go up or not in the near future.”, I took the bait. You shouldn’t.

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