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.


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.


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.