Blog - 5/16 - Eran Raviv

Portfolio Construction Tilting towards Higher Moments

Blog, Finance and Trading, Statistics and EconometricsPosted on 06/10/2019

When you build your portfolio you must decide what is your risk profile. A pension fund’s risk profile is different than that of a hedge fund, which is different than that of a family office. Everyone’s goal is to maximize returns given the risk. Sinfully but commonly risk is defined as the variability in the portfolio, and so we feed our expected returns and expected risk to some optimization procedure in order to find the optimal portfolio weights. Risk serves as a decision variable. You choose the risk, and (hope to) get the returns.

A new paper from Kris Boudt, Dries Cornilly, Frederiek Van Hollee and Joeri Willems titled Algorithmic Portfolio Tilting to Harvest Higher Moment Gains makes good progress in terms of our definition of risk, and risk-return trade-off. They propose a quantified way in which you can adjust your portfolio to account not only for the variance, but also for higher moments, namely skewness and kurtosis. They do that in two steps. The first is to simply set your portfolio based on whichever approach you follow (e.g. minvol, equal risk contribution or other). In the second step you tilt the portfolio such that the higher moments are brought into focus and get the attention they deserve. This is done by deviating from the original optimization target so that higher moments are utility-improved: less variance, better skew and lower kurtosis.

Adaptive Huber Regression

Blog, Finance and Trading, Risk, Statistics and EconometricsPosted on 05/19/2019

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.

Intuitive Explanation of Entropy in Statistics

Blog, Statistics and EconometricsPosted on 04/24/2019

This post is about the concept of entropy in the context of information-theory. Where does the term entropy comes from? What does it actually mean? And how does it clash with the notion of robustness?

Matrix-style screensaver in R

Blog, MiscTips, RPosted on 03/31/2019

This post shares short code snippet to make your own screen saver in R, The Matrix-style:

Day of the week and the cross-section of returns

Blog, Finance and TradingPosted on 03/15/2019

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.

R Journal publication

Blog, Code, RPosted on 03/01/2019

The R Journal is the open access, refereed journal of the R project for statistical computing. It features short to medium length articles covering topics that should be of interest to users or developers of R.

Christoph Weiss, Gernot Roetzer and myself have joined forces to write an R package and the accompanied paper: Forecast Combinations in R using the ForecastComb Package, which is now published in the R journal. Below you can find a few of my thoughts about the journey towards publication in the R journal, and a few words about working with a small team of three, from three different locations.

What is a Latent Variable?

Blog, Statistics and EconometricsPosted on 02/23/2019

This post provides an intuitive explanation for the term Latent Variable.

Most popular machine learning R packages – part 2

Blog, Statistics and EconometricsPosted on 02/10/2019

In a previous post: Most popular machine learning R packages, trying to hash out what are the most frequently used machine learning packages, I simply chose few names from my own memory. However, there is a CRAN task views web page which “aims to provide some guidance which packages on CRAN are relevant for tasks related to a certain topic.” So instead of relying on my own experience, in this post I correct for the bias by simply looking at the topic
Machine Learning & Statistical Learning. There are currently around 100 of those packages on CRAN.

R tips and tricks – higher-order functions

Blog, RPosted on 01/27/2019

A higher-order function is a function that takes one or more functions as arguments, and\or returns a function as its result. This can be super handy in programming when you want to tilt your code towards readability and still keep it concise.

Most popular posts – 2018

BlogPosted on 01/13/2019

2019 is well underway. 2018 was personally difficult, so I am happy it’s behind us. Without further ado, here is what my analytics report shows to be the three most popular posts for 2018:

Reproducible Finance with R – book review

Blog, RPosted on 01/05/2019

Reproducible Finance with R is a clever book, with modern treatment of classical concepts. Here below is what I liked- and disliked about the book.

Create own Recession Indicator using Mixture Models

Blog, Finance and Trading, Statistics and EconometricsPosted on 11/27/2018

Context

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.

Price Movement Prediction – another paper

Blog, Finance and TradingPosted on 10/14/2018

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.

Test of Equality Between Two Densities

Blog, Statistics and EconometricsPosted on 10/08/2018

Are returns this year actually different than what can be expected from a typical year? Is the variance actually different than what can be expected from a typical year? Those are fairly light, easy to answer questions. We can use tests for equality of means or equality of variances.
But how about the following question:

is the profile\behavior of returns this year different than what can be expected in a typical year?

This is a more general and important question, since it encompasses all moments and tail behavior. And it is not as trivial to answer.

In this post I am scratching an itch I had since I wrote Understanding Kullback – Leibler Divergence. In the Kullback – Leibler Divergence post we saw how to quantify the difference between densities, exemplified using SPY return density per year. Once I was done with that post I was thinking there must be a way to test the difference formally, rather than just quantify, visualize and eyeball. And indeed there is. This post aim is to show to formally test for equality between densities.

Orthogonality in Statistics

Blog, Statistics and EconometricsPosted on 09/23/2018

Orthogonality in mathematics

The word Orthogonality originates from a combination of two words in ancient Greek: orthos (upright), and gonia (angle). It has a geometrical meaning. It means two lines create a 90 degrees angle between them. So one line is perpendicular to the other line. Like so:

Even though Orthogonality is a geometrical term, it appears very often in statistics. You probably know that in a statistical context orthogonality means uncorrelated, or linearly independent. But why?

Why use a geometrical term to describe a statistical relation between random variables? By extension, why does the word angle appears in the incredibly common regression method least-angle regression (LARS)? Enough losing sleep over it (as you undoubtedly do), an extensive answer below.