# MovX: Research Analysis — Two Optimization-based Approaches to Portfolio Construction

## Analysis and Summation of the paper, done by Elias Kassell Raymond.

#### Information on the Paper

Title: Two Optimization-based Approaches to Portfolio Construction

Authors: Debarghya Das

Publish Date: 2015? Unclear

#### Star Ratings (Out of 5)

Technical Difficulty: ****

Length: ***

Scientific Process: ***

#### My Take

What I really like about this paper is that it neatly lays out two practical algorithms. It was not published in any journal I can find, and clearly written as part of a wider set of interests. He currently works for Google and in the past has worked for Facebook, but at the time of writing he was just a student. He has an incredibly good website here. What I don’t like about this paper is that as he was a student at the time of writing so lacks the experience to know the importance of properly introducing the maths he uses, which can be confusing; most of it is standard though to someone acquainted with bishop.

The first paper outlines an algorithm for risk aversion, while the other outlines an algorithm predicting the direction of movement of a 1 dimensional data set. In order to understand the outcome of paper you will need a decent amount of knowledge of statistics, but an understanding of machine learning is very useful too.

In brief, the first algorithm uses the correlation between investment risk and the Chicago Board Options Exchange (CBOE) volatility index for the S&P 500 (VIX) in order to create a mathematical model that avoids investing during risky periods. The model required a lot of specific parameters to train, which were tested out through trial and error by the author in order to come to a successful result. Some particular things to note about this algorithm are:

• Nice use of a lognormal distribution
• Good constraints for the model
• Good use of assuming VIX correlation with volatility backed by clear references
• Generates significant improvement over the Markowitz model, though not as good as the SPDR ETFs
• One of the conclusion points that “we confirm the volatility index as a suitable predictor for stock market prices” is not entirely accurate as this was one of the assumptions they used in creating the model, rather than a hypothesis they proved

Also in brief, the second algorithm uses a SVM (Support Vector Machine) to predict changes in a 1 dimensional series of 782 observations. Some things to note are:

• Successfully predicted the direction of movement 63.03% of the time. There was however no mention of statistical analysis of this binary classification, such as an F1 score. What if the the model always predicted the next sequential item would always increase, and 63.03% of the testing data increased from the previous item?
• Transaction costs not incorporated into the model
• Had a 10–20 minute run time to backtest in their set up, potentially limiting the opportunity for real time deployment

Overall this paper was a good read and presents some interesting algorithms that cover a lot of ground for further work.

I implemented a trading algorithm very similar to his using SVMs, feel free to have a play around with it. I have not tested it much due to this being a weekly blog post; if you get decent results then be sure to cite me and Mov38! Some potential improvements would be:

• Training the model on a large data set before applying, saving in a JSON or equivalent (JSON is pretty easy to use with Python)
• Using a variety of different equities
• Exploring creating models for different sectors, as different equities likely act differently in situations

Disclaimer: The reviews made here are informal and based purely on my own experience and education, the things I have read and the conclusions I have drawn. Your own investment choices should be made based on immense amounts of research resulting in educated decisions that are made at your own discretion; I am merely suggesting interesting sources of information and therefore not liable for the decisions you make. If you’d like to leave feedback, point out errors in my writing or logic, or simply want to discuss my reviews then I’d love for you to contact me personally at eliaszoharkr@gmail.com.