Market intraday momentum

I recently spotted the following intriguing paper: Market intraday momentum.
From the abstract of that paper:

Based on high frequency S&P 500 exchange-traded fund (ETF) data from 1993–2013, we show an intraday momentum pattern: the first half-hour return on the market as measured from the previous day’s market close predicts the last half-hour return. This predictability, which is both statistically and economically significant is stronger on more volatile days, on higher volume days, on recession days, and on major macroeconomic news release days.

Nice! Looks like we can all become rich now. I mean, given how it’s written, it should be quite easy for any individual with a trading account and a mouse to leverage up and start accumulating. Maybe this is so, but let’s have an informal closer look, with as little effort as possible, and see if there is anything we can say about this idea.


R tips and tricks – the assign() function

The R language has some quirks compared to other languages. One thing which you need to constantly watch for when moving to- or from R, is that R starts its indexing at one, while almost all other languages start indexing at zero, which takes some getting used to. Another quirk is the explicit need for clarity when modifying a variable, compared with other languages.

Take python for example, but I think it looks the same in most common languages:


Curse of dimensionality part 3: Higher-Order Comoments

Higher moments such as Skewness and Kurtosis are not as explored as they should be.

These moments are crucial for managing portfolio risk. At least as important as volatility, if not more. Skewness relates to asymmetry risk and Kurtosis relates to tail risk.

Despite their great importance, those higher moments enjoy only a small portion of attention compared with their lower more friendly moments: the mean and the variance. In my opinion, one reason for this may be the impossibility of estimating those moments, estimating them accurately that is.

It is yet another situation where Curse of Dimensonality rears its enchanting head (and an idea for a post is born..).


Portfolio Construction with R


Constructing a portfolio means allocating your money between few chosen assets. The simplest thing you can do is evenly split your money between few chosen assets. Simple as it is, good research shows it is just fine, and even better than other more sophisticated methods (for example Optimal Versus Naive Diversification: How Inefficient is the 1/N). However, there is also good research that declares the opposite (for example Large Dynamic Covariance Matrices) so go figure.

Anyway, this post shows a few of the most common to build a portfolio. We will discuss portfolios which are optimized for:

  • Equal Risk Contribution
  • Global Minimum Variance
  • Minimum Tail-Dependence
  • Most Diversified
  • Equal weights

We will optimize based on half the sample and see out-of-sample results in the second half. Simply speaking, how those portfolios have performed.


Machine learning is simply statistics

Note: I usually write more technical posts, this is an opinion piece. And you know what they say: opinions are like feet, everybody’s got a couple.

Machine learning is simply statistics

A lot of buzz words nowadays. Data Science, business intelligence, machine learning, deep learning, statistical learning, predictive analytics, knowledge discovery, data mining, pattern recognition. Surely you can think of a few more. So many you can fill a chapter explaining and discussing the difference (e.g. Data science for dummies).

But really, we are all after the same thing. The thing being: extracting knowledge from data. Perhaps it is because we want to explain something, perhaps it is because we want to predict something; the reason is secondary. All those terms fall under one umbrella which is modern statistics, period. I freely admit that the jargon is different. What is now dubbed feature space in machine learning literature is simply independent, or explanatory variables in the statistical literature. What one calls softmax classifier in the deep learning context, another calls multinomial regression in a basic 1-0-1 statistics course. Feature engineering? Call it variable transformation rather.


Bitcoin exponential growth

Is bitcoin a bubble? I don’t know. What defines a bubble? The price should drastically overestimate the underlying fundamentals. I simply don’t know much about blockchain to have an opinion there. A related characteristic is a run-away price. Going up fast just because it is going up fast.


Most popular posts – 2017

Writing this, I can’t believe how quickly the year 2017 has gone by. Also weird, we are already three weeks into 2018, unreal. Time flies when you’re having fun I guess.

The analytics report shows that the three most popular posts for 2017 are:


Understanding Kullback – Leibler Divergence

It is easy to measure distance between two points. But what about measuring distance between two distributions? Good question. Long answer. Welcome the Kullback – Leibler Divergence measure.

The motivation for thinking about the Kullback – Leibler Divergence measure is that you can pick up questions such as: “how different was the behavior of the stock market this year compared with the average behavior?”. This is a rather different question than the trivial “how was the return this year compared to the average return?”.


R tips and tricks – the pipe operator

The R language has improved over the years. Amidst numerous splendid augmentations, the magrittr package by Stefan Milton Bache allows us to write more readable code. It uses an ingenious piping convention which will be explained shortly. This post talks about when to use those pipes, and when to avoid using pipes in your code. I am all about that bass readability, but I am also about speed. Use the pipe operator, but watch the tradeoff.


Bitcoin investing

Bitcoin is a cryptocurrency created in 2008. I have never belonged with team “gets it” when it comes to Bitcoin investing, but perhaps time has come to reconsider.


Visualizing Tail Risk

Tail risk conventionally refers to the risk of a large and sharp draw down of the portfolio. How large is subjective and depends on how you define what is a tail.

A lot of research is directed towards having a good estimate of the tail risk. Some fairly new research also now indicates that investors perceive tail risk to be a stand-alone risk to be compensated for, rather than bundled together with the usual variability of the portfolio. So this risk now gets even more attention.