Trading in a low vol world

I wanted to take a look at what works in low vol environments, such as we are currently experiencing. I am open to the idea we have entered a period of structurally low volatility due to increased regulatory burden and flow on effects from the decline of institutional FICC trading. Or it may just be a function of QE, and post-tapering we will see a return to higher levels.

The plan

The main idea is to compare mean reversion (MR) vs. follow through (FT). For simplicity I define mean reversion as an up day being followed by a down day, and a down day being followed by an up day. Conversely, follow through sees an up day followed by another up day, and a down day followed by a down day.

I took a look at the major US equity indices, SPX (GSPC), NDX and RUT.

For each series we calculate daily log returns for the current period and shift the forward to get the return for the next period. Then we calculate realized volatility (RV) and split the data set into "low volatility" and "high volatility", by looking at median realized vol for the whole series.

Then, for each series, we use bootstrapped samples to simulate a number of trajectories/equity curves for each strategy (MR/FT) under the two classes of RV. Finally we take an average of the total return of each trajectory to get a ballpark idea of how they went.

Results

The data is from the start of 1999 to the present, so roughly 15 years. Each run generates 1000 trajectories with a sample size of roughly 950.

For the low vol case, the results are unfortunately ambiguous. Follow through in a low vol environment seemed to do well for NDX and RUT, but the opposite was the case for SPX.

The TR column is the sum of the series over the whole period for the volatility class (i.e. a simple long only strategy), giving an idea of a directional bias that may be present in the sampling.

In the high vol environment, mean reversion was a clear winner, and consistent over the different underlyings.

The results seem relatively stable across trajectory size/sample size.

Outro

I'm not really sure what is going on SPX. My intuition was that FT would do well in low vol environments, but that doesn't seem to be the case, at least not for SPX.

I was actually getting consistent votes for FT in the low vol case, then restarted R to run with a clean environment and started getting the above instead. You can't spell argh without R it seems.

Source is up here. As always you can find me on twitter here. Thanks for stopping by.

Book Review: Applied Predictive Modeling by Max Kuhn and Kjell Johnson

This is a gem of a book.

From the introduction:

We intend this work to be a practitioner’s guide to the predictive modeling process and a place where one can come to learn about the approach and to gain intuition about the many commonly used and modern, powerful models.

…it was our goal to be as hands-on as possible, enabling the readers to reproduce the results within reasonable precision as well as being able to naturally extend the predictive modeling approach to their own data.

The book is structured into four main sections. First is General Strategies, which provides an introduction and discusses things like pre-processing and tuning. 

The next two sections cover regression and classification, each with chapters on linear and non-linear methods, as well as tree and rule based methods, with one to two chapters on practical issues such as measuring performance. 

The final section covers feature selection, predictor importance and a discussion around model performance. 

Features

There are a few things I really like:

It is not an academic or mathematical treatise; the emphasis is on practice, discussing the issues that commonly arise and how they can be approached. Plenty of references are provided for those wanting to dig deeper.

Every example has its data set and code available so one can work through the examples as presented. In most cases they are real world datasets and there is great discussion of the real world issues that arise, what should be considered and the various tradeoffs that can be made.

Discussion and code are separate. Aside from the excellent content, this is probably what I appreciate the most. Each chapter presents its content, with charts where appropriate, while the actual walk through of the code and raw output is in a separate section of the chapter. 

This makes it much easier to focus on the material being presented. It is always difficult to present source code along with discussion. This is not a book about programming per-se, it is about using existing tools to make intelligent and reasoned decisions about the task at hand. It makes a lot of sense to have the code presented separately.

Also, as far as I have read, each chart is at most only one page away from the text discussing it. This is a small thing but I feel there has been serious consideration about the presentation of the material and it has been done very well. [Update: This is not strictly true but is mostly the case throughout the book]

It is not a book about caret, the package of author Max Kuhn. To be honest I would be pretty happy even if it were about caret, which certainly does get some use in the code, but it is relatively package agnostic. 

Final thoughts

This is a great book, providing both the trees and the forest so to speak. I am unaware of any other book with similar content, and I wish I had something like this when I was first getting interested in machine learning. 

There are books that are very introductory, books that cover the details of the algorithms, and books that provide rigorous coverage of the theory, but these are not really accessible to those without a serious amount of mathematics. There are a few equations presented where appropriate, but it is certainly not the focus of the book.  

There are no real shortcomings, though if there were ever a second edition, coverage of time series methods and deep learning would be welcome. I appreciate they are both book worthy topics by themselves, and the latter is still very much a moving target. 

In summary: Great content, well written and well presented. This book would be my top recommendation to anyone looking to get started or working with predictive modeling. Well worth checking out. 

You can read more reviews on amazon here: Applied Predictive Modeling

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