Asset pricing models are important because they help us understand which factors explain the variation of returns across diversified portfolios. However, models are not like cameras that provide a perfect picture of the world. If models were perfectly correct, they would be laws, like we have in

Investors have a tendency to sell assets that have earned them positive returns and are reluctant to let go of those that have brought them losses. This behavioural bias is called “disposition effect” and is attributed to loss aversion and regret avoidance. It has been widely documented by

As a private investor, the sheer amount of information that can be found on the internet is rather daunting. Trying to understand what type of companies or ETFs are available is incredibly challenging with there being millions of companies amd derivatives available on the market. Sure, the most

Since the financial crisis in 2008 the number of anomaly related academic papers exploded and has grown so quickly that it is impossible to keep up with the full scope of research. To accommodate the need of an overview in this interesting research field we will summarize the most prominent market

This is the third article of the copula-based statistical arbitrage series. You can read the previous two articles: Copula for Pairs Trading: A Detailed, But Practical Introduction. Copula for Pairs Trading: Sampling and Fitting to Data. Introduction Systematic approaches of pairs trading gained

Coastlines are fractal curves. When you zoom in, you will see similar shaped curves on every scale. The same is true for market data. On a naked chart you can hardly tell if it is a daily or hourly chart. This article will explore this feature of crinkly curves and show how much markets and

Environmental, Social, and Governance (ESG) investing has become a priority for a lot of investors. We have previously written on ESG being combined with factor investing here and here. However, if one chooses to ignore our previous musings on the subject and only pursue ESG, how would that decision

ArbitrageLab is a python library filled with algorithms from the best academic journals and graduate-level textbooks, which focuses on the branch of statistical arbitrage known as pairs trading. This playlist is a series of lecture videos that explore advanced topics and highlight how your team can

Editor’s note: Seeing how the results may have shifted since the “ARK phenomenon” would be a great robustness test for this paper. ETFs are growing at a rapid pace and becoming a significant contributor to intraday activity (and we are only making the problem worse!). Naturally, some will

Why Are High Exposures to Factor Betas Unlikely to Deliver Anticipated Returns? Chris Brightman (Research Affiliates) et al. January 11, 2021 By choosing investment strategies that intentionally create exposure to factor betas, investors may be obtaining uncompensated risks. We show across a wide

Broadly, there are three types of systematic trading strategy that can “work.” In order of increasing turnover they are: Risk premia harvesting Economically-sensible, statistically-quantifiable slow-converging inefficiencies Trading fast-converging supply/demand imbalances This post provides an

A couple of days ago we were seeing in the news the story about GameStop, and how small investors made some hedge funds abandon their short-selling positions after some big losses. After reading the article I couldn’t resist thinking about short-selling strategies and their performance in the

I have not posted many price-action studies to the blog lately, so I thought I would share this one from last night’s subscriber letter. A theme I have seen many times over the years is that persistent uptrends don’t often end abruptly. The study below is an example of this. It considers what

The ISEE sentiment index is the ratio of opening long call options to opening long short options. The idea is that the greater the ratio of calls, the more bullish the sentiment, and that this is a more reliable indicator (compared to other sentiment indices) because it’s based on actual trades as

If you’re a value investor who has determined that you have better things to do with your time, at some point you may have decided to outsource the investment task to a fund manager. And if you read our blog (especially this post) you’re probably looking to oursource to a systematic process

Our last post parsed portfolio optimization outputs and examined some of the nuances around the efficient frontier. We noted that when you start building portfolios with a large number of assets, brute force simulation can miss the optimal weighting scheme for a given return or risk profile. While

Contagion and self-fulfilling feedback loops are propagation mechanisms at the heart of systemic financial crises. Contagion refers to the deterioration of fundamentals through the financial network, often through a cascade of insolvencies. A critical factor is the similarity of assets held by

This is the second article of the copula-based statistical arbitrage series. You can read the first article: Copula for Pairs Trading: A Detailed, But Practical Introduction. Overview Whether it is for pairs trading or risk management, two natural questions to ask before putting copula for use are:

Animating time series is a very powerful tool to show evolution over time, but matplotlib default animations are boring and they are not well suited for comparison purposes. Along this blog, animations are widely used: from explaining how neural networks train, to showing synthetic time-series

Following up on my previous post, below is the chart of the temporal turning points that I have come up with. This particular example happens to be 10 minute candlesticks over the last two days of the GBP_USD forex pair. The details I have given about various turning points over the course of my

As my co-author Andrew Berkin and I explain in our new book “Your Complete Guide to Factor-Based Investing,” there is considerable evidence of cross-sectional return predictability. Citing more than 100 academic papers, we presented evidence of predictability for both equity and bond factors.

Estimating how individual assets are moving together is an important part of many financial applications1 and the most commonly used measure for this is the Pearson correlation. Unfortunately, for a variety of reasons, what sometimes appears to be a correlation matrix is actually not a valid

Principal component analysis (PCA from here on) is performed via linear algebra functions called eigen decomposition or singular value decomposition. Since you are actually reading this, you may well have used PCA in the past, at school or where you work. There is a strong link between PCA and the

Recent public reports have underscored a crisis of replicability in numerous fields of science: In 2012, Amgen researchers reported that they were able to replicate fewer than 10 of 53 cancer studies. In March 2014, physicists announced with fanfare that they had detected evidence of gravitational

One of the upsides of having a (very, very minor) public profile is that you get a lot of people asking you for advice, which is flattering (and if you say otherwise, you need to consider just how first world that particular 'problem' is). The only downside of this is you get asked the

High equity valuations are frequently justified by low interest rates There is no long-term evidence in the US to support this theory P/E ratios in Japan and Europe have remained low, despite zero or negative yields INTRODUCTION One of the more peculiar transactions I worked on as an investment

More and more evidence seems to suggest that social Media impacts daily momentum and volatility. Some hedge funds that were short GME the past couple of months should have read these blog posts. In a similar vein, there is plenty of twitter chatter on the topic and anecdotal evidence that during the

Our last few posts on risk factor models haven’t discussed how we might use such a model in the portfolio optimization process. Indeed, although we’ve touched on mean-variance optimization, efficient frontiers, and maximum Sharpe ratios in this portfolio series, we haven’t discussed portfolio

In 2020 Bitcoin delivered us another spectacular bull run. It was as impressive as the one we witnessed in 2017. The analysis of Bitcoin price time-series during its bull runs can uncover interesting results. By comparing a selected set of characteristics we could find some commonalities in trading.

In the following code box there are the results from the temporal clustering routine of my last few posts on the four forex majors pairs of EUR_USD, GBP_USD, USD_CHF and USD_JPY. This is based on 10 minute bars over the last year or so. Readers should read my last few previous posts for background.

Financial markets are not stationary: price curves can swing all the time between trending, mean reverting, or entire randomness. Without a filter for detecting trend regime, any trend following strategy will bite the dust sooner or later. In Stocks & Commodities February 2021, Richard Poster

Congratulations you made it to part2 of our tutorial. Give yourself a round of applause. If you stumbled upon part2 before reading part1 we advise you to start from the beginning and read part1 first. In Part2 we dive into mean variance portfolio optimization, mean CVar portfolios and backtesting.

This article explains candlesticks and why we like to use candlesticks when displaying charts. Moreover, we test quantitatively 23 different candlestick formations. Perhaps surprisingly, some of the formations work pretty well. Some of the formations can highly likely be improved by adding one more

The existence of a quality premium in stocks that has been persistent over time, pervasive around the globe, and robust to various definitions have been well documented by studies such as “Buffett’s Alpha,” “Global Return Premiums on Earnings Quality, Value, and Size,” and “The Excess

Data cleaning is the time-consuming but the most important and rewarding part of the data analysis process. The process of data analysis is incomplete without cleaning data. But what happens if we skip this step? Suppose we had certain erroneous data in our price data. The incorrect data formed

At the core of modern finance is the proposition that beta (market) risk is the dominant factor that drives performance. But numerous empirical tests of the capital asset pricing model (CAPM) over the decades suggest otherwise. There have be various attempts to adjust CAPM to find a closer mapping

Whilst backtesting architectures is a topic on its own, this article dives into how to correctly backtest a pairs trading investment strategy using a vectorized (quick methodology) rather than the more robust event-driven architecture. This is a technique that is very common amongst analysts and is

Benjamin Graham, often considered a strong candidate for the “the father of quantitative value investing“, developed an investment strategy that involved purchasing securities for less than their “current-asset value”, “a rough index of the liquidating value”. We uncovered ten research

Technical analysis of price and volume history won’t cut it alone nowadays. When we want to perform value investing and/or measure a security’s intrinsic value, we need to make a fundamental analysis of the security. To perform fundamental analysis we need data, lots of data. We want fundamental

In this post, we will investigate and showcase a machine learning selection framework that will aid traders in finding mean-reverting opportunities. This framework is based on the book: “A Machine Learning based Pairs Trading Investment Strategy” by Sarmento and Horta. A time series is known to

How have value, quality, low-volatility and momentum equity factors, and combinations of these factors, performed in recent years. In their October 2020 paper entitled “Equity Factor Investing: Historical Perspective of Recent Performance”, Benoit Bellone, Thomas Heckel, François Soupé and

Stock market returns were highly positive when the variance risk premium (VRP) was negative Returns were slightly negative across markets when the VRP was positive This relationship can not be exploited for market timing INTRODUCTION The US stock market in 1999 and 2020 had probably more

Market volatility measures the size of variations of asset returns. Macroeconomic uncertainty measures the size of unpredictable disturbances in economic activity. Large moves in macroeconomic uncertainty are less frequent and more persistent than shifts in market volatility. However, macroeconomic

The purpose of portfolio optimization is to minimize risk while maximizing the returns of a portfolio of assets. Knowing how much capital needs to be allocated to a particular asset can make or break an investors portfolio. In this article we will use R and the rmetrics fPortfolio package which

One major impediment to widespread adoption of machine learning (ML) in investment management is their black-box nature: how would you explain to an investor why the machine makes a certain prediction? What's the intuition behind a certain ML trading strategy? How would you explain a major

In 1998, Charles Ellis wrote “Winning the Loser’s Game,” in which he presented evidence that while it is possible to generate alpha and win the game of active management, the odds of doing so were so poor that it’s not prudent for investors to try. At the time, roughly 20 percent of actively

When trading in markets such as equities or currencies it is important to identify value areas to inform our trading decisions. One way to do this is by looking at the volume profile. In this post, we explore quantitative methods for examining the distribution of volume over a period of time. More

Part 1 of this analysis, which is available here, examines filters modeled on second-order processes from a digital signal processing (DSP) perspective to illustrate their properties and limitations. To briefly recap, a time series based on a second-order process consists of a mean a and a linear

Suppose that you encountered a promising pair of stocks that move closely together, the spread zig-zagged around 0 like some fine needle stitching that sure looks like a nice candidate for mean-reversion bets. What’s more, you find out that the two stocks’ prices for the past 2 years are all

Cointegration, a concept that helped Clive W.J. Granger win the Nobel Prize in Economics in 2003 (see Footnote 1), is a cornerstone of pairs and multi-asset trading strategies. Anecdotally, forty years have passed since Granger coined the term “cointegration” in his seminal paper “Some