Imagine we’re traders in a market where the cross-section of returns is related to V \geq 1 variables: In the equation above, \alpha^\star denotes the mean return, and each \beta_v^\star captures the relationship between returns and the vth right-hand-side variable. Some notation: I’m going to

The term statistical arbitrage (stat-arb) encompasses a wide variety of investment strategies that typically aim to exploit a statistical equilibrium relationship between two or more securities. The general principal is that any divergence from the equilibrium is a temporary effect and that bets

Throughout this series, which has been a window into the workflow of professional quant trading firms, we’ve encouraged you to submit questions and requests for further clarification. So, in this episode, being the final installment, Delaney answers as many of these questions as possible (within

Position sizing is often the result of portfolio construction and is therefore largely overlooked in manager selection. Risks introduced by active strategies can change not only the absolute risk level of the portfolio, but also the relative composition of risk. Active risk can also create tracking

In addition to the "usual" tricks of statistical arbitrage, trend-following and fundamental analysis, many quant shops (and retail quants!) engage in natural language processing (NLP) techniques to build systematic strategies. Such techniques fall under the banner of Sentiment Analysis. In

Risk Management… It’s not as sexy as the latest hot indicator… Or the undiscovered penny stock poised for an explosive move… Or the trading guru who appeared out of nowhere and is now promising to share the “secrets” to making million dollar profits overnight… But there are a whole

The CBOE PutWrite Index has outperformed the BuyWrite Index by approximately 1.1 percent per year between 1986 and 2015. That is pretty impressive. But troubling. Yes – troubling – because the theory of put-call parity tells us that such outperformance should be almost impossible via a

A decision tree is one of the widely used algorithms for building classification or regression models in data mining and machine learning. A decision tree is so named because the output resulting from it is the form of a tree structure. Visualizing a sample dataset and decision tree structure

Welcome back! This week’s post will backtest a basic mean reverting strategy on a cointegrated ETF pair time series constructed using the methods described in part I. Since the EWA (Australia) – EWC (Canada) pair was found to be more naturally cointegrated, I decided to run the rolling linear

Shiller’s Cyclically Adjusted Price to Earnings Ratio (CAPE ratio) is at 27.8, which is 11.1 above its long-term mean of 16.7, signifying overvaluation of stocks and low forward returns. According to Jeremy Siegel it incorporates time-inconsistent data, and the failure to correct for changes in

Traders are constantly looking for variables that predict returns. If x is the only candidate variable traders are considering, then it’s easy to use the Bayesian information criterion to check whether x predicts returns. Previously, I showed that using the univariate version of the Bayesian

Can you distinguish alpha from beta? Child’s play, right? Measure an investment portfolio against a relevant benchmark and, voila, all is clear. But as a new paper reminds, analyzing risk and return based on time horizon changes a black-and-white world of equity factors into 50 shades of gray.

I’m starting to feel like a rancourous curmudgeon, but I am frustrated by some of the misguided commentary on asset allocation and how diversification is a myth. We have posted a lot of research on fairly complex asset allocation topics, but I think many readers would be surprised to learn that I

I’m a huge fan of hard-core academics that produce incredible research, and yet, very few are familiar with their research. I call these folks, “undiscovered gems.” One might ask why undiscovered gems exist. On one hand, if a researcher produces incredible research, they should be widely

This post is about using Docker - a containerisation tool - to run automated trading strategies. I'll show you a simple example of how to use Docker with my python back testing library pysystemtrade to run a backtest in a container, and get the results out. However this post should hopefully be

These are some of the questions that popular forums get inundated with from aspiring novice algorithmic traders around the world. A good starting point for a wannabe trader would be to pick up a good book, immerse oneself, and absorb all that the book has to offer. This post details down the core

This is a test of a tactical bond strategy from Paul Novell of Investing for a Living. The model rotates among a broad basket of bond asset classes based on rules similar to Gary Antonacci’s Dual Momentum. Results from 1970, net of fees, follow. Read more about our backtests or let AllocateSmartly

In the last post, I compared three systems that traded the same instrument (SPY) in different ways, and also compared the combination of the three systems. Combining those systems reduced risk, which allowed us to increase our position size (either through more cash or using leverage). We could then

Opex week in January is one that the market has seen some struggles over the last 18 years. Below is the list of January op-ex weeks from 1999 – 2016 with their full week performance results. There have been 7 years in which January op-ex week occurred in conjunction with Martin Luther King Day.

This article looks at iron condors (IC) entered at 45 days to expiration (DTE). The introduction to this series, here, describes the different variations of SPX iron condors (IC) and exits that were tested. As mentioned in the 38 DTE IC results summary post, these tests covered 9 IC variations, with

In this paper we consider the question of how to improve the efficacy of strategies designed to capture factor premiums in equity markets and, in particular, from the value, quality, low risk and momentum factors. We consider a number of portfolio construction approaches designed to capture factor

Ben Carlson at Ritholtz Asset Management reminds us that backtesting offers no shortcuts to investment nirvana. As he correctly points out, there are numerous shortcomings in the art/science of reconstructing the historical results of an investment strategy. But it’s also true that backtesting, if

Last year was not a good year for trend following, with many commenting that the performance for the strategy has been declining over the last few years. We decided to look at the performance of the Wisdom State of Trend Following index on a long timeframe, to let the results speak over the long

Last week’s commentary highlighted why we believe traditionally built portfolios may face return headwinds going forward. Traditionally built stock/bond allocations also exhibit extremely high risk concentrations. Non-traditional exposures, now available as low-cost ETFs, can help introduce

In previous articles the concept of cointegration was considered. It was shown how cointegrated pairs of equities or ETFs could lead to profitable mean-reverting trading opportunities. Two specific tests were outlined–the Cointegrated Augmented Dickey-Fuller (CADF) test and the Johansen

The next two blog posts will explore the basics of the statistical arbitrage strategies outlined in Ernest Chan’s book, Algorithmic Trading: Winning Strategies and Their Rationale. In the first post we will construct mean reverting time series data from cointegrated ETF pairs. The two pairs we

January is here again and market commentators are already telling stories about the so-called January Effect. Some articles (examples here and here) are saying the effect is an illusion, while others are claiming the effect can help you make some profits (examples here and here). Before we dig into

Skewness is a statistical measure of how returns behave in the tails of a probability distribution. Wikipedia has a more robust definition of skewness with some good visuals here. If an investment (e.g., stocks) has negative skewness this means that the extreme returns are more likely to be negative

Bloomberg Gadfly's Lisa Abramowicz (follow her on twitter here) outlined in a recent piece The Credit Boom that Just Won't Die the insatiable demand for investment grade credit. Last month, bankers and investors told Bloomberg's Claire Boston that they expected U.S. investment-grade

Asset returns based on low frequency prices (e.g. end-of-day quotes) are still dominating modern portfolio analysis. To make portfolio metrics more relevant intraday and improve the precision of estimates, new data frequency needs to be explored. In this presentation we demonstrate how using high

The guest for this episode is Jack Vogel from Alpha Architect, a quantitative asset management and consulting firm. Jack has published a number of papers on SSRN and also co-authored a couple of books including “Quantitative Momentum: a practitioners guide to building a momentum-based stock

Existing research has documented cross-sectional seasonality of stock returns – the periodic outperformance of certain stocks relative to others during the same calendar month, weekday, or pre-holiday periods. A model based on the differential sensitivity of stocks to investor mood explains these

POST OUTLINE Motivation Get Data Default Plot with Recession Shading Add Chart Titles, Axis Labels, Fancy Legend, Horizontal Line Format X and Y Axis Tick Labels Change Font and Add Data Markers Add Annotations Add Logo/Watermarks MOTIVATION Since I started this blog a few years ago, one of my

I am very excited to finally share some of my research exploring Meucci’s (Meucci (2005)) portfolio optimization methods, and how the resulting portfolios compare to the use of historical data. For those unfamiliar with Attilio Meucci, he runs an annual Advanced Risk and Portfolio Managment

Which color do you like better? Green or brown? I’m partial to the green curve myself. That green curve comes from writing puts…sort of. Writing puts can be a lower volatility play that makes you money in choppy or flat markets, falls more softly in down markets, and seriously under-performs

Two bits of site news: First, after 4+ years of running this site mostly gratis, I’ve decided to dabble in adding advertisements, so expect to begin seeing the first baby steps with a handful of ads from Google. I’ve tried to keep the ads as unobtrusive as possible and my hope is that your

After reviewing the 2016 performance of trend-following (-18.15%), its unclear why anyone would mention the word “trend following” in a public forum. But we’ll give it a whirl anyway… The comedian Victor Borge once famously observed, “Santa Claus has the right idea – visit people only

My last post on using PercentRank to measure mean reversion proved very popular. A reader looked at the trades and wondered if it would be best to exit after five days because the average trade with longer holds was a loser. I am surprised I have not covered this topic before. Background Early in

Happy new year to all readers! With best wishes for your trading in the coming twelve months, which — I’m sure you’ll agree — will prove interesting from several perspectives. We start the year by looking back at the performance of trend following over the year just passed. Unsurprisingly

The ninth annual R/Finance conference for applied finance using R will be held on May 19 and 20, 2017 in Chicago, IL, USA at the University of Illinois at Chicago. The conference will cover topics including portfolio management, time series analysis, advanced risk tools, high-performance computing,

Happy New Year! To kick off the year, we want to share a white paper we penned mid-December containing our views on building a modern strategic asset allocation. The white paper covers: Why we believe tailwinds from the last 30 years are turning into headwinds for traditionally allocated stock-bond

December 2016 Trend Following: UP +1.38% / 2016: -18.15% December closed 2016 on a slight positive note, avoiding six straight months of negative returns for our State of Trend Following index. An inflection point was felt in the markets towards the close of the year, but this was obviously not

The 2017 American Finance Association conference is kicking off later this week in Chicago. If you haven’t been before — check it out. The conference is the biggest meeting of top-tier academic researchers on the planet. You can review all the research being presented at the following link. Some

Imagine that we’re trying to predict the cross-section of expected returns, and we’ve got a sneaking suspicion that x might be a good predictor. So, we regress today’s returns on x to see if our hunch is right, \begin{align*} r_{n,t} = \hat{\mu}_{\text{OLS}} + \hat{\beta}_{\text{OLS}} \cdot

In the last post, 38 DTE Iron Condor Results Summary, I showed the backtest results from 97,416 iron condor (IC) trades. All of those test results were based on weekly expiration data at 38 days to expiration (DTE). In this post, we'll look at a few key metrics and how those metrics differ

This is a summary of the recent performance of a number of excellent tactical asset allocation strategies. These strategies are sourced from books, academic papers, and other publications. While we don’t (yet) include every published TAA model, these strategies are broadly representative of the

In a recent posting, I compared the prices of US active mutual fund to estimates of future pre-fee excess returns. In summary, I found that the annual expenses of most active funds met or exceeded a generous estimate of their potential before-fee excess returns. That is, many funds look like

Happy new year! I have noticed that my quantitative posts get the most readership and discussion. So this year, I’ll be posting a lot more research and will start the year off by exploring momentum’s robustness. There are two good ways to test the robustness of a rules-based trading strategy:

Overfitting the data is a serious problem when constructing financial models. One way to guard against this is to have lots of data. This helps you determine if your results are robust by seeing how they hold up over different time periods. But this assumes the underlying market dynamics remain

Statistical Arbitrage , A.K.A StatArb is a pair trading strategy that invloves buying and selling a pair of stocks based on a underlying correlation between them. This correlation usually exist in a given sector or competitors, for example Pepsi (PEP) and Coca-Cola (KO) is a pretty popular pair. The