The basic Vector Autoregression (VAR) model is heavily used in macro-econometrics for explanatory purposes and forecasting purposes in trading. In recent years, a VAR model with time-varying parameters has been used to understand the interrelationships between macroeconomic variables. Since

Guess what? The model we built in our last post actually suffers from snooping. We did this deliberately to show how easy it is to get mixed up when translating forecasting models into trading signals. Let’s explain. Our momentum model uses a 12-week cumulative return lookback to forecast the next

Unlucky 13! Or contrarian indicator? There’s really nothing so heartwarming as magical thinking. Whatever the case, on Day 12 we iterated through the 320 different model and train step iterations to settle on 10 potential candidates. Today, we look at the best performing candidate and discuss the

In probability and statistics, distributions are often classified as either “thin-tailed” or “fat-tailed,” a distinction that reflects the likelihood of extreme deviations from the mean. The lognormal distribution, however, defies this binary classification. It possesses characteristics that

In Day 11, we presented an initial iteration of train/forecast steps to see if one combination performs better than another. Our metric of choice was root mean-squared error (RMSE)1 which is frequently used to compare model performance in machine learning circles. The advantage of RMSE is that it is

On Day 10, we analyzed the performance of the 12-by-12 model by examining the predicted values and residuals. Our initial takeaway suggested the model did seem not overly biased or misspecified in the -10% to 10% region. But when it gets outside that range, watch out! We suspected that there was

While portfolio optimization typically focuses on risk and return prediction, implementation costs critically matter. Unfortunately, predicting trading costs is challenging because the largest component for a large investor is price impact, which depends on the size of the trade, the amount traded

On Day 9 we conducted a walk-forward analysis on the 12-by-12 week lookback-look forward combination. We then presented the canonical the actual vs. predicted value graph with a 45o line overlay to show what a perfect forecast would look like. Here’s the graph again. As noted previously, we

Yesterday we finished up our analysis of the regression models we built using different combinations of lookback and look forward momentum values. Today, we see if we can generate good forecasts using that data. If you’re wondering why we still haven’t tested Fibonacci retracements with

Understanding the “invisible tail” of a power law distribution is crucial for accurate extreme value analysis, especially in fields where rare, extreme events have a large impact. In finance, natural disaster modeling, and engineering, rare events, or outliers, are disproportionately impactful.

Yesterday, we discussed the size effects, their statistical significance (e.g., p-values), and some other summary statistics for the various momentum combinations – namely, 3, 6, 9, and 12 week lookback and look forward returns. We found that size effects were small, but a few were significant,

Welcome to the last day of the first week of 30 days of backtesting! We hope you’re enjoying the ride. If you have any questions or concerns, you can reach us at the contact details listed at the bottom of this post. On Day 6 we defined momentum rather roughly and ran a bunch of tests to identify

In the previous post of this series on covariance matrix forecasting, I reviewed both the simple and the exponentially weighted moving average covariance matrix forecasting models, which are straightforward extensions of their respective univariate volatility forecasting models to a multivariate

Yesterday we examined the eponymous Fama-French factors to see if we could find something that will help us develop an investment strategy to backtest. It turned out the best performing factor was the market risk premium, which is essentially the return to the market in excess of the risk-free rate.

If the task is to identify a firm’s true profitability, can AI outsmart seasoned analysts? Given the increasingly bloated nature of financial reports, decoding the twists and turns associated with events like obscure one-time gains and out-of-nowhere expenses to extract core earnings has become

Our article explores a simple mean reversion trading strategy applied to FX futures, focusing on identifying undervalued and overvalued currencies to generate returns. Using FX futures rather than spot rates allows for the inclusion of interest rate differentials, simplifying the analysis. The

I would like to share the youtube video of my online seminar at Minnesota Center for Financial and Actuarial Mathematics and presentation slides. I discuss the motivation behind introducing the log-norml stochastic volatility (SV) model in our IJATF paper with Parviz Rakhmonov. I briefly highlight

I just published Part 1 of my new YouTube series, and I'm excited to share it with you all! After my recent post about automating trading strategies with AWS Cloud, many of you asked for a deeper dive into the technical implementation. Well, here it is! What's in Part 1? In this first

The day has finally arrived! Time to start backtesting! We’ve always wanted to test how Fibonacci retracements with Bollinger Band breakouts filtered by Chaikin Volatility would perform while implementing rolling stop-loss updates based on the ATR scaled by the 7-day minus 5-day implied volatility

We’re four days in and you’re probably wondering when are we actually going to start backtesting?! The answer is that while it is natural to want to rush to the fun part – the hope and elation of generating outsized returns and Sharpe Ratios greater than 2 – the reality is getting the

Yesterday we investigated the effect of using the 200-day simple moving average (200SMA) as a proxy for a rules-based investing method. The idea was to approximate what a reasonably rational actor/agent might do in addition to the buy-and-hold approach. When folks talk about research, backtesting,

On Day 1, we decided on a few benchmarks to use for our backtest. That is, a 60-40 and 50-50 weighting of the SPY and IEF ETFs. What we want to add in now is the Hello World version of trading strategies – the 200-DAY MOVING AVERAGE! Why are we adding this to our analysis? As we pointed out

Yesterday we set out our plan to backtest a strategy using the SPY ETF, which tracks the S&P 500. Before we commence, we obviously need to establish a baseline. What metrics will we use to assess the strategy? How will we define success? What benchmarks will we use? Typically, for a single asset

Reinforcement learning (RL) is one of the most exciting areas of Machine Learning, especially when applied to trading. RL is so appealing because it allows you to optimise strategies and enhance decision-making in ways that traditional methods can’t. One of its biggest advantages? You don’t have

I recently posted a paper, “Transforming Stock Market Forecasts with Variable Expected Returns,” on the SSRN online repository. This paper resolves an issue that has been bugging me for years. The link is: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=495384 This paper is not about making

"What we know is a drop; what we don't know is an ocean.” Isaac Newton. Many of Isaac Newton's early theories and ideas were met with skepticism or outright failure. Newton spent years working on problems related to motion, optics, and gravity, often facing dead ends and revisions.

Artificial Intelligence (AI) offers the intriguing potential to revolutionize investment decision-making by providing important advantages such as: Enhanced Data Analysis: AI can process and analyze vast amounts of data from various sources, including financial news, market trends, and company

Our research will explore the intriguing phenomenon of the Pre-Holiday effect in commodities, particularly crude oil and gasoline. Historical data reveals a short-term price drift prior to major U.S. holidays, suggesting a trend in these markets. We hypothesize that this anomaly may be driven by

In the initial post of the series on volatility forecasting, I described the simple and the exponentially weighted moving average forecasting models, that are both easy to understand and relatively performant in practice. Beyond (univariate) volatility forecasting, these two models are also widely

A weaker-than-expected July jobs report, with the unemployment rate increasing to 4.3%, officially triggered the Sahm Rule, causing investors to worry that the Federal Reserve may be behind the curve in cutting interest rates to prevent a recession. (The August report showed an increase in payroll

In this article, we explore the historical performance of sector momentum strategies and examine how their alpha has diminished over time. By analyzing the underlying causes behind this decline, we identify key factors contributing to the underperformance. Most importantly, we introduce an enhanced

This year I launched a strategy subscription service for a long-only ETF strategy developed in house. I learned a lot through this process but I made several mistakes that pushed me to learn new skills and improve the product offering. In this series I will discuss my initial mistakes, and how

What are the Research Questions? The research questions are as follows: How can textual analysis of business news, specifically The Wall Street Journal (WSJ), be used to measure the state of the economy? What is the structure of news coverage related to economic events, and how do these topics

As the annual SPIVA studies demonstrate, index funds persistently outperform the vast majority of actively managed funds, even before considering taxes. With that said, most investors are unaware that there are weaknesses of index funds that result from their strategy to replicate the return of an

"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.” Alan Turing. It's hard to find anyone in Computer Science who doesn't hold Alan Turing in deep admiration. Widely regarded as

Recently on QuantStart we wrote a tutorial article that discussed the mean-reverting Ornstein-Uhlenbeck process, outlining some of its applications as well as providing some Python snippets to generate sample paths. In this article we are going to introduce the Vasicek Model, which is example of a

The annual SPIVA has documented that retail mutual funds underperform with great persistence, with any persistence of outperformance not significantly greater than would be randomly expected. The large body of research on the failure of active management led Charles Ellis to famously call it a

Today we spoke with Corey Hoffstein, a well-known market practitioner with a deep and broad knowledge across quantitative trading & trend following, but also across developing investment products for wider advisor distribution. I’m super interested in almost every aspect of the financial

You are most likely familiar with the idea of calculating averages with an exponential weighting. The idea is that you have a higher weight to more recent information. The weights for an exponentially weighted average look like: for . And the exponentially weighted average of a series looks like:

Some time ago on QuantStart we wrote an article on generating Brownian Motion paths for simulating stock price assets. In this tutorial article we are going to consider a more advanced stochastic process model known as the Ornstein-Uhlenbeck (OU) process that can be used to model time series that

The research team at Verdad does some of the most interesting and innovative empirical financial research that is consistently rigorous and based on systematic approaches that are implementable and replicable, providing confidence in the findings. In a recent piece, “Analogous Market Moments,”

Regression analysis is a statistical method used to estimate and model the relation between a dependent variable and one or more independent variables. The dependent variable, also called the observation, is the variable being explained or predicted. The Independent variables are used to explain or

Momentum is one of the most researched market anomalies, well-known and widely accepted in both public and academic sectors. Its concept is straightforward: buy an asset when its price rises and sell it when it falls. The goal is to take advantage of these trends to achieve better returns than a

Over the past few years, significant shifts in the financial landscape have reshaped the dynamics of global markets, including the cryptocurrency sector. Events such as the ongoing war in Ukraine, rising inflation rates, the soft landing scenario in the US economy, and the recent Bitcoin halving

“The group coined a name for the difference between the prices they were getting and the theoretical trades their model made without the pesky costs. They called it The Devil.” Gregory Zuckerman. The quote above is from the great book The Man Who Solved the Market. In it, Gregory Zuckerman tells

The paper examines several key questions related to how retail investors’ trading behaviors in cryptocurrencies differ from their behaviors in traditional asset classes like stocks and commodities. Are cryptos different? Evidence from retail trading Shimon Kogan, Igor Makarov, Marina Niessner,

Bond futures are often assumed to be more tax-efficient than bond ETFs. My analysis indicates that this assumption is frequently incorrect. Although investors might view the 60/40 tax treatment of futures as advantageous, a futures strategy faces several challenges compared to a bond ETF, including

Empirical research, including the 2020 study “An Empirical Evaluation of Tax-Loss Harvesting Alpha” and the 2023 study “Expected Loss Harvest from Tax-Loss Harvesting with Direct Indexing,” has found that tax-loss harvesting strategies in separately managed accounts (SMAs) can improve the

Semivolatility-managed portfolios Daniel Batista da Silva (U. of Geneva) and M. Fernandes (Getulio Vargas Fnd.) July 2024 There is ample evidence that volatility management helps improve the risk-adjusted performance of momentum portfolios. However, it is less clear that it works for other factors

For anyone looking to dive into the world of quantitative finance and systematic trading, Python is an indispensable tool. As the go-to programming language for many quant developers, Python offers a vast ecosystem of libraries that streamline everything from data analysis to strategy execution.