Embeddings are used in neural networks to transform large, sparse data into manageable, dense formats. In other words, they simplify complex data, making it easier to analyze. We can use embeddings to capture dense information about drivers of stock returns. This approach is a great way to select

Market-neutral multi-factor products have reached all-time highs However, long-only multi-factor products have consistently underperformed Portfolio construction and implementation matters INTRODUCTION Investors have been style investing since the inception of stock markets. Some chase trends, while

Can AI models improve on the failures in predicting returns strictly from a practical point of view? In this paper, the possibilities are tested with a battery of AI models including linear regression, dimensional reduction methods, regression trees and neural networks. These machine learning models

The equal risk contribution (ERC) portfolio, introduced in Maillard et al.1, is a portfolio aiming to equalize the risk contributions from [its] different components1. Empirically, the ERC portfolio has been found to be a middle-ground alternative1 to an equally weighted portfolio and a minimum

Last week, we looked at simple data analysis techniques to test for persistence. But we only looked at a feature that is measured over a single day – the absolute range. Such a feature makes it easy to test persistence because you don’t have the problem of overlapping data. Each data point is

Diversification is the cornerstone of investing. This principle, fundamentally understood as not concentrating all resources into a single investment, inherently seeks to minimise risk while potentially smoothing out returns over the long term. By spreading investments across uncorrelated assets,

It’s been almost 11 years now since I posted my introduction to quantitative investing. It’s kind of hard to believe as I’m typing these words. A lot has happened since that summer day in 2013. And a lot has stayed the same. Learning about, implementing, and allocating to this type of

While economic information undeniably wields a significant and widespread influence on financial markets, the systematic incorporation of macroeconomic data into trading strategies has thus far been limited. This reflects skepticism towards economic theory and serious data problems, such as

Quality and low volatility stocks provide substantially different exposures Neither has outperformed the stock market, but both were less volatile Low volatility stocks have done poorly in recent years INTRODUCTION If you believe that the economy is entering a recession and can only invest in

This blog is more a note to self for experimenting further with DSPy (arXiv, GitHub) than a pedagogical or original intro to the framework. It essentially follows this weaviate tutorial with small adaptations, notably removing the weaviate part of it, and replacing their retrieval module by a very

In the fast-paced world of cryptocurrencies, understanding market sentiment can provide a crucial edge. As investors and traders seek to anticipate the volatile movements of Bitcoin, innovative approaches are continuously explored. One such method involves leveraging Google Trends data to gauge

The justification for neutralizing sectors in factor strategies is a work in progress. To date, academic researchers haven’t had an empirical model to mimic the impact of removing sector “effects” on the measurement and performance of factor strategies. The authors develop and test a

It’s rumored that Renaissance Technologies uses hidden Markov models in their trading. In fact, the Baum-Welch algorithm used with Markov models was partially invented by Leonard Baum who would help found RenTec. In today’s newsletter, we’ll look an example of using a Markov model to detect

Macroeconomic Announcement Premium Hengjie Ai (University of Wisconsin-Madison), et al. November 2023 The paper reviews the evidence on the macroeconomic announcement premium and its implications on equilibrium asset pricing models. Empirically, a large fraction of the equity market risk premium is

While empirical research on cross-sectional (long-short) momentum has shown high returns, investors have also experienced huge drawdowns—momentum exhibits both high kurtosis and negative skewness. Since 1926, there have been several momentum crashes that featured short but persistent periods of

After my last post on using trend following in Crypto markets I thought I’d continue on that thread and look at applying trend following on a newish concept (similar concepts have existed at the institutional level for a long time) in creating diversified portfolios, called return stacking. First,

Some factor trends continued from 2023, but there were also two significant rotations Momentum performed the best, size the worst Most long-short multi-factor products have generated positive excess returns INTRODUCTION We present the performance of five well-known factors on an annual basis for the

It has been a while since I’ve updated the blog. These days I spend most of my time writing for subscribers of my newsletter but I’d like to get back to writing publicly again. So, to launch myself back into public blogging I thought I would write about Crypto and how classic trend following

Regression-based statistical learning helps build trading signals from multiple candidate constituents. The method optimizes models and hyperparameters sequentially and produces point-in-time signals for backtesting and live trading. This post applies regression-based learning to macro trading

Market indices are vital in finance, offering investors a quick look at the overall performance of a specific market or sector. They act as benchmarks for assessing the performance of different investment portfolios. Investors can copy the performance of an index for exposure to securities without

An assumption we often make in trading research is that the future will be at least a little like the past. I see a lot of beginners making this assumption implicitly without recognising that they’re making it or thinking about whether it’s reasonable to do so. That’s a mistake. If you are

Macroeconomic trends affect stocks differently, depending on their lines of business and their home markets. Hence, point-in-time macro trend indicators can support two types of investment decisions: allocation across sectors within the same country and allocation across countries within the same

Out of the hundreds of exhibits in the factor zoo, momentum was one of just five equity factors that met all the criteria (persistent, pervasive, robust, implementable, and intuitive) Andrew Berkin and I established in our book Your Complete Guide to Factor-Based Investing. Because of the strong

Consider a financial asset whose price, Xt​, follows a mean-reverting stochastic process. A common model for mean reversion is the Ornstein-Uhlenbeck (OU) process, defined by the stochastic differential equation (SDE): Objective The trader aims to maximize the expected cumulative profit from

Stocks can have a high, low, or negative sensitivity to interest rates The duration profile of stocks changes frequently Having rates exposure in an equities portfolio is not necessarily a concern INTRODUCTION The goal of conducting research is to provide clarity by answering questions or confirming

In the rapidly evolving landscape of cryptocurrency markets, understanding the underlying dynamics that drive price movements and investor sentiment can be a matter of survival. However, there are myriad facets of trading reality, and the only thing that we can do is to slowly understand them one

Recently a reader sent me a leveraged ETF strategy that he wanted tested for the blog. Over the last couple of months, I have been noticing renewed interest in leveraged ETF trading. More clients are coming to me to test out leverage trading ideas. I have been testing my own ideas. What I liked

Inflation-themed ETFs have heterogeneous portfolios However, commodities and oil have been better inflation hedges And offer higher diversification benefits INTRODUCTION In November 2021 we analyzed inflation-themed ETFs (read Inflation-Themed ETFs: As Complicated as Inflation) and concluded that

Here’s a thing that I suspect will make money, but that I haven’t yet tested (for reasons that I will explain shortly): Every day, at the start of the trading day, get the SPX straddle price and convert it to an expected SPX price move. Then at the end of the trading day, take the SPX price and

Macroeconomic trends affect stocks differently, depending on their lines of business and their home markets. Hence, point-in-time macro trend indicators can support two types of investment decisions: allocation across sectors within the same country and allocation across countries within the same

The benefits of diversification are well known. In fact, it’s been called the only free lunch in investing. Investors who seek to benefit from diversification of the sources of risk and return of their portfolios must accept that adding unique sources of risk means that their portfolio will

This is a test of the 12-Month High Switch Model, a Tactical Asset Allocation (TAA) strategy from Meb Faber. Meb has done more than anyone to popularize TAA as a trading style, including many of the fundamental concepts used today. This is another of his simple but effective ideas. Backtested

Stocks for a low-growth & high-interest rate environment should have high-quality characteristics However, there are many ways to define quality stocks Historically quality portfolios have not generated excess returns INTRODUCTION Ignoring the past is one of the biggest investing mistakes.

The lifeblood of quant finance is data. The problem is that data is sometimes hard to come by. It may be expensive or just not available. What if we had a way to generate synthetic market data? Artificially recreating a dataset is a complex process. The new data needs to mimic the existing data

Jerry Kaufman, known for his technical indicators bible, presented in TASC 1/24 a trading strategy based on upwards and downwards gaps. For his system, he invented the Gap Momentum Indicator (GAPM). Here I’m publishing the C version of his indicator, and a simple trading system based on it. The

Perhaps the most well-documented and researched asset pricing anomaly is momentum—the tendency of past winner stocks to outperform past loser stocks over the next several months. While average time-series momentum (trend following) returns have been high, strategies employing trend following have

Cryptocurrencies are already one of the major asset classes. They fill the top pages of magazines and are a topic of a day to day conversation. There are a lot of ways to buy them through a lot of different channels. But some of the hardcore HODLers like to keep their coin portfolio safe – they

In the previous post of this series on volatility forecasting, I described the simple and the exponentially weighted moving average volatility forecasting models. In particular, I showed that these two models belong to the generic family of weighted moving average volatility forecasting models1,

Financial modeling has long sought to develop frameworks that accurately capture the complex dynamics of asset prices. Traditional models often focus on either momentum or mean reversion effects, struggling to incorporate both simultaneously. In this blog post, we introduce a two-factor model that

In February 2023, peer Wouter Keller and JW Keuning published a study of an interesting strategy, Dual and Canary Momentum with Rising Yields/Inflation: Hybrid Asset Allocation (HAA), which uses the Treasury Inflation-Protected Securities (TIPS) markets to decide when a strategy should be invested

P/E and ROE factors were highly correlated in recent years However, this is counterintuitive as cheap stocks should not be highly profitable We can explain this perplexity with stocks with negative earnings INTRODUCTION In our recent article “Value vs Quality: More Correlated than Ever?” we

Academic research, including the studies “Do Investors Overpay for Stocks with Lottery-like Payoffs? An Examination of the Returns on OTC Stocks,” “Lottery Preference and Anomalies” and “Do the Rich Gamble in the Stock Market? Low Risk Anomalies and Wealthy Households,” has found that

Market Risk Premium Expectation: Combining Option Theory with Traditional Predictors Hong Liu (Washington University in St. Louis), et al. December 2022 In general, the slackness between the Martin lower bound (solely based on option prices) and the market risk premium depends on economic state

Our article “Log-normal Stochastic Volatility Model with Quadratic Drift” co-authored with Parviz Rakhmonov is published in International Journal of Theoretical and Applied Finance with open access https://www.worldscientific.com/doi/10.1142/S0219024924500031 The log-normality of realised and

Joe Biden will be giving his State of the Union Address tonight, and people are wondering how his talk might impact the market over the next several days. I have looked at performance following State of the Union before and decided to update that research today. The data table below looks back to

Here at Robot Wealth, we trade with Interactive Brokers (IB) primarily because they offer access to global markets at a reasonable price. In recent times, IB has put some time and effort into upping its tech game, including development of an API for interacting with its desktop trading applications.

I've talked at some length before about the question of fitting forecast weights, the weights you use to allocate risk amongst different signals used to trade a particular instrument. Generally I've concluded that there isn't much point wasting time on this, for example consider my

P/E and ROE long-short factors have become highly correlated During certain periods investors favor expensive and unprofitable stocks However, it is difficult explaining the positive correlation outside of bubbles INTRODUCTION The older I get, the less I seem to know for certain about investing. The

This is the final article in our recent stat arb series. The previous articles are linked below: A short take on stat arb trading in the real world A general approach for exploiting stat arb alphas Ideas for crypto stat arb features Quantifying and combining crypto alphas A simple and effective way

Let me present our recent research paper with Parviz Rakhmonov on the stochastic volatility model for Factor Heath-Jarrow-Morton (HJM) interest rate framework (available on SSRN: Stochastic Volatility for Factor Heath-Jarrow-Morton Framework). Factor Heath-Jarrow-Morton (HJM) model Under the