Dividend yield has long been a cornerstone of equity valuation. In this post, we explore how dividend yield predicts stock returns, its impact on stock volatility, and why it holds unique significance for mature, dividend-paying firms. Relationship Between Implied Volatility and Dividend Yield(...)

Building upon the established research on market seasonality and the potential for front-running to boost associated profits, this article investigates the application of seasonal strategies within the context of crisis hedge portfolios. Unlike traditional asset allocation strategies that may(...)

Every Monday, I get an email from CMC with the new Crypto listings and top trending coins. Here’s the one from this past Monday. I usually give it a quick look and then delete it, but not so long ago, I started wondering: should I give a #@%! about this? It bugged me so I decided to look into it. I(...)

We’re back! It’s 2025 and we are planning a cracker of a year! Stay tuned! It was strangely comforting talking to Ernie Chan. Whilst I was completely out of my depth talking about AI and Machine Learning, I came away broadly reinforced in my own belief that great trading still requires a human(...)

The PDF version of the Portfolio Construction and Risk Management book is freely available online at the bottom of this post. The accompanying code to the book is available on GitHub at https://github.com/fortitudo-tech/pcrm-book1. The book has been written through a crowdfunding campaign that you(...)

In the previous post the framework for Generalized Downside Implied Correlations was introduced. You can use this correlation matrix derived from joint risk metrics to replace or augment/blend with traditional correlations for use in analysis or optimization. The challenge is that the resulting(...)

Monte Carlo simulations are widely used in science, engineering, and finance. They are an effective method capable of addressing a wide range of problems. In finance, they are applied to derivative pricing, risk management, and strategy design. In this post, we discuss the use of Monte Carlo(...)

Academics have long been aware of the risks of data mining—torturing the data until it confesses. The concern is that correlation of variables doesn’t imply that the correlation is a result of causation. That is the reason that the prevailing academic standard for researchers is that they should(...)

An Investigation into the Causes of Stock Market Return Deviations from Real Earnings Yields Austin Murphy (Oakland University), et al. December 2024 This research demonstrates that the simple difference between the current earnings yield on the S&P500 and the long-term real TIPS yield has(...)

"If I have seen further, it is by standing on the shoulders of giants.” Sir Isaac Newton. First of all, Happy New Year! When I started Quantitativo a few months ago, I could never expect to gather such an amazing group of like-minded people in such a short time. Your enthusiasm, curiosity, and(...)

Factor Investing Origins and Implications The roots of factor investing can be traced to work published in the early 1990s by two academics: Ken French and Eugene Fama. In two of their publications[1], they identified a set of risk factors priced to consistently and robustly provide a return(...)

Can we simplify the complexities of the stock market and distill them into a simple set of quantifiable metrics? A lot of academic papers suggest this, and they offer formulas that should make the life of a stock picker easier. Some of the most compelling methodologies within this realm are the(...)

The general acceptance of cryptocurrencies, especially Bitcoin, was a blessing from Wall Street, which institutionalized them as ETFs for comprehensive access by the general public and institutional investors. There is little to no denying now that this new asset class is becoming more traditional,(...)

Principal Component Analysis (PCA) is a dimensionality reduction technique used to simplify complex datasets. It transforms the original variables into a smaller set of uncorrelated variables called principal components, ranked in order of their contribution to the dataset’s total variance. In this(...)

Machine learning models have proven effective in predicting stock returns using lagged stock characteristics, but their success is influenced by a wide range of modeling choices. One critical, yet often overlooked, choice is how stocks are weighted in the objective function during training, with(...)

Today’s research introduces a refined ETF asset momentum strategy by combining a correlation filter with selective shorting. While traditional long-short momentum strategies usually yield suboptimal results, the long leg proves effective on its own, and the correlation filter demonstrates(...)

This is a test of two stock market seasonality strategies from Fred Piard’s book Quantitative Investing: Strategies to Exploit Stock Market Anomalies for All Investors. Strategy results from 1970 follow. Results are net of transaction costs – see backtest assumptions. Learn about what we do and(...)

In the previous post I introduced a Drawdown Implied Correlation (DIC) that is a joint time-series measurement which converts maximum drawdowns into a correlation coefficient using a simple formula derived from portfolio math. The DIC had some unique features such as a “point-in-time” reference to(...)

Beta is a measure of an asset’s sensitivity to market movements, indicating how much its price is expected to change in relation to the overall market. Beta is often used in CAPM and the calculation of WACC. However, it can also be applied in trading, specifically in arbitrage. In this post, I’ll(...)

As most of you know, one of the many projects / things I am involved with is the TTU Systematic Investor podcast series where I'm one of the rotating cast of co-hosts. On a recent episode (at 24:05) we discussed the reasons why 'alt' CTAs tend to do better than traditional CTAs.(...)

By examining data going back to 1792, McQuarrie’s study comes up with a surprising observation : stocks are not as dominant as once thought. The variability of the performance of stocks vs. bonds across various time periods is dramatic. So buckle up, stocks do not invariably outperform bonds.(...)

I tweet a lot (from @saeedamenfx and at BlueSky at @saeedamenfx.bsky.social)! In amongst, the tweets about burgers, I tweet out a quant paper or link every day under the hashtag of #QuantLinkDay, mostly around FX, rates, economics, machine learning etc. Some are directly relevant to what we’re(...)

Investing formulas are simple, easy-to-implement, systematic, stock screeners that provide instructions on how to outperform the total stock market. Marcel Schwartz and Matthias Hanauer, authors of the December 2024 study, “Formula Investing,” evaluated the effectiveness of four such popular(...)

Overall, the last day of the year used to be consistently bullish for the market. But that has changed since the turn of the century. This is true across a number of indices. The most dramatic example is the NASDAQ, which I highlighted a few years ago. I have updated the chart below. NASDAQ last(...)

This paper investigates the puzzling decline in the price impact of S&P 500 index additions and deletions over the past four decades, despite the rapid growth of passive investing. It explores potential explanations, including changes in market liquidity and efficiency, shifts in the(...)

The year 2024 is nearly behind us, so it’s an excellent time for a short recapitulation. In the previous 12 months, we have been busy again (as usual) and have published over 70 short analyses of academic papers and our own research articles. The end of the year is a good opportunity to summarize(...)

Rather than describe it, I'll just paste the "help" description below:- "This function takes an input series and smooths it by projecting a 5 bar rolling linear fit 3 bars into the future and using these 3 bars plus the last 3 bars of the rolling input to fit a FIR filter with a(...)

Gold, one of the oldest and most enduring asset classes, had an exceptional run in 2024, capturing attention across financial markets. Its role in investment portfolios continues to spark interest, acting as a hedge against uncertainty. On the other end of the spectrum, cryptocurrencies represent(...)

Some years ago we wrote a range of articles on random number generation (RNG) using C++. These techniques are primarily used for Monte Carlo simulations that underpin modern derivatives pricing methods. The articles included one that implemented a particular algorithm known as a Linear Congruential(...)

Diversification is a concept that is critical to most asset managers and traders. The foundation of this body of research is built upon the Pearson correlation coefficient, which is the most popular metric to determine whether adding an asset to a portfolio might enhance diversification. Despite(...)

Systematic factor-driven value strategies have underperformed broad market indices (such as the S&P 500) over the past 15+ years. That has led many to question whether intangible assets, such as patents and proprietary software, are properly treated. Current accounting standards, which require(...)

This is an independent test of a series of interesting studies from Quantpedia (here and here) related to seasonality in commodity ETFs. We’ve more than doubled the length of the author’s original test using relevant index data (1). Test #1: Front running commodity seasonality In all of our tests,(...)

Seasonality plays a significant role in financial markets and has become an essential concept for both practitioners and researchers. This phenomenon is particularly prominent in commodities, where natural cycles like weather or harvest periods directly affect supply and demand, leading to(...)

This paper from Goldman Sachs made big headlines a couple of months back for forecasting an abysmal 3% nominal annual return for US stocks in the coming decade. For anyone who didn’t read GS’s analysis, the biggest contributor to that poor return was “market concentration”, or the market cap of the(...)

Getting fundamental assumptions right is essential for successful investment and risk management. The aspects that enable us to build portfolios intelligently and outperform the market are subtle nuances that are not easily accessible to most investors. If you do not believe me, check out this(...)

This paper examines various frameworks and proxies for forecasting long-term expected returns (E(R)) over periods of 10 to 20 years, focusing on out-of-sample performance and the impact of these forecasts on investment decisions. It compares models based on yield, valuation, and the combination of(...)

Financial models and strategies are usually universal and can be applied across different asset classes. However, in some cases, they must be adapted to the unique characteristics of the underlying asset. In this post, I’m going to discuss option pricing models and trading strategies in(...)

This strategy from NLX Finance is an alternative version of a strategy we’ve covered previously: Dr. Keller & Keuning’s Hybrid Asset Allocation (HAA). It trades based on all the same rules as the original HAA with one exception: rather than allocating 100% to US stocks when risk on, it holds a(...)

In the domain of quantitative finance, the juxtaposition of mean reversion and trend-following strategies constitutes a pivotal dialogue in the formulation of robust trading paradigms. Each methodology is underpinned by unique theoretical and empirical foundations, presenting distinct opportunities(...)

The RSI (Relative Strength Index) is a popular indicator used in many trading systems for filters or triggers. In TASC 12/2024 John Ehlers proposed a replacement for this indicator. His USI (Ultimate Strength Index) has the advantage of symmetry – the range is -1 to 1 – and, especially important,(...)

On Day 29, we conducted our out-of-sample test on the four strategies and found that the adjusted strategy came out on top. We made this conclusion after ranking a cross section of the following metrics: cumulative return, Sharpe Ratio, and max drawdown. If we wanted to commit capital, there would(...)

Active Share is a metric introduced to quantify the degree to which a portfolio differs from its benchmark index. It is expressed as a percentage, ranging from 0% (fully overlapping with the benchmark) to 100% (completely different). The concept gained popularity because it was believed that higher(...)

It was my absolute pleasure to chat with Kris Abdelmessih about markets and life. Kris was an options market maker who started out in the trading pits of New York and later flipped the script to set up the commodity options business for hedge fund Parallax Advisory. Today, Kris writes the Moontower(...)

“I always say that you could publish trading rules in the newspaper and no one would follow them. The key is consistency and discipline.” Richard Dennis. Richard Dennis is one of the greatest trend-following traders in history, renowned for transforming a small loan into a fortune in the(...)

This article analyzes various reasons why momentum strategies might work outside US borders. While the US story is firmly rooted in behavioral biases, is the same true on an international scale? That seems logical and likely. In fact, the authors conclude that a “slow diffusion of news best(...)

It’s well known that there is a negative relationship between an equity’s price and its volatility. This can be explained by leverage or, alternatively, by volatility feedback effects. In this post, I’ll discuss practical applications to exploit this negative correlation between equity prices and(...)

Programming note: This post has been in draft since ... 2016! One question you will see me asked a lot is 'how much money do I need to become a full time trader?'. And I usually have a handwaving answer along the lines of 'Well if you think your strategy will earn you 10% a year,(...)

The moment of truth has arrived! On Day 28, we iterated through all the metrics we had previously used to identify and analyze the robustness of our strategy. We found the new adjusted strategy performed better than the original and adjusted strategies. Such performance was also statistically(...)

This is a two-part blog where we’ll explore how Ito’s Lemma extends traditional calculus to model the randomness in financial markets. Using real-world examples and Python code, we’ll break down concepts like drift, volatility, and geometric Brownian motion, showing how they help us understand and(...)

Since the turn of the century portfolios have been exposed to four periods of crisis: the bursting of the tech bubble and the events of September 11, 2001, from 2000-2002; the Great Financial Crisis in 2007-2008, the COVID-19 pandemic in 2020, and the period of persistent inflation in 2022 when(...)