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(...)

Limits to Diversification: Passive Investing and Market Risk Lily H. Fang (INSEAD), et al. September 2024 We show that the rise of passive investing leads to higher correlations among stocks and increased market volatility, thereby limiting the benefit of diversification. The extent to which a(...)

I am occasionally asked about historical backtests “proving” that CVaR is a better risk measure than variance. I provide such a backtest in Section 2.6 of the Portfolio Construction and Risk Management book1 and explain why it is naive (see the PDF at the bottom of this article). Thanks for reading(...)

Seasonality is a well-known phenomenon in the commodity markets, with certain sectors exhibiting predictable patterns of performance during specific times of the year. These patterns often attract investors who aim to capitalize on anticipated price movements, creating a self-reinforcing cycle. But(...)

On Day 27, we had our strategy enhancement reveal. By modifying the arithmetic behind our error correction, we chiseled another 16% points of outperformance vs. buy-and-hold and the original 12-by-12 strategy. All that remains now is to run the prediction scenario metrics and conduct circular block(...)

On Day 26, we extended the comparative error analysis to the original, 12-by-12 strategy and showed how results were similar to the unadjusted strategy relative to the adjusted one. The main observation that emerged was that the adjusted strategy performed better than the others due to identifying(...)

One of my favourite ways to characterize the market regime is by using the Hurst exponent. However, its applications are not limited to identifying market regimes. There are innovative ways to utilize it. In this post, I will discuss two approaches to applying the Hurst exponent. Using the Hurst(...)

The last five days! On Day 25, we compared the peformance of the adjusted vs. unadjusted strategy for different prediction scenarios: true and false positives and negatives. For true positives and false negatives, the adjusted strategy performed better than the unadjusted. For true negatives and(...)

This paper examines the time-varying roles of subjective expectations in driving stock price and return variations. Specifically, it focuses on how subjective cash flow expectations (CF) and discount rate expectations (DR) contribute to stock price fluctuations across different economic conditions,(...)

UVXY is an ETF that targets 1.5x the daily returns of a 30-day constant-maturity position in VX futures – the SPVIXSTR index. Before 2018, it targeted 2x returns – but Volmageddon ruined the fun. UVXY has to trade every day: To rebalance its notional exposure back to its target due to: Movements in(...)

In [part 1] [youtube video link] we covered the data pipeline portion of the AWS trading bot architecture. I demonstrated how to set up your AWS environment, including creating a simple dynamoDB database to hold our price and strategy data. Then we walked through the data pipeline code in detail(...)

An anomaly is a pattern in stock returns that deviates from what is expected based on established financial theories or models. These patterns can sometimes present opportunities for abnormal returns. However, they are often inconsistent and challenging to exploit. Many anomalies have achieved(...)

On Day 24, we explained in detail how the error correction term led to somewhat unexpected outperformance relative to the original and unadjusted strategies. The reason? We hypothesized that it was due to the the error term adjusting the prediction in a trending direction when or if the current(...)

The strong breadth readings over the last few days triggered one of my oldest and most favorite studies. It looks at other times that breadth came in strong for 3 days in a row. I have shown this study many times over the years. I often refer to it as a Triple-70 Thrust, because it requires the(...)

The Kelly Criterion is good enough for long-term trading where the investor is risk-neutral and can handle big drawdowns. However, we cannot accept long-duration and big drawdowns in real trading. To overcome the big drawdowns caused by the Kelly Criterion, Busseti et al. (2016) offered a(...)

On Day 23 we dove into the deep end to understand why the error correction we used worked as well as it did. We showed how traditional machine learning uses loss functions and then hypothesized how our use helped improve predictions through its effect on the correlation of the signs of the(...)

Do we have a chaotic “factor zoo” as some critics maintain? Is there a replication crisis in the research on factors? The authors of this research answer in the negative and argue that 82% of factors are replicable, the factor zoo is well-organized, and the factors are legit. Such bold statements(...)

Data analysis plays a central role in making sense of financial markets. But how can you verify the conclusions others draw, or better yet, uncover your own insights? Microsoft Excel remains one of the most powerful and accessible tools for financial data analysis, allowing anyone—from beginners to(...)

In this post, I will continue exploring various aspects of the volatility index and the associated volatility futures. Data To conduct this study, data is essential. Below are the data sources: Spot VIX: Yahoo Finance provides data but no longer allows direct downloads. With some programming, a(...)