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

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, then

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

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 both

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 stock

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

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 [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 NYSE

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

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

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

One of the big problems for the first formal asset pricing model developed by financial economists, the CAPM, was that it predicts a positive relationship between risk and return while, empirical studies have found the actual relationship to be basically flat, or even negative. In addition,

On Day 22 we saw a meaningful improvement in our strategy by waiting an additional week to quantify model error and then using that error term to adjust the prediction on the most recently completed week of data. What was even more dramatic was comparing this improved strategy to one that followed

Asset allocation is commonly split into strategic asset allocation (SAA) and tactical asset allocation (TAA). Strategic usually refers to investment horizons above one year, while tactical usually refers to investments horizons below one year. Almost all institutional investors are required to have

Key Point: Markets have potentially become less efficient in recent decades. There are several reasons why this might be the case. Implication: Market inefficiency means more opportunities for outperformance for sufficiently equipped investors. ____________ The question of market efficiency is of

One common question we often receive from our readers is: “How do you evaluate the effectiveness of a trading strategy?” In this post, we’ll explore two fundamental techniques used in quantitative research to assess whether a trading strategy may genuinely offer an advantage or if its

So, first I should apologise for the LONG.... break between blogposts. This started when I decided not to do my usual annual review of performance - it is a lot of work, and I decided that the effort wasn't worth the value I was getting from it (in the interests of transparency, you can still

On Day 21, we wrung our hands with frustration over how to proceed. The results of our circular block sampling suggested we shouldn’t expect a whole lot of outperformance in our 12-by-12 model out-of-sample. To deal with this our choices were, back to the drawing board or off to the waterboard to

On Day 20 we completed our analysis of the 12-by-12 strategy using circular block sampling on the 3 and 7 blocks. We found the strategy did not outperform buy-and-hold on average and its frequency of outperformance was modest – in the 28-31% range – insufficient to warrant actually executing the

As mentioned in my prior post Arbitrage in DEFI (p1), have been building and improving a MEV strategy in DEFI to perform both atomic and non-atomic arbitrage, backrunning, liquidations, etc. In this article we continue to focus on algorithms to detect and optimise arbitrage paths through the pool

Building on the first paper, Reference [2] investigates machine learning techniques for trading VIX futures. It proposed using Constant Maturity Futures (CMF) to generate trading signals for VIX futures. It applied machine learning models to create these signals. Findings The experiment results show

On Day 19, we introduced circular block sampling and used it to test the likelihood the 200-day SMA strategy would outperform buy-and-hold over a five year period. We found that the 200-day outperformed buy-and-hold a little over 25% of the time across 1,000 simulations. The frequency of the

Measures of asset growth add considerable explanatory power to asset pricing models, but wait, there’s a twist. The formulation for measuring asset growth in risk models, such as the 5-Factor Fama-French (FF5F) or the Hou-Xue-Zhang (HXZ), do not necessarily align with traditional measures of firm

A reader sent a strategy to test which is a basic monthly rotation strategy between stocks and bonds. What caught my attention was the use of SSO, the 2x of S&P 500. The main idea being to use SSO when in a low volatility bull market. Looking over the rules, I could tell this strategy was

On Day 18 we started to discuss simulating returns to quantify the probability of success for a strategy out-of-sample. The reason for this was we were unsure whether or how much to merit the 12-by-12’s performance relative to the 200-Day SMA. We discussed various simulation techniques, but we

As interest in cryptocurrencies continues to surge, driven by each new price rally, crypto assets have solidified their position as one of the main asset classes in global markets. Unlike traditional assets, which primarily trade during standard working hours, cryptocurrencies trade 24/7, presenting

I have been building and improving a MEV strategy in DEFI to perform both atomic and non-atomic arbitrage, backrunning, liquidations, etc. In this post will focus on one of the hard algorithmic problems, namely, determining the optimal size and path of arbitrage through swap pools and other

On Day 17 , we compared the 12-by-12 and 200-day SMA strategies in terms of magnitude and duration of drawdowns, finding in favor of the 200-day. We also noted that most of the contributors to the differences in performance were due to two periods at the beginning and end of the period we were

On Day 16, we showed the adjusted 12-by-12 strategy with full performance metrics against buy-and-hold, the 60-40 SPY-IEF ETF portfolio, and the 200-day SMA strategy. In all cases, it tended to perform better than the benchmarks. However, against the 200-day SMA that performance came primarily at

On Day 15 we adjusted our model to use more recent data to forecast the 12-week look forward return. As before, we used that forecast to generate a trading signal that tells us to go long the SPY if the forecast is positive, and exit (or short for the long-short strategy) if otherwise. We saw this

"The holy grail of investing is to have 15 or more good, uncorrelated return streams.” Ray Dalio. I find Ray Dalio's story truly inspiring. From founding Bridgewater Associates in his two-bedroom apartment and growing it into the largest hedge fund in the world to publicly sharing the

People often ask me for book recommendations. But here’s a better question: What’s going to help you make money today? Reading a book probably isn’t the answer. I’m not saying books aren’t useful. They absolutely are. But you’re not preparing for a PhD defence – you’re trying to turn

Pairs trading is a market-neutral strategy that involves trading two correlated stocks or assets. The idea is to identify pairs that historically move together, and then take a long position in one and a short position in the other when they diverge, with the expectation that they will eventually

Among the earliest challenges to the efficient markets hypothesis was the observation that stock prices react to investor demand unrelated to fundamentals. One example is the abnormal returns to additions and deletions to the S&P 500 Index. Robin Greenwood and Marco Sammon, authors of the

Climate Risk and Predictability of Global Stock Market Volatility Mingtao Zhou and Yong Ma (Hunan University) March 2024 Our study investigates the informative role of climate risk in improving the predictability of global stock market volatility. By extracting the composite component from the four

On Day 14 we showed how the trading model we built was snooping and provided one way to correct it. Essentially, we ensure the time in which we actually have the target variable data aligns with when the trading signals are produced. We then used the value of the next time step to input into the