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

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.