Month: April 2025

Machine learning (ML) has made a lot of progress in recent years. However, there are still skeptics, especially when it comes to its application in finance. In this post, I will feature articles that discuss the pros and cons of ML. In future editions, I’ll explore specific techniques.

How Accurate is Machine Learning Prediction in Finance?

Machine Learning has many applications in finance, such as predicting stock prices, detecting fraudulent activities, and automating investment decisions. However, the accuracy of ML prediction can vary widely depending on the type of data used and the model chosen.

Reference [1] discusses the problems that Machine Learning is facing in finance.

Findings

-Recent research suggests that machine learning (ML) is valuable in asset pricing due to its ability to capture nonlinearities and interaction effects that traditional models often miss.

-Machine learning is highly effective for applications with large datasets and high signal-to-noise ratios, but financial market data often lacks these characteristics.

-Financial markets evolve over time, meaning anomalies detected by ML can be arbitraged away, rendering past data less relevant for future predictions.

-An analogy highlights the challenge: once an ML algorithm learns to recognize “cats” in an image, all “cats” could morph into “dogs,” requiring the algorithm to relearn from scratch.

-There is a risk of positive publication bias, overfitting, and reliance on the assumption that past relationships will persist in the future.

-Human expertise remains crucial due to the low signal-to-noise ratio in financial data and the limitations of ML models.

In summary, the paper concludes that while ML does show promise, its superior performance is often overstated. When practical challenges are taken into account, the performance gap between ML and traditional methods narrows. However, investors who follow a rigorous and disciplined research process can still benefit meaningfully from ML-based strategies.

Reference

[1] Blitz, David and Hoogteijling, Tobias and Lohre, Harald and Messow, Philip, How Can Machine Learning Advance Quantitative Asset Management? (2023), SSRN 4321398

Machine Learning: Is More Data Always Better?

Reference [2] discusses the question whether more data is always beneficial in machine learning.

Findings

-The paper delves into the nuanced aspect of data quantity, questioning the assumption that more data necessarily leads to better machine learning outcomes.

-It argues that older data may lose relevance over time and including it can actually reduce model accuracy.

-Increasing the flow of data, or collecting data at a higher rate, tends to improve model accuracy but requires more frequent model retraining.

– Quality vs. Quantity: It discusses the trade-off between the quality and quantity of data, suggesting that the relevance and quality of the data are crucial factors in the effectiveness of machine learning models.

-The business value of machine learning models does not necessarily scale with the amount of stored data, especially if the data becomes outdated.

-Firms should adopt a growth policy that balances the retention of historical data with the acquisition of fresh data.

-Real-world Applications: Examples from various industries, such as healthcare, are presented to illustrate scenarios where the volume of data may not be the sole determinant of success in machine learning applications.

What implication does this paper have for trading and portfolio management? Should we use more data?

The short answer is probably no. In fact, using more data can actually lead to sub-optimal results. The reason is that, in the financial world, data is often noisy and contains a lot of irrelevant information. If you use too much data, your machine learning models will end up picking up on this noise, which can lead to sub-optimal results.

Reference

[2] Valavi, Ehsan, Joel Hestness, Newsha Ardalani, and Marco Iansiti. Time and the Value of Data. Harvard Business School Working Paper, No. 21-016

Closing Thoughts

In this post, I discussed the advantages and disadvantages of machine learning techniques as applied in finance. However, as the field is progressing rapidly, many of the current limitations, such as overfitting, interpretability, and data relevance, are being actively addressed by researchers and practitioners. With a disciplined research process and model design, investors can harness the strengths of machine learning to enhance forecasting, risk management, and strategy development.

Calendar anomalies in the stock market refer to recurring patterns or anomalies that occur at specific times of the year, month, or week, which cannot be explained by traditional financial theories. These anomalies often defy the efficient market hypothesis and provide opportunities for investors to exploit market inefficiencies. In this post, I will feature some calendar anomalies and discuss whether they work in the current market or not.

Do Calendar Anomalies Still Exist?

Calendar anomalies were discovered long ago. Reference [1] examines whether they still persist in the present-day stock market. Specifically, the author investigates the turn-of-the-month (TOM), turn-of-the-quarter (TOQ), and turn-of-the-year (TOY) effects in the US stock market.

Findings

– The paper identifies the presence of the turn-of-the-month (TOM), turn-of-the-quarter (TOQ), and turn-of-the-year (TOY) effects in the US stock market, with the TOY effect being the most prominent.

-The analysis uses panel regression models on four-day return windows for individual stocks listed on the NYSE, AMEX, and NASDAQ from 1986 to 2021.

– The TOM, TOQ, and TOY effects are found to be present, and their strength varies based on firm characteristics.

– The TOY effect primarily affects small stocks with volatile prices, indicating that individual investors may sell their losses for tax purposes before the year-end.

– Stocks with low momentum are more susceptible to the TOY effect, suggesting that institutional investors may engage in performance hedging by selling underperforming stocks.

– The calendar effects have evolved over time, with the TOM and TOY effects resurfacing in recent decades, while the TOQ effect has diminished, potentially due to increased disclosure regulations.

– Companies with low Google search volumes are significantly more impacted by all three effects, indicating a relationship between information accessibility and the magnitude of calendar anomalies.

-A trading strategy is developed to identify stocks with the highest expected returns over TOM and TOY windows. The return exceeds realistic trading costs, indicating that calendar effects can be used to construct profitable trading strategies.

In summary, calendar anomalies continue to exist in the US stock market. Furthermore, they can be exploited to gain abnormal returns. For instance, every four-day TOY window yields an average profit of 1.66% when holding all stocks exclusively over the TOY windows. Similarly, an average profit of 0.55% is generated every four-day TOM window by exclusively holding all stocks over the TOM windows.

Replication

Vahid Asghari and his team at Academic Quant Lab have replicated the strategy presented in this paper. The results and codes can be found here.

Reference

[1] Idunn Myrvang Hatlemark and Maria Grohshennig, Calendar Effects in the US Stock Market: Are they still present?, 2022, Norwegian University of Science and Technology

How End-of-Month Returns Predict the Next Month’s Performance

Reference [2] introduced a novel calendar anomaly known as the end-of-month reversal effect. The study showed that end-of-month returns, i.e. returns from the fourth Friday to the last trading day of the month, are negatively correlated with returns in the following month.

Findings

-This paper identifies a novel 1-month aggregate market reversal pattern, which is driven by the previous end-of-month market return.

– It demonstrates that end-of-the-month returns of the S&P 500 are negatively correlated with returns one month later.

-The reversal effect is statistically significant both In-Sample and Out-of-Sample, confirming its robustness.

-Unlike traditional cross-sectional reversals, this pattern is stronger in high-priced and liquid stocks and follows an economic cycle.

-A simple rule-based trading strategy and more sophisticated models leveraging this pattern generate significant economic gains. The strategy is cyclical in nature and does not rely on short-selling.

-The reversal effect strengthens over the following month, aligning with pension fund inflows and reinforcing the payment cycle explanation.

In short, a simple trading strategy based on this effect, that is buying if the end-of-month return is negative and selling if it is positive, outperforms the buy-and-hold strategy over a 45-year period.

The author also provides an explanation for this anomaly, attributing it to pension funds’ liquidity trading, as they adjust their portfolios to meet pension payment obligations.

Reference

[2] Graziani, Giuliano, Time Series Reversal: An End-of-the-Month Perspective, 2024, SSRN

Closing Thoughts

In this post, I discussed several calendar anomalies. Some of these patterns were discovered long ago and have proven to be persistent in today’s market. One of them represents a newly identified anomaly with promising characteristics. In all cases, profitable trading strategies were developed to take advantage of these recurring effects, highlighting the continued relevance of calendar-based insights in quantitative investing.

A catastrophe (CAT) bond is a debt instrument designed to transfer extreme event risks from insurers to capital market investors. They’re important for financial institutions, especially insurers and reinsurers, because they offer a way to manage large, low-probability. In this post, I feature research on CAT bonds, how they’re priced, and why they matter more than ever in a world of rising tail risks.

A Pricing Model for Earthquake Bonds

An earthquake bond is a type of catastrophe bond, in which an insurer, reinsurer, or government, transfers a portion or all of the earthquake risk to investors in return for higher yields. Earthquake bonds are crucial in countries prone to earthquakes. However, pricing them presents challenges.

Reference [1] developed a pricing model for pricing earthquake bonds. The authors modeled the risk-free interest rate using the Cox–Ingersoll–Ross model. They accommodated the variable intensity of events with an inhomogeneous Poisson process, while extreme value theory (EVT) was used to model the maximum strength.

Findings

– Earthquake bonds (EBs) connect insurance mechanisms to capital markets, offering a more sustainable funding solution, though pricing them remains a challenge.

– The paper proposes zero-coupon and coupon-paying EB pricing models that incorporate varying earthquake event intensity and maximum strength under a risk-neutral framework.

– The models focus on extreme earthquakes, which simplifies data processing and modeling compared to accounting for continuous earthquake occurrences.

– The earthquake event intensity is modeled using an inhomogeneous Poisson process, while the maximum strength is handled through extreme value theory (EVT).

– The models are tested using earthquake data from Indonesia’s National Disaster Management Authority covering 2008 to 2021.

– Sensitivity analyses show that using variable intensity instead of constant intensity significantly affects EB pricing.

– The proposed pricing model can help EB issuers set appropriate bond prices based on earthquake risk characteristics.

– Investors can use the sensitivity findings to select EBs that align with their individual risk tolerance.

In summary, the authors modeled the risk-free interest rate using the Cox–Ingersoll–Ross model. They accommodated the variable intensity of events with an inhomogeneous Poisson process, while extreme value theory (EVT) was used to model the maximum strength.

Reference

[1] Riza Andrian Ibrahim, Sukono, Herlina Napitupulu and Rose Irnawaty Ibrahim, Earthquake Bond Pricing Model Involving the Inconstant Event Intensity and Maximum Strength, Mathematics 2024, 12, 786

No-arbitrage Model for Pricing CAT Bonds

Pricing models for catastrophic risk-linked securities have primarily followed two methodologies: the theory of equilibrium pricing and the no-arbitrage valuation framework.

Reference [2] proposed a pricing approach based on the no-arbitrage framework. It utilizes the CIR stochastic process model for interest rates and the jump-diffusion stochastic process model for losses.

Findings

– This paper explores the concept of CAT bonds and explains how they are modeled using financial mathematics.

– Through a semi-discretization approach, a PIDE and a first-order differential equation were derived.

– A key component, the market price of risk of damage, was unavailable, so a quadratic term was constructed using market ask and bid prices to estimate this variable.

– By utilizing the Euler-Lagrange equation, a Poisson PDE was derived.

– The paper concludes by presenting an approach and numerical results for determining the market price of risk.

We find the stochastic model, equation (1), to be particularly insightful and effective in describing catastrophic losses.

Last year has witnessed numerous hurricanes across Asia, Europe, and America, leading to significant claims for insurers. This paper represents a contribution to advancing risk-sharing practices in the insurance industry.

Reference

[2] S. Pourmohammad Azizi & Abdolsadeh Neisy, Inverse Problems to Estimate Market Price of Risk in Catastrophe Bonds, Mathematical Methods of Statistics, Vol. 33 No. 3 2024

Closing Thoughts

In this post, I discussed catastrophe bonds and why they matter for investors navigating extreme event risks. The first paper focused on earthquake bonds, which present a challenge to model due to their rare and severe nature. Interestingly, both pricing models in the paper relied on the Cox–Ingersoll–Ross framework for interest rates, a reminder that even in the world of tail-risk instruments, some core quantitative models remain consistent.