I am pleased to announce that my new paper is now available:
“Cross-Sectional Topological Anomaly Scores and Intraday Return Predictability: BallMapper Descriptors, Decoder-Conditional VAE, and Function-on-Function Regression on S&P 500 Intraday Data”
The chart visualizes rolling risk–return–volume dynamics for ten highly liquid S&P 500 constituents — AAPL, AMZN, AVGO, GOOG, GOOGL, META, MSFT, NVDA, PLTR, and TSLA — selected, over the April 2025–March 2026 period, by ranking all index members on the Amihud (2002) illiquidity ratio — a widely used measure of price impact per unit of trading volume — and retaining the ten most liquid stocks. Intraday OHLCV data for that period were sourced from EODHD (eodhd.com) at 5‑minute resolution and then aggregated to the 15‑, 30‑, and 60‑minute frequencies.
When evaluating trading algorithms, it is common to compare their average performance across the entire dataset. But if algorithms are used differently across market regimes, aggregated performance can produce a completely false ranking. The example below shows how an algorithm that is worse in every regime can appear superior overall.
This post presents an accessible introduction to the Exponential GARCH (EGARCH) model—a widely used tool in financial econometrics for modeling time-varying volatility in asset returns. Unlike standard GARCH models, EGARCH captures both volatility clustering and the leverage effect, whereby negative shocks tend to increase future volatility more than positive shocks of equal magnitude. The post demonstrates how EGARCH achieves this using a simplified form, with an emphasis on the asymmetry function’s role in shaping variance dynamics. The dynamic visualization of EGARCH volatility asymmetry presented in this post was created by the author using Desmos.
Volatility is widely used as a proxy for risk, largely because it is easy to compute and fits neatly into different models such as CAPM. Yet treating volatility as the measure of risk can be…
Minimum Sample Size Formula To determine how many observations are required to assess, with confidence level (1 – alpha), that a trading strategy achieves a claimed target Sharpe ratio, the following approximation can be used…
Kelly allocation to a single risky security with volatility twice the expected return. The Kelly Allocation to a Single Security We consider a portfolio with two assets: a risk-free asset and a risky asset. Let…
This post introduces a simulation-based test using the Marčenko–Pastur distribution to assess the randomness of covariance matrices. By comparing the proportion of eigenvalues within theoretical MP bounds to those from simulated random matrices, the test produces an empirical p-value that helps determine whether a matrix reflects real structure or noise. Implemented in both R and Python, the method is especially useful for high-dimensional data analysis in finance. The mp_randomness_test function presented here is an original contribution by Dr Krzysztof Ozimek.
This post presents a method for calculating the return on an investment denominated in a base currency X, when the actual investment is made in a foreign currency Y. The approach considers both the performance of the asset in Y and the movement of the exchange rate between X and Y. A general formula is derived and explained in detail, along with a simplified approximation for practical use. The analysis also accommodates trade costs, taxes, and inflation. Several scenarios are discussed to illustrate how currency appreciation or depreciation affects investment returns. A numerical example is provided, alongside R and Python implementations of the calculation.
This post explores how joint probabilities over bounded regions — known as hyperrectangles — can be expressed as combinations of cumulative distribution functions (CDFs). A general formula is presented and illustrated through a simplified three-variable cases. We demonstrate how this structure can be used in practice with toy data, using my R function (jp()) to automate the calculation. Finally, we discuss its relevance in algorithmic trading, where such joint probabilities may serve as reliable triggers for short-term allocation strategies.
