Hi! I'm Mustehsan.

Abstract

The generative-AI boom of 2021–2025 drove technology stocks to unprecedented highs and raised pressing questions about how extreme downside risk in these high-growth names stacks up against traditional large-value equities. In this thesis, we quantify and compare the one-day 99% Value-at-Risk (VaR) of an equally weighted portfolio of ten AI-growth stocks versus ten large-value stocks, using both nonparametric Historical Simulation (HS) and symmetric GARCH(1,1) models with Gaussian and Student-t innovations. We then subject each VaR estimate to regulatory-style back-tests: Kupiec’s Unconditional Coverage and Christoffersen’s Conditional Coverage, to assess their adequacy for capital calculation. Empirically, the AI portfolio exhibits a mean one-day 99% VaR of 4.997%, more than double the 2.084% observed for the Value portfolio. Violation rates under HS, Student-t GARCH, and Gaussian GARCH are 1.49%, 1.60%, and 1.95% for AI versus 1.03%, 1.26%, and 1.38% for Value. Only HS and Student-t GARCH pass all back-tests. These findings underscore the critical importance of fat-tailed or nonparametric methods when measuring risk for high-growth equity portfolios, with direct implications for setting regulatory capital.

Abstract

This blog post addresses the design of a sustainable logistic network for GreenForwarder—a multinational freight company—by balancing profitability, environmental emissions, and regional reach. A multi-objective network optimization problem is formulated over a graph that represents cities and potential transport connections. Using a modified Minimum Spanning Tree (MST) algorithm that incorporates capacity constraints and investment costs, the approach has been inspired by the Steiner Tree Problem and evaluates candidate edges dynamically by considering cost, emission factors, and a bonus for expanding regional reach. POC and LIVE differ significantly in their approaches, particularly in their starting points. POC begins by simplifying the “full” graph and focusing on optimizing its objective function, whereas LIVE prioritizes satisfying its unique constraint from the outset. For the MVP, two methods are employed to determine which approach would yield a better outcome, as the significance of profit’s contribution was unknown during the project’s initial stages. Detailed experimental results, analysis, and comparisons are provided in later sections.

Abstract

In this blog post, I rigorously analyze the forecasting performance of commodity price inflation models. I compare a conventional univariate autoregressive (AR) model with two mixed frequency models—the unrestricted MiDAS model and the HAR-MiDAS model. By integrating daily stock returns with monthly inflation data, I aim to capture market dynamics that standard techniques overlook. I evaluate model performance using robust statistical tests, RMSE comparisons, and the Diebold-Mariano test, and I explore the benefits of a rolling forecast origin. Throughout the analysis, I include detailed mathematical formulations, estimation results, tables, and graphical visualizations.

Introduction

The idea for this blog originated on an 1 hour long boarding process on my last trip. The process of boarding an airplane appears deceptively simple; yet, it exhibits surprisingly high delays compared to boarding other forms of transportation such as buses or trains. This document aims to provide a mathematically rigorous explanation of why the boarding process is so inefficient. We build a model that captures both stochastic delays (due to bag stowing, seating interference, etc.) and systematic constraints imposed by the boarding procedure.

Introduction

Bootstrapping is a resampling method that enables the estimation of the sampling distribution of a statistic by drawing repeated samples with replacement from the observed data. In simple terms, imagine you have a jar filled with cookies. Instead of baking a new jar of cookies to see how the average size might vary, you repeatedly pick a handful of cookies from the same jar (with replacement), calculate the average size for each handful, and then study how these averages vary. This variation gives you an insight into the reliability and variability of your original measurement.