Mustehsan Fazal

The Self You Cannot Grade

Sat, 20 Jun 2026 00:00:00 +0000

On desire, the limits of self-knowledge, and what actually makes a person worth something

A note from me before you start

A brief word on scope and intent. This blogpost draws on ideas and evidences from theology, religious texts, and the work of various scholars, and uses them as the raw material for a framework of my own. I am not a scholar or an expert in any of these fields: the sources belong to the people I cite, but the way I have woven them together — and the conclusions I draw from them — are mine, and mine to be wrong about. Read what follows as one person’s attempt to digest these questions, not as a settled account of them.

Comparative Analysis of Market Risk in AI-Driven Tech Stocks vs. Large Value Stocks Using Value at Risk

Fri, 27 Jun 2025 00:00:00 +0000

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.

A Multi-Objective Network Optimization Problem

Wed, 12 Mar 2025 00:00:00 +0000

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.

Forecasting Commodity Prices: A Comparative Analysis of Common and Mixed Frequency Approaches

Wed, 19 Feb 2025 00:00:00 +0000

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.

Queuing Theory and Markov Chains in Airplane Boarding: An Econometric Approach

Sat, 12 Oct 2024 00:00:00 +0000

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.

Bootstrapping in R: A Mathematical and Computational Approach

Sun, 07 Apr 2024 00:00:00 +0000

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.

Portugal: A Macroeconomic Risk Analysis

Tue, 02 Jan 2024 00:00:00 +0000

Abstract

This blog post presents an innovative and comprehensive analysis of Portugal’s macroeconomic performance over the period 1970–2005. By integrating classical economic theory with advanced econometric modeling—including Vector Autoregression (VAR) and ARIMA approaches—we examine the intricate interplay between GDP growth, unemployment, and inflation. Our study revisits the traditional Phillips Curve framework and proposes an accelerated variant to better capture the nuances of Portuguese economic dynamics. The analysis not only identifies key recession periods but also offers robust policy implications for economic stabilization and investment strategy formulation.

Game Theoretic Approaches to Competitive Location Choice: A Mathematical Perspective

Sun, 17 Dec 2023 00:00:00 +0000

In this post, I present an in‐depth analysis of a project that investigates optimal location choices for competing firms using concepts from graph theory and game theory. The project models a set of cities as nodes in a graph and employs two primary methods: the iterated elimination of strictly dominated strategies and local search dynamics. I provide a detailed exposition of the mathematical foundations, algorithms, and extensions implemented to reflect more realistic scenarios. This is my answer to a university assignement.

Writing myself into understanding

Sun, 12 Nov 2023 00:00:00 +0000

From the moment I read my very first book as a curious 14-year-old — eager to decode the world of ideas and innovation — a singular insight has quietly echoed across disciplines: from developers and engineers to designers, project managers, and entrepreneurs alike:

Writing is not merely a communication tool — it is a thinking tool.

It is through the act of writing that thought becomes visible, coherent, and subject to refinement. The process doesn’t simply mirror what we already know; it constructs, tests, and often reshapes what we believe to be true. Over time, I’ve come to see writing not as a task, but as a technology of thought — a slow, deliberate form of cognition that disciplines the mind.

Even a Key Can Expire: A Comprehensive Analysis of Internet Security Principles

Fri, 21 Jun 2019 00:00:00 +0000

The ubiquitous nature of digital communication demands robust security measures to protect sensitive information across an increasingly interconnected world. This blog post provides an extensive analysis of Internet security, tracing its evolution from classical encryption techniques to modern cryptographic protocols and blockchain technologies. The work explores foundational principles, advanced cryptographic methodologies, and emerging trends such as quantum-resistant algorithms and zero-knowledge proofs. In addition, practical applications—including secure wireless protocols, HTTPS, and the development of a custom cryptocurrency—are critically examined. The study concludes with recommendations for future research and the implementation of next-generation security systems.

The Mind in Revolt: Cultivating Critical Thought in a Conforming World

Mon, 15 Jan 2018 00:00:00 +0000

To cultivate genuine critical thinking, one must first confront an uncomfortable but essential truth:

From the moment we are born, we are not taught how to think — we are taught what to think.

From childhood onward, we are immersed in a web of inherited ideas — shaped by parents, teachers, media, games, institutions, and cultural norms. We are not blank slates, but rather vessels gradually filled with beliefs we did not choose and assumptions we rarely question. The philosopher Michel Foucault might call this our epistemic conditioning: the invisible framework of thought shaped by power, culture, and history.