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Nonlinear dynamics induced by single-stock leveraged ETF

During July 2026, the Korean stock market experienced an unprecedented series of circuit-breaker and sidecar activations. Although global trade tensions and macroeconomic uncertainty initiated the market decline, the subsequent price movements were amplified by endogenous market mechanisms, resulting in substantial deviations of stock prices from their underlying fundamental values. The phenomenon was particularly pronounced in Samsung Electronics and SK Hynix. Despite reporting record earnings and maintaining robust business fundamentals, both companies experienced sharp price declines. Unlike most developed equity markets, Korea combines two distinctive structural characteristics: Samsung Electronics and SK Hynix account for a substantial fraction of the KOSPI capitalization, while both are actively traded through single-stock leveraged ETFs. Because these products concentrate leveraged exposure on individual stocks rather than diversified portfolios, their mandatory daily rebalancin...
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Why Correct Predictions Are Not Enough: Survival Comes First

Recently, I came across a news headline that caught my attention: “Why Did the 25-Year-Old AI Genius of Wall Street, Leopold Aschenbrenner, Fail?” The headline prompted me to write this blog post because I have seen friends go through somewhat similar experiences in their own investing. I should also mention that I am not a professional investor. What follows is simply my personal attempt to think about investing through the lens of mathematics, with substantial assistance from ChatGPT. On July 30, 2026, Leopold Aschenbrenner, the 25-year-old founder of the San Francisco-based hedge fund *Situational Awareness*, sent a letter to his investors. A former OpenAI researcher, Aschenbrenner graduated from Columbia University in 2021 as valedictorian with a B.A. in economics, mathematics, and statistics. In the letter, he acknowledged that his fund had lost **67% of its value in July alone**. For someone who had been widely regarded as a highly promising thinker in AI investing, the disclosur...
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Sovereign AI Is an Ecosystem, Not a Model

 Artificial intelligence has become an irreversible force. Whether we welcome it or not, frontier models developed by companies such as OpenAI, Google DeepMind, Anthropic, and Meta will continue to define the technological frontier for the foreseeable future. No nation can realistically ignore these models, nor should it attempt to isolate itself from global AI progress. Before proceeding, I would like to make one point clear. I am not an AI expert . I am a retired professor whose work has primarily focused on theoretical analysis. The views presented here therefore reflect my perspective as an observer of technological and industrial systems rather than as a practitioner in AI. This is not simply a matter of technological competition. As populations age, workforces shrink, and healthcare costs continue to rise, AI is becoming an economic necessity rather than a technological luxury. Sustaining productivity across government, healthcare, manufacturing, finance, education, and other...
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Beyond Optimality: Lessons from Shin Jin-seo's Victory over KataGo

Shin Jin-seo's recent victory  (2026-07-21) over KataGo demonstrates a subtle but profound distinction between optimal decision making and winning against a particular opponent. The result suggests that maximizing an objective function is not always equivalent to maximizing the probability of defeating an adversary whose own decision process is constrained by optimization. One moment in the third and final game was particularly striking. Shin intentionally accepted a slight local loss in the corner, but in return secured outside thickness by steering the game into an essentially single-path sequence that even KataGo was forced to follow.  Although this exchange was locally suboptimal, it significantly simplified the subsequent game and ultimately became one of the decisive factors in his victory.  KataGo is designed to maximize its expected winning probability. Formally, it selects an action $a\in A$ by solving $a^*=\arg\max_{a\in A}\mathbb{E}[U(a)]$, where $U(a)$ d...
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Dynamic Valuation of Memory Semiconductor Stocks

Recently (July 2026), financial markets have exhibited behavior that appears irrational over short time horizons. In particular, memory semiconductor stocks have experienced unusually large price fluctuations despite exceptionally strong earnings. Leading companies such as Samsung Electronics, SK hynix, and Micron have traded at only 5--7 times forward P/E , a low valuation given their record profitability.  The apparent contradiction reflects uncertainty about the appropriate valuation multiple. The market is caught between two opposing forces: robust earnings growth driven by AI infrastructure investment and the possibility that aggressive capital expenditures may eventually create excess capacity, leading to oversupply and weaker future profitability. Consequently, the key investment question is no longer, "How large are today's earnings?" Instead, the market asks, "Can today's earnings be sustained over many years?" Equivalently, investors focus less on ...
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The Limits of Black–Scholes Framework

 In this blog, I provide a brief introduction to the famous Black–Scholes partial differential equation and examine it from Charlie Munger's critical perspective. While the equation revolutionized option pricing and became a cornerstone of modern quantitative finance, its assumptions may limit its usefulness when applied to long-term stock investing. Before proceeding, I should note that I am not an expert in this field. The Black–Scholes framework begins with the assumption that a stock price follows a stochastic process, $dS=\mu Sdt+\sigma S dW$, where $S$ denotes the stock price, $\mu$ is the expected growth rate, $\sigma$ represents volatility, and $dW$ is Brownian motion. In essence, stock prices are modeled as evolving continuously through a combination of deterministic growth and random uncertainty. Using stochastic calculus, one arrives at $\frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2V}{\partial S^2}+rS\frac{\partial V}{\partial S}-rV=0,$ where $V$ i...
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What UFC Taught Me About Education

I have watched a few recent UFC fights, and the bout between Ilia Topuria and Justin Gaethje in mid-June 2026 was particularly memorable. Most people predicted a victory for Ilia, but the outcome was different from expectations. Both fighters displayed exceptional stamina and endurance, suggesting that they had invested a tremendous amount of time in training. However, some analysts believe that although Ilia preferred high-intensity training camps, he may have absorbed fewer realistic punches in sparring because his training partners were reluctant to engage him at full intensity due to the risk of being knocked out by his formidable punching power. Many critics dismiss mixed martial arts as little more than a modern version of Roman gladiatorial combat.  (The comparison, however, is imperfect. Gladiators were often forced into combat, whereas UFC fighters voluntarily dedicate years of their lives to earning a place among the sport's elite. Countless athletes train relentlessly fo...
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