#Quantitative Trading
- 1.1. MPT - Modern Portfolio Theory - Markowitz 1952
- 1.2. CAPM - Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk - Sharpe 1964
- 1.3. Common Risk Factors in the Returns on Stocks and Bonds - Fame and French 1993
- [Foundational Papers Explained]
- 2.1. MPT - Modern Portfolio Theory - Markowitz 1952
- 2.2. CAPM - Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk - Sharpe 1964
Imagine you have a big bag of different toys. If you only have one kind of toy, like only glass marbles, and you drop the bag, they might all break at once. But if you have some marbles, some soft stuffed animals, and some wooden blocks, even if you drop the bag, the stuffed animals and blocks will be fine. MPT is just a fancy way of saying: "Don't put all your eggs in one basket." It teaches us how to pick a mix of toys so that if one gets "broken" (loses money), the others help keep the whole bag safe.
- Mean-Variance Optimization: Used to calculate the best possible return for a specific level of risk.
- Efficient Frontier: Helps managers find the set of optimal portfolios that offer the highest expected return for a defined risk level.
- Diversification: Reducing overall volatility by combining assets that are not perfectly correlated.
MPT assumes that asset returns follow a Normal Distribution (the Bell Curve). In reality, markets have "Fat Tails"—black swan events happen way more often than the math predicts.
- Garbage In, Garbage Out: MPT is hyper-sensitive to input. If your estimate for a stock's future return is off by just 1%, the model might tell you to put 100% of your money in it.
- The Correlation Problem: MPT assumes correlations are static. In a crash, correlations go to 1.0. Everything falls together, and the "diversification" MPT promised vanishes exactly when you need it most.
- The Theory (MPT): If the math says a stock will return 10%, you bet exactly based on 10%.
- The Disaster: If the stock returns 9% instead, your whole portfolio collapses because you were too confident.
Imagine you are jumping across a stream. The academic model says the stream is exactly 3 feet wide, so you jump exactly 3 feet. But what if the map is slightly wrong? You fall in the water! The "Citadel Tweak" is to act like the stream is 5 feet wide even if the map says 3. You add "safety padding" to your jump so that even if the map is wrong, you land safely on the grass.
- The Quantitative Reality:
- Bayesian Shrinkage: Quants "shrink" their estimates toward a common average. If a model predicts a crazy 50% return, the system automatically pulls that number down to something more "realistic" (like 8%) before placing the trade. This prevents the "Garbage In, Garbage Out" problem.
Relates to: Portfolio Selection (1952) by Harry Markowitz.
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The Original Paper says: If you input the expected returns (
$\mathbb{E}[R]$ ) and the risk (covariance matrix$\Sigma$ ), the math outputs the perfect portfolio weights ($w$ ). -
The Problem: The math is "fragile." Small errors in your return guesses lead to wildly unstable portfolios.
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The Tweak (Shrinkage): Firms use Ledoit-Wolf Shrinkage or Black-Litterman.
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The Math: Instead of using raw data for the covariance matrix (
$\hat{\Sigma}$ ), they "shrink" it toward a structured target ($F$ ):
- Simple Explanation: They take the "crazy" raw data and pull it back toward a "boring" average to make sure the portfolio doesn't overreact to noise.
CAPM - Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk - William Sharpe 1964
Think of the whole stock market like a big ocean. When the tide goes up, almost every boat goes up. When it goes down, they all go down. This paper explains that some boats move exactly like the tide (Beta), while some special boats move faster or slower because of how they are built (Alpha). It tells us that you shouldn't get a reward just for owning a boat; you only get a special reward if your boat is better at sailing than the others.
- Alpha and Beta: Quantitative researchers use this to distinguish between market-driven returns (Beta) and skill-based returns (Alpha).
- Systematic Risk: Identifies that only market-wide risk should be compensated, as specific risks can be diversified away.
CAPM relies on the Efficient Market Hypothesis (EMH) — the idea that all information is already in the price and you can't beat the market. If this were 100% true, Renaissance Technologies and Citadel wouldn't exist.
- Beta is Not Risk: CAPM says "Beta" (volatility relative to the market) is the only measure of risk. But a stock can be volatile and safe, or steady and "cheap" until it goes to zero (like a fraudulent company).
- Borrowing Constraints: The model assumes you can borrow money at the "risk-free rate" to leverage your bets. In the real world, your broker will charge you much more, and they’ll margin call you at the worst possible time.
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The Theory (Diversification): Stocks and Bonds move in different directions, so you are safe.
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The Disaster: In a rainstorm (market crash), everything gets wet. Correlations go to 1.0.
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The 5-Year-Old Explanation: The academic says, "I have an umbrella for rain and sunglasses for sun, so I'm always ready!" But the expert knows that sometimes there is a hurricane where it’s sunny one second and pouring the next. The "Renaissance Tweak" is a machine that changes your outfit every single second based on the wind, rather than just picking one outfit for the whole day.
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The Quantitative Reality:
- Regime Switching: Instead of assuming correlations are fixed, these firms use Hidden Markov Models (HMM). These are "Mood Detectors" for the market. If the market's "mood" shifts from "Calm" to "Panic," the portfolio instantly re-calculates all its math using "Panic Data" instead of "Calm Data."
Relates to: CAPM by William Sharpe and MPT by Markowitz.
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The Original Paper says: Diversification works because assets move independently (low correlation), and "Beta" is a constant number that tells you how much a stock moves with the market.
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The Problem: In a crash, Beta is not constant. It spikes. Everything that was supposed to be "different" starts moving in the exact same downward direction.
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The Tweak (Dynamic Regime Switching): Firms use Engle’s DCC-GARCH (Dynamic Conditional Correlation).
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The Math: Instead of a fixed correlation (
$\rho$ ), they treat correlation as a moving variable that depends on yesterday's volatility. -
Simple Explanation: They acknowledge that "the weather changes." When volatility rises, they automatically assume everything will start moving together, so they cut their total "risk budget" before the crash actually happens.
Common Risk Factors in the Returns on Stocks and Bonds (1993) by Eugene F. Fama and Kenneth R. French.
Imagine if you could look at a piece of fruit and know exactly why it tastes good—maybe it’s because it’s small, or because it grew in the sun, or because it’s very fresh. This paper says stocks have "traits" too. Some are small companies, some are "cheap" compared to what they own (Value), and some are very profitable (Quality). By looking for these traits, we can guess which stocks might do better than others over a long time.
- Multi-Factor Models: Firms like Point72's Cubist Systematic use these to identify measurable characteristics that explain asset returns.
- Risk Control: Identifying factors like momentum, value, and quality to enhance asset allocation and risk management.
- Modern Evolution: Recent research explores "Causal Factor Investing" to fix errors in older factor models.
Factor investing worked brilliantly until everyone started doing it. This is known as "Factor Crowding."
- Data Mining: If you look at enough historical data, you will find something that looks like a pattern. Many "factors" discovered in papers don't actually exist in the future; they were just coincidences in the past.
- The Value Trap: The "Value" factor (buying cheap stocks) underperformed for over a decade (2010–2020). If a Portfolio Manager followed Fama-French blindly during that time, they would have been fired.
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The Theory (CAPM/Factors): If a stock is "Value," buy it! The price doesn't matter.
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The Disaster: If everyone else is buying "Value" at the same time, you'll get crushed when you all try to leave through the same tiny door.
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The 5-Year-Old Explanation: Imagine you hear there are free cupcakes in the kitchen. The academic rule says "Run to the kitchen!" But the "Expert Tweak" is to look at how many other kids are already running. If the hallway is jammed with 100 kids, you’ll get stepped on, and the cupcakes will be gone by the time you get there. You only run if the hallway is empty.
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The Quantitative Reality:
- Market Impact Models: Firms model the "liquidity" of a trade. If the trade is too "crowded," they scale back the size or wait. They use Almgren-Chriss models to calculate exactly how much their own buying will push the price up, and they only trade if the profit is bigger than that "push."
Relates to: Common Risk Factors in the Returns on Stocks and Bonds (1993) by Fama and French.
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The Original Paper says: You can get extra returns by systematically buying stocks with certain traits (e.g., Small-Cap or Value).
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The Problem: The paper assumes you can buy these stocks for free. In reality, because everyone reads Fama-French, thousands of hedge funds are trying to buy the same "Value" stocks at the same time.
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The Tweak (Crowd/Liquidity Modeling): Firms use models based on Kyle (1985) or Almgren-Chriss (2000).
- The Strategy: They don't just ask "Is this a Value stock?" they ask "How many people are already in this trade?"
- Simple Explanation: If the Fama-French signal says "Buy," but the TCA model says "The hallway is too crowded," a firm like Citadel will either skip the trade or trade it much more slowly to avoid paying too much in "slippage."