Quantitative Methods in Finance: From Descriptive Statistics to Factor Models
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Key Insights
- Foundation of quantitative finance — statistical methods, risk measures, and multi-factor models used in institutional portfolio management.
Why Quantitative Methods?
Quantitative methods bring mathematical rigor to investment analysis, replacing intuition with systematic, testable frameworks. They underpin:
- Risk management — Value at Risk, expected shortfall, stress testing
- Portfolio construction — mean-variance optimization, risk parity
- Alpha generation — factor-based strategies, statistical arbitrage
- Execution — algorithmic trading, optimal order placement
Key Statistical Concepts
Essential statistics for financial analysis:
- Distribution — returns are approximately normal but fat-tailed (excess kurtosis ~3-10)
- Correlation — assets become correlated during crises (correlation breakdown)
- Volatility clustering — high-vol periods follow high-vol (GARCH effects)
- Stationarity — many financial time series are non-stationary (unit roots)
import numpy as np
import pandas as pd
# Annualized volatility from daily returns
daily_returns = prices.pct_change().dropna()
ann_volatility = daily_returns.std() * np.sqrt(252)
# Sharpe ratio
sharpe = (annualized_return - risk_free_rate) / ann_volatility
# Maximum drawdown
cumulative = (1 + daily_returns).cumprod()
running_max = cumulative.cummax()
drawdown = (cumulative - running_max) / running_max
max_drawdown = drawdown.min()Factor Models
Factor models explain asset returns through exposure to systematic risk factors:
# Fama-French 3-Factor Model
# Ri - Rf = alpha + b1*(Rm-Rf) + b2*SMB + b3*HML + epsilon
# Returns decomposition:
# Market risk (beta) — compensation for systematic risk
# Size (SMB) — small minus big cap returns
# Value (HML) — high book-to-market minus low
# Alpha — idiosyncratic return (skill or luck)
# Implementation with statsmodels
import statsmodels.api as sm
X = sm.add_constant(portfolio_returns - risk_free_rate)
model = sm.OLS(excess_returns, X).fit()
print(model.summary())Article Metadata
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Feynman Concept Cards
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Risk Parity is a concept in strategies. In simple terms, Risk Parity covers trading and investment strategies for Markets. This markets concept addresses key topics in the trading and investment strategies for markets domain. Also known as: risk-balanced po
Analogy
Example
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Explain Risk Parity as if teaching a colleague who is new to strategies. Cover: what it is, how it works, and why it matters.
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Create a calc that demonstrates Risk Parity in a real-world strategies scenario. Walk through your design decisions.
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A calc for Risk Parity should include: 1. The core components of risk parity 2. How they interact 3. Expected outcomes or outputs
Statistical Arbitrage is a concept in strategies. In simple terms, Statistical Arbitrage covers trading and investment strategies for Markets. This markets concept addresses key topics in the trading and investment strategies for markets domain. Also known as: stat a
Analogy
Example
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Explain Statistical Arbitrage as if teaching a colleague who is new to strategies. Cover: what it is, how it works, and why it matters.
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Create a calc that demonstrates Statistical Arbitrage in a real-world strategies scenario. Walk through your design decisions.
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A calc for Statistical Arbitrage should include: 1. The core components of statistical arbitrage 2. How they interact 3. Expected outcomes or outputs
Algorithmic Trading is a concept in advanced techniques. In simple terms, Algorithmic Trading covers advanced techniques in Markets. This markets concept addresses key topics in the advanced techniques in markets domain. Also known as: algo trading, automated trading, execu
Analogy
Example
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Portfolio Optimization is a concept in strategies. In simple terms, Portfolio Optimization covers trading and investment strategies for Markets. This markets concept addresses key topics in the trading and investment strategies for markets domain. Also known as: asset
Analogy
Example
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Explain Portfolio Optimization as if teaching a colleague who is new to strategies. Cover: what it is, how it works, and why it matters.
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A calc for Portfolio Optimization should include: 1. The core components of portfolio optimization 2. How they interact 3. Expected outcomes or outputs
Factor Investing is a concept in strategies. In simple terms, Factor Investing covers trading and investment strategies for Markets. This markets concept addresses key topics in the trading and investment strategies for markets domain. Also known as: smart beta,
Analogy
Example
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Explain Factor Investing as if teaching a colleague who is new to strategies. Cover: what it is, how it works, and why it matters.
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A calc for Factor Investing should include: 1. The core components of factor investing 2. How they interact 3. Expected outcomes or outputs
High Frequency Trading is a concept in advanced techniques. In simple terms, High Frequency Trading covers advanced techniques in Markets. This markets concept addresses key topics in the advanced techniques in markets domain. Also known as: HFT, algorithmic trading, low laten
Analogy
Example
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Mean Reversion Strategies is a concept in trading strategies. In simple terms, Mean Reversion Strategies covers trading strategies for Markets. This markets concept addresses key topics in the trading strategies for markets domain. Also known as: statistical arbitrage, pairs tra
Analogy
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