Sophos Alpha Research

Quantitative Finance Education & Research

Educational resources for understanding quantitative finance — from foundational concepts to advanced trading strategies.

1 Get Started

1.1 Foundations

Returns, volatility, Sharpe ratio, drawdowns, and correlation.

1.2 Portfolio Theory

Mean-variance optimization, efficient frontiers, and asset allocation.

1.3 Derivatives

Black-Scholes pricing, the Greeks, and volatility surfaces.

1.4 Time Series

Stationarity, GARCH models, and volatility forecasting.

1.5 Risk Management

Value at Risk, Expected Shortfall, and tail risk measurement.

1.6 Strategies

Momentum, mean reversion, and backtesting frameworks.

1.7 Microstructure

Order flow, bid-ask spreads, and market impact modeling.

1.8 Fixed Income

Yield curves, duration, convexity, and interest rate risk.

1.9 Machine Learning

Reinforcement learning, neural networks, and feature engineering.

2 Interactive Charts

Every article includes interactive charts. Drag to rotate, scroll to zoom, hover for details.

Example: Implied volatility surface showing the smile and term structure — key inputs for derivatives pricing.

3 Browse by Topic

Foundations
Portfolio Theory
Risk Management
Derivatives
Time Series
Trading Strategies
Market Microstructure
Fixed Income
Machine Learning

4 Clear Derivations

Every formula is explained with its components. For example, sample standard deviation:

\[ \sigma = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2} \]

Where:

  • \(\sigma\) — standard deviation
  • \(n\) — number of observations
  • \(x_i\) — each individual return
  • \(\bar{x}\) — mean of returns
  • \(n-1\) — Bessel’s correction for sample estimation

5 Code Examples

All formulas come with Python implementations using real data.

import numpy as np

# Sample returns data
returns = np.array([0.02, -0.01, 0.03, -0.02, 0.01, 0.04, -0.03, 0.02])

# Calculate standard deviation step by step
mean_return = np.mean(returns)
squared_deviations = (returns - mean_return) ** 2
variance = np.sum(squared_deviations) / (len(returns) - 1)
std_dev = np.sqrt(variance)

print(f"Mean return: {mean_return:.4f}")
print(f"Variance: {variance:.6f}")
print(f"Standard deviation: {std_dev:.4f}")
Mean return: 0.0075
Variance: 0.000621
Standard deviation: 0.0249

6 How to Use This Site

  • New to quant finance? Start with Foundations to build core intuition
  • Looking for something specific? Use the collapsible topics above or browse all articles
  • Browse by category? View all articles with category filters
  • Each article is self-contained — Read in any order, with links to prerequisites where needed
  • Latest articles? Browse all articles sorted by date
  • Learn more? Visit the About page for details on methodology and contact

This content is for educational purposes only and does not constitute financial advice. See full disclaimer.

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