TrueBeta

Dynamic stock beta estimation using Kalman filtering.

TrueBeta is a web application that estimates time-varying stock betas using a Kalman filter state-space model, compared side-by-side against traditional rolling OLS regression. It lets you look up any ticker and instantly see how its market sensitivity has changed over time — with interactive charts, confidence bands, and cumulative alpha analysis.

Why TrueBeta?

Traditional beta estimation uses a fixed rolling window of historical returns (e.g., 252 days). This approach has fundamental problems:

• Arbitrary window choice — different windows give dramatically different results
• Lagging — slow to react to regime changes
• Abrupt jumps — extreme observations entering/leaving the window create discontinuities
• Equal weighting — treats data from 11 months ago the same as yesterday

TrueBeta uses a Kalman filter to model beta as a continuously evolving state variable. The filter optimally balances new observations against its model prediction at every time step, producing smooth, adaptive beta estimates with built-in uncertainty quantification.

The Model

All estimates use excess returns (net of the risk-free rate via the 13-week Treasury bill), consistent with the CAPM framework:

Observation:  (r_stock - r_f) = α + β · (r_market - r_f) + ε
State:        β_t = β_{t-1} + w_t    (random walk)

The Kalman filter recursively updates α and β at each time step, with the Kalman gain determining the optimal weighting between the model prediction and new market data.

Features

• Kalman filter beta with 95% confidence bands
• Rolling OLS beta for comparison, with configurable window (3M, 6M, 1Y, 2Y)
• Configurable display range (1Y, 2Y, 3Y, 5Y, 10Y)
• Interactive Plotly charts — beta comparison, normalized prices, cumulative alpha
• Autocomplete ticker search from S&P 500 constituents
• Excess return estimation using the 13-week T-bill rate (^IRX)
• On-the-fly computation with in-memory TTL caching
• KaTeX-rendered mathematics explaining the methodology

Tech Stack

• FastAPI — async Python web framework
• NumPy — Kalman filter implementation (~50 lines, no external filter library)
• Pandas / statsmodels — data handling and rolling OLS
• yfinance — stock price and Treasury rate data
• Plotly.js — interactive client-side charts
• TailwindCSS — styling (via CDN)
• KaTeX — LaTeX math rendering (via CDN)

Project Structure

truebeta/
├── main.py              # FastAPI app entry point
├── requirements.txt     # Python dependencies
├── Procfile             # Railway deployment
├── core/
│   ├── kalman.py        # Kalman filter beta estimation
│   ├── ols.py           # Rolling OLS beta estimation
│   ├── data.py          # yfinance data fetching + caching
│   ├── charts.py        # Plotly chart builders
│   └── sp500.py         # S&P 500 ticker list from Wikipedia
└── web/
    ├── router.py        # FastAPI routes
    └── templates/
        ├── base.html    # Layout with nav, footer, autocomplete
        ├── index.html   # Landing page with methodology explanation
        ├── ticker.html  # Ticker results with interactive charts
        └── 404.html     # Not found page

Running Locally

pip install -r requirements.txt
python main.py

Then open http://localhost:8000.

Deployment

Deployed on Railway with automatic deploys from this repo. The Procfile runs uvicorn on the $PORT provided by Railway.

Data Sources

• Stock prices & S&P 500 index — Yahoo Finance via yfinance
• Risk-free rate — 13-week Treasury Bill (^IRX) from Yahoo Finance
• S&P 500 constituents — Wikipedia

License

MIT