MLOps: Portfolio Optimization

Nattawut Boonnoon

• LinkedIn: www.linkedin.com/in/nattawut-bn
• Email: nattawut.boonnoon@hotmail.com

Overview

Link: https://nattawut-port.streamlit.app/

My Portfolio optimization pipeline covering Black-Litterman and risk parity allocation, Brownian motion and Heston stochastic volatility simulation, and FFT tail risk hedge pricing. Built as an MLOps project: a scheduled batch pipeline computes and versions every result on a Streamlit dashboard displays the latest output.

System Architecture

The pipeline runs in two separate stages.

A scheduled batch job (GitHub Actions), run on the 1st and 16th of each month, extracts prices, computes returns and covariance, estimates expected returns, optimizes portfolio weights, simulates risk, and prices a tail risk hedge. Results are published to the repository's "latest" GitHub Release rather than committed to git. Each run overwrites the same release assets in place, so repo size and commit count stay constant no matter how often the pipeline runs. The pipeline's own keep-alive signal is pushed to a separate branch, never to main, which stays fully protected and human-only.

A Streamlit dashboard fetches only the finished output of that job. It never recomputes anything and never touches the data source directly.

Data moves through three layers on disk. (Bronze -> Silver -> Gold)

Design decisions:

• The data source sits behind a single interface. The original source was replaced during development after it started blocking scripted requests. Swapping providers again touches one file, not the pipeline.
• Portfolio construction and risk simulation each have two interchangeable implementations behind a shared interface: max-Sharpe and risk parity for optimization, geometric Brownian motion and Heston for simulation.
• The dashboard never imports the compute modules directly. It reads only the parquet files those modules produce.

Mathematical Model

Returns and covariance

$$r_t = \ln\left(\frac{P_t}{P_{t-1}}\right)$$

Log returns, used in place of price levels since they are close to stationary.

$$\hat{\Sigma} = (1 - \alpha)S + \alpha F$$

Ledoit-Wolf shrinkage covariance. S is the sample covariance, F is the shrinkage target, alpha is estimated from the data.

Expected returns

$$\pi = \delta \Sigma w_{mkt}$$

Black-Litterman equilibrium return. With no investor views, this is the model's output directly.

$$E[R] = \left[(\tau\Sigma)^{-1} + P^T\Omega^{-1}P\right]^{-1}\left[(\tau\Sigma)^{-1}\pi + P^T\Omega^{-1}Q\right]$$

Black-Litterman posterior return, blending the equilibrium with investor views P, Q, and view uncertainty Omega.

Portfolio construction

$$\max_{w} \frac{w^T\mu - r_f}{\sqrt{w^T\Sigma w}} \quad \text{subject to} \sum_i w_i = 1,\ w_i \geq 0$$

Max-Sharpe, long only, solved with SLSQP.

$$w_i(\Sigma w)_i = w_j(\Sigma w)_j \quad \forall\, i, j$$

Risk parity. Every asset contributes equally to total portfolio variance.

Simulation

$$dS_t = \mu S_t\,dt + \sigma S_t\,dW_t$$

Geometric Brownian motion, constant volatility.

$$dS_t = \mu S_t\,dt + \sqrt{v_t}\,S_t\,dW_t^S \qquad dv_t = \kappa(\theta - v_t)\,dt + \xi\sqrt{v_t}\,dW_t^v \qquad dW_t^S dW_t^v = \rho\,dt$$

Heston stochastic volatility, simulated with a full truncation Euler scheme so variance cannot go negative.

$$\text{VaR}_\alpha = \inf\{l : P(L > l) \leq 1-\alpha\} \qquad \text{CVaR}_\alpha = E[L \mid L \geq \text{VaR}_\alpha]$$

Hedge pricing

$$C(K) = \frac{e^{-\alpha k}}{\pi}\int_0^{\infty} e^{-ivk}\,\psi(v)\,dv$$

Heston option price via the Carr-Madan FFT method, using the model's characteristic function. Priced against two independent methods, FFT and Monte Carlo, cross-checked against each other on every run.

$$P = C - S_0 + Ke^{-rT}$$

Put-call parity, converting the FFT call price into a put price.

Acknowledgments

Dependencies

Streamlit · Pandas · Numpy · Plotly · Scikit-Learn · PyTorch · MLFlow · PyArrow · SciPy

Academic Papers & References

• Markowitz, H. (1952). "Portfolio Selection." The Journal of Finance, 7(1), 77-91.
• Black, F., & Scholes, M. (1973). "The Pricing of Options and Corporate Liabilities." Journal of Political Economy, 81(3), 637-654.
• Sharpe, W. F. (1966). "Mutual Fund Performance." The Journal of Business, 39(1), 119-138.
• Black, F., & Litterman, R. (1992). "Global Portfolio Optimization." Financial Analysts Journal, 48(5), 28-43.
• Ledoit, O., & Wolf, M. (2004). "A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices." Journal of Multivariate Analysis, 88(2), 365-411.
• Heston, S. L. (1993). "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options." The Review of Financial Studies, 6(2), 327-343.
• Carr, P., & Madan, D. (1999). "Option Valuation Using the Fast Fourier Transform." Journal of Computational Finance, 2(4), 61-73.
• Maillard, S., Roncalli, T., & Teiletche, J. (2010). "The Properties of Equally Weighted Risk Contribution Portfolios." The Journal of Portfolio Management, 36(4), 60-70.
• Rockafellar, R. T., & Uryasev, S. (2000). "Optimization of Conditional Value-at-Risk." Journal of Risk, 2(3), 21-41.
• Howell, E., (2025), "Modern Boiler plate to build an end-to-end ML project"., ML-Project-Starter.