Paper: arXiv 2307.00459

Abstract

This paper presents a method for predicting stock returns using principal component analysis (PCA) and the hidden Markov model (HMM) and tests the results of trading stocks based on this approach. Principal component analysis is applied to the covariance matrix of stock returns for companies listed in the S&P 500 index, and interpreting principal components as factor returns, we apply the HMM model on them. Then we use the transition probability matrix and state conditional means to forecast the factors returns. Reverting the factor returns forecasts to stock returns using eigenvectors, we obtain forecasts for the stock returns. We find that, with the right hyperparameters, our model yields a strategy that outperforms the buy-and-hold strategy in terms of the annualized Sharpe ratio.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts like spectral theorem for symmetric matrices, eigen-decomposition, and Gaussian HMMs, resulting in high math complexity. It also demonstrates strong empirical rigor by applying the method to S&P 500 data, implementing trading strategies, and reporting performance metrics like annualized Sharpe ratio against a benchmark.

Research Flowchart

  flowchart TD
  Goal["Research Goal: Forecast Stock Returns & Outperform Buy-and-Hold"] -->|Input| Data["Data: S&P 500 Historical Returns"]
  Data -->|Process 1| PCA["PCA: Decompose Covariance Matrix into Principal Components (Factors)"]
  PCA -->|Output| Factors["Factor Returns (Eigenvectors)"]
  Factors -->|Process 2| HMM["HMM: Model Factor Dynamics & Forecast Returns"]
  HMM -->|Output| Forecast["Forecasted Stock Returns"]
  Forecast -->|Process 3| Strategy["Trading Strategy: Reconstruct & Trade"]
  Strategy -->|Result| Outcome["Outcome: Annualized Sharpe Ratio > Buy-and-Hold"]