Forecasting Equity Risk Premium

This project investigates the forecastability of the equity risk premium using historical macroeconomic and financial predictors. The analysis is fully implemented in Python within a Jupyter notebook environment and forms part of a quantitative finance group coursework project.

The study focuses on predictive regression frameworks, where excess market returns are modeled as a function of lagged predictor variables such as valuation ratios, interest rate spreads, and macro indicators. Both in-sample and out-of-sample forecasting performances are evaluated.

Methodology

1. Data Preparation

   • Load and clean historical time series data of the equity market excess return and multiple predictive variables.
   • Align and lag predictors to ensure information availability consistency.
   • Handle missing values and normalize predictors when necessary.

2. Predictive Regressions

   • Estimate univariate and multivariate predictive regressions of the form

   $$r_{t+1} = \alpha + \beta x_t + \varepsilon_{t+1}$$

   where $(r_{t+1})$ is the equity risk premium and $(x_t)$ represents one or more lagged predictors.

   • Evaluate the statistical significance of coefficients to identify meaningful predictors.

3. Out-of-Sample Forecasting

   • Implement expanding and rolling window forecasts to simulate real-time prediction.

   • Compute performance metrics such as:

     • Out-of-sample $(R^2)$,
     • Mean Squared Forecast Error (MSFE),
     • Economic utility gains relative to a historical mean benchmark.

4. Model Comparison & Robustness

   • Compare single-predictor and kitchen-sink (multi-predictor) models.
   • Assess model stability and robustness across different sample periods.
   • Visualize forecast performance and error behavior over time.

5. Interpretation

   • Discuss which variables exhibit genuine predictive power.
   • Link model outcomes to theoretical explanations of time-varying risk premia and business-cycle dynamics.

The notebook and accompanying report document the full empirical workflow – from data import and regression estimation to out-of-sample evaluation and interpretation – highlighting the methodological rigor behind forecasting the equity risk premium in a reproducible way.