Implied Risk Premia for Factors
Theory, Estimation, and Applications - Academic Research Paper
Abstract
This paper develops a comprehensive framework for estimating implied risk premia in multi-factor asset pricing models. We extend inverse optimization techniques from single-factor CAPM to the Fama-French three-factor and five-factor settings. Using data from the Kenneth French Data Library (July 1963 - December 2023, T=726 months), we demonstrate the practical implementation and empirical properties of implied factor premia.
Key contributions include: (1) a unified theoretical framework linking portfolio weights to implied expected returns via factor models; (2) two calibration methods for the risk aversion parameter - market-based (M1) and historical (M2); (3) an R-squared-based hybrid approach for regime-adaptive estimation; and (4) extensive empirical validation using real Fama-French data.
Paper Contents
1. Introduction
Motivation, literature review, and paper organization.
2. Theoretical Framework
Mean-variance optimization, factor models, inverse optimization.
3. Lambda Calibration
Market-based (M1) and historical (M2) methods with hybrid blending.
4. Empirical Analysis
Fama-French data, factor premia estimation, validation results.
5. Applications
Portfolio construction, risk budgeting, timing strategies.
6. Conclusion
Summary, limitations, and future research directions.
Key Figures
All figures use real Fama-French data (July 1963 - December 2023). Click to view PDF.
Factor Premia History (1963-2023)
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Rolling Factor Premia
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Implied vs Realized Returns
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Hansen-Jagannathan Bound
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Factor Correlation Matrix
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Timing Strategy Backtest
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Data Source
Kenneth French Data Library
All empirical results use publicly available data from Kenneth French's website. The dataset covers 726 months of factor returns (July 1963 - December 2023), including the market factor (Mkt-RF), size factor (SMB), value factor (HML), profitability factor (RMW), and investment factor (CMA).