Jacquier-Polson (2010) Bayesian Methods in Finance

Summary

A 92-page handbook survey of Bayesian methods in empirical finance, published in the Handbook of Bayesian Econometrics (Geweke, Koop, and Van Dijk, eds., Oxford University Press). Covers five areas in sequence: portfolio optimization under parameter uncertainty (§2), return predictability (§3), asset pricing and Arbitrage Pricing Theory (APT) (§4), volatility models and options (§5–6), and particle filtering with parameter learning (§7). No new methodology is introduced; the chapter's value lies in synthesis and cross-referencing a decade of Bayesian finance research.

Key Claims

• Bayesian portfolio allocation properly incorporating parameter uncertainty decreases with investment horizon, contrary to Merton's horizon-invariance; the long-run risky allocation $w^* = (\hat\alpha - r_0) / [\sigma^2(\gamma(1+H/T)-H/T)]$ has $H$ in the denominator, increasing effective risk aversion at long horizons.
• The Savage density ratio $\mathrm{BF} = p_C(\psi=0|y) / p_C(\psi=0)$ gives an exact Bayes factor for testing the leverage null $\psi=0$ without computing a separate marginal likelihood; requires only the posterior ordinate at $\psi=0$, evaluated by averaging log Student-t densities over Markov chain Monte Carlo (MCMC) draws.
• Particle filtering with sufficient-statistics parameter learning (Carvalho-Johannes-Lopes-Polson, CJLP, 2010) extends the standard particle filter to joint state+parameter estimation in real time; sequential odds ratios at 40,000 particles match MCMC accuracy for stochastic-volatility (SV) model comparison.
• Bayesian model averaging handles return predictability (Avramov 2002; Cremers 2002) without pre-test distortion by weighting models by posterior probability.
• APT factor structure is evaluated via McCulloch-Rossi (1990, 1991) posterior/predictive utility approaches and Geweke-Zhou (1995) pricing-error regression; factor parsimony evidence is mixed.

Concepts Introduced or Extended

• Estimation Risk and Asset Allocation
• Stochastic Volatility
• Contingent Claim Model Error
• MCMC Maximum Likelihood

Entities Mentioned

• Eric Jacquier
• Nicholas Polson
• Michael Johannes

Quotes

"The predictive distribution is the fundamental Bayesian object: it averages the likelihood over parameter uncertainty and thereby avoids the plug-in fallacy."

My Take

Useful as a reference map of Bayesian finance circa 2010. The portfolio section (§2) is the most quantitatively precise, with the horizon-allocation formula being the clearest exportable result. The §7 particle filtering discussion foreshadows the CJLP (2010) framework. As a survey chapter it is necessarily incomplete — option pricing and APT discussions are thin compared to the SV material — but the bibliography alone is worth consulting.