Robustness of the Risk-Return Relationship in the U.S. Stock Market

Lanne, Markku and Luoto, Jani (2007): Robustness of the Risk-Return Relationship in the U.S. Stock Market.

Abstract

In this paper, we study the risk-return relationship in monthly U.S. stock returns (1928:1— 2004:12) using GARCH-in-Mean models. In particular, we consider the robustness of the relationship with respect to the omission of the intercept term in the equation for the expected excess return recently recommended by Lanne and Saikkonen (2006). The existence of the relationship is quite robust, but its estimated strength is dependent on the prior belief concerning the intercept. This is the case in particular in the first half of the sample period, where also the coefficient of the relative risk aversion is found to be smaller and the equity premium greater than in the latter half.

• Item Type: MPRA Paper
• Institution: HECER
• Language: English
• Keywords: ICAPM model; relative risk aversion; GARCH-in-Mean model; Bayesian analysis
• Subjects: G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General

References

Bauwens, L., and M. Lubrano (1998), Bayesian inference on GARCH models using Gibbs sampler, Econometrics Journal, 1, 23–46.

Bauwens, L., and M. Lubrano (1998), Bayesian option pricing using asymmetric GARCH models, Journal of Empirical Finance, 9/3, 321-344.

Bauwens, L., A. Preminger, and J. Rombouts (2006), Regime Switching GARCH Models, CORE Discussion Paper 2006/11.

Bollerslev, T. (1986), Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–327.

Brooks, S.P., and A. Gelman (1997), General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7, 434–455.

Engle, R.F., D.M. Lilien, and R.P. Robins (1987), Estimating time-varying risk premia in the term structure: the ARCH-M model. Econometrica 55, 391–407.

Fama, E.F., and K.R. French (2002), The equity premium. Journal of Finance 57, 637–659.

Gelfand, A., and D. Dey (1994), Bayesian model choice: Asymptotic and exact calculations, Journal of Royal Statistical Society, Ser. B 56, 501–514.

Gelman, A., J.B. Carlin, H.S. Stern, and D.B. Rubin (2004), Bayesian Data Analysis, 2nd edition, Chapman & Hall/CRC.

Gelman, A, and D.B. Rubin (1992), Inference from iterative simulation using multiple sequences, Statistical Science, 7, 457–511.

Geweke, J. (1989), Exact predictive densities in linear models with ARCH disturbances, Journal of Econometrics, 40, 63-86.

Geweke, J. (1993), Bayesian treatment of the independent studentt linear model, Journal of Applied Econometrics, 8, 19–40.

Ghysels, E., P. Santa-Clara, and R. Valkanov (2005), There is a risk-return tradeoff after all. Journal of Financial Economics 19, 3–29.

Hansen, P.R., and A. Lunde (2005), A forecast comparison of volatility models: Does anything beat a GARCH(1,1)? Journal of Applied Econometrics 20, 873–889.

Jeffreys, H. (1961). Theory of Probability, 3rd edition, Oxford Univiersity Press, Oxford.

Kaufmann, S. and S. Fruhwirth-Schnatter (2002). Bayesian analysis of switching ARCH models, Journal of Time Series Analysis, 23, 425–458.

Kleibergen, F. and H. van Dijk (1993). Nonstationarity in GARCH models: a bayesian analysis, Journal of Applied Econometrics, 8, 41–61.

Lanne M., and P. Saikkonen (2006), Why is it so difficult to uncover the risk-return tradeoff in stock returns? Economic Letters, 92, 118–125.

Mehra, R., and E.C. Prescott (1985), The equity premium: A puzzle. Journal of Monetary Economics 15, 145–161.

Merton, R.C. (1973), An intertemporal capital asset pricing model. Econometrica 41, 867–887.

Miazynskaia, T. S., and G. Dorffner (2004), A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models, Statistical Papers, 47, 525-549.

Nakatsuma, T. (2000), Bayesian analysis of ARMA-GARCH models: a Markov chain sampling approach, Journal of Econometrics, 95, 57–69.

Vrontos, D., P. Dellaportas and D.N. Politis (2000), Full Bayesian inference for GARCH and EGARCH models, Journal of Business and Economics Statistics, 18, 187-198.

Vrontos, D., P. Dellaportas and D.N. Politis (2003), A fullfactor multivariate GARCH model, Econometrics Journal, 6, 312-334.

Wasserman, L. (1997). Bayesian model selection and model averaging, Technical report, Statistics Department, Carnegie Mellon University.

Zellner, A., (1971), An Introduction to Bayesian Inference in Econometrics, Wiley, New York.