Abstract
We solve a one-period asset allocation problem with a Bayesian copula-Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. Investors invest among risk-free assets, a passive fund and an active fund, and maximize their expected utility. Posterior distributions of model parameters are drawn by the ‘Metropolis-within-Gibbs’ algorithm. Our results show significant percentage of holdings in active funds with different levels of risk aversion. With low risk aversion, Bayesian models yield similar portfolio weights and returns with non-Bayesian models. As risk aversion increases, however, Bayesian models imply more conservative weights in active funds and lead to significantly lower volatility of realized out-of-sample returns and utilities.
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Notes
See Patton (2004, 2006a, 2006b), Hu (2006), Jondeau and Rockinger (2002) and Tasfack (2006).
Random-walk H-M algorithm generates highly correlated data points and we usually need to extract each data point from a relatively large number of simulated points. For example, in our case, we extract each data point for every 20 simulated data points.
See Nelson (1998) and Joe (1997) for a formal treatment of copula theory, and Bouye et al (2000), Cherubini et al (2004) and Embrechts et al (2002) for applications of copula theory in finance.
See Patton (2004).
For a detailed survey on the estimations of copula-GARCH model, see Chapter 5 of Cherubini et al (2004).
See Mueller (1991, 1993), Casella and George (1992) and Chib and Greenberg (1995) for a general overview on Gibbs sampling, Metropolis-Hastings sampling and ‘Metropolis-within-Gibbs’ algorithm.
We will not explore this aspect in this article.
The two websites are http://finance.yahoo.com and http://reseaerch.stlouisfed.org/fred2, respectively.
We omit the figures for the other two asset groups to save some space, and they have very similar patterns. Meanwhile, Table 7 covers the statistical patterns of the optimal portfolios for all three asset groups.
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Kang, L. Asset allocation in a Bayesian copula-GARCH framework: An application to the ‘passive funds versus active funds’ problem. J Asset Manag 12, 45–66 (2011). https://doi.org/10.1057/jam.2010.6
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DOI: https://doi.org/10.1057/jam.2010.6