Abstract
Portfolio selection is one of the most important areas of modern finance, both theoretically and practically. Reliance on a single model is fraught with difficulties, so attempting to combine the strengths of different models is attractive; see, for example, Geweke and Amisano (J Econom 164(1):130–141, 2011) and the many references therein. This paper contributes to the model combination literature, but with a difference: the models we consider here are making statements about different sets of assets. There appear to be no studies making this structural assumption, which completely changes the nature of the problem. This paper offers suggestions for principles of model combination in this situation, characterizes the solution in the case of multivariate Gaussian distributions, and provides a small illustrative example.
Highlights
Suppose that you are faced with the problem of choosing a portfolio position in a universe of N assets, where N may be many hundreds
We propose that all those models which speak about the assets in a given tile are combined by Bayesian model averaging2
Since we demand that the tile marginals of g are the laws q j, there is no freedom for the means of g, so without much loss of generality we shall for clarity of exposition suppose that the bα and the a j are all zero, leaving us to consider only centred Gaussians
Summary
Suppose that you are faced with the problem of choosing a portfolio position in a universe of N assets, where N may be many hundreds. It is generally understood that a simple-minded direct attempt to build a portfolio involving all N of the assets will be a dismal failure, for various reasons, chief among them being the difficulty in forming accurate estimates of the covariance matrix of returns; see, for example, the book by Fan et al [2]. If we believe we can make a reasonable combination of up to ten assets (say) we could in principle use such a ‘divide and conquer’ approach, but it would not allow us to exploit the correlations between sets of assets, and the problem still remains of how to weight the different portfolios formed from the subsets. We propose that all those models which speak about the assets in a given tile are combined by Bayesian model averaging.
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