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A Bayesian Approach to a Portfolio Selection Problem
Mar 22, 2001
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Abstract:
This talk covers some ideas that form the foundation of my work
at the research center of Deutsche Asset Management. References to the
finance literature will be given in the talk.
The first part of this talk is a brief look at portfolio selection and asset pricing. The basic setting is that we have a certain amount of money to invest, and a range of choices of assets in which we may invest. The returns on the various assets may be random, but we know their joint distribution. This question leads us through the basics of portfolio theory and, with a market clearing condition, the Capital Asset Pricing Model. We then turn to the more practical question of how to use data in the process of portfolio selection. Historical data gives some information on future returns, but it is well known that simple-minded use of this information often leads to nonsense because estimation risk -- the loss due to estimating parameters rather than using the exact values -- overwhelms the value of the information in the data. At a more fundamental level, the simple model of (log-) normal returns with unknown mean and covariance takes on a special flavor in finance, since the uncertainty in the parameters is itself a source of risk, and investors will expect compensation for exposing themselves to that risk. A standard Bayesian approach handles this problem elegantly. The idea is to treat estimation risk on a par with randomness in returns. We explain an appropriate choice of priors, and discuss some details associated with Monte Carlo implementation of the Bayesian method. We also touch on priors based on asset pricing models, such as CAPM. This talk is based on work by Zellner and Chetty, Klein and Bawa, Stambaugh, and Stambaugh and Pastor, among others. It is related to ongoing work at Deutsche Bank. |
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