A Robust Approach to Variance Bound Calculations

This paper studies the consequences of a minor change to the present value formula for stock prices. In place of the squared-error-loss minimizing expected present value of future dividends, we use a predictor optimal for the min-max preference relationship appropriate in cases of ambiguity. With such \robust" predictions, the variance bound of Shiller (1981) and LeRoy-Porter (1981) is reversed in spectacular fashion in that prices are predicted to be far more volatile than what is observed in the data. We also investigate an intermediate \partially robust" case in which the degree of ambiguity is limited, and discover that such an intermediate model cannot be rejected in favor of an unrestricted time series model with more than twice as many parameters.

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