Dynamic Asset Allocation Under Inflation

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Abstract
This paper develops a simple framework for analyzing the asset allocation problem of a long-horizon investor when there is inflation and only nominal assets are available for trade. The investor's optimal investment strategy is given in simple closed form using the equivalent martingale method. The investor's hedge demands depend on both the investment horizon and the maturities of the bonds in which he invests. The optimal strategy can be decomposed into three components: first, a portfolio that mimics a hypothetical indexed bond with maturity equal to the investment horizon; secondly, the mean-variance tangency portfolio; thirdly, an additional investment in the hypothetical indexed bond to hedge against changes in the investment opportunity set. When short positions are precluded, the investor's optimal strategy consists of investments in cash, equity and a single nominal bond. When the model is calibrated to recent data on US interest rates and inflation, only high frequency movements in real interest rates are detected so that the optimal allocation between stock and bond is found to be relatively insensitive to the horizon. A longer calibration period reveals low frequency variation in real interest rates that induces more pronounced horizon effects. Reasons for the differences in the two calibration exercises are suggested.

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