Intertemporal Investment Strategies under Inflation Risk

This paper studies intertemporal investment strategies under inflation risk by extending Merton’s intertemporal framework (1973) to include a stochastic price index. The stochastic price index gives rise to both real and nominal terms of valuation: agents maximize their utility of consumption in real terms while investment activities and wealth evolution are evaluated in nominal terms. We include inflationindexed bonds in agents’ investment opportunity set and study their hedging function against inflation risk. A new multi-factor term structure model is developed to price both inflation-indexed bonds and nominal bonds, and the optimal rules of intertemporal portfolio allocation, both with and without inflation-indexed bonds are obtained in closed form. The theoretical model is estimated using real market data and the estimation results are employed to construct the optimal investment strategy for the real market situation. Wachter (2003) pointed out that without inflation risk, the most risk averse agents (with an infinite risk aversion parameter) will invest all their wealth in the long term nominal bond maturing at the end of the investment horizon. We extend this to the case with inflation risk and conclude that the most risk averse agents will now invest all their wealth in the inflationindexed bond maturing at the end of the investment horizon.