This paper studies intertemporal investment strategies under inflation risk by extending the intertemporal framework of Merton (1973) to include a stochastic price index. The stochastic price index gives rise to a two-tier evaluation system: agents maximize their utility of consumption in real terms while investment activities and wealth evolution are evaluated in nominal terms. We include inflation-indexed bonds in the agents' investment opportunity set and study their effectiveness in hedging against inflation risk. A new multifactor term structure model is developed to price both inflation-indexed bonds and nominal bonds, and the optimal rules for intertemporal portfolio allocation, both with and without inflation-indexed bonds are obtained in closed form. The theoretical model is estimated using data of US bond yield, both real and nominal, and S&P 500 index. The estimation results are employed to construct the optimal investment strategy for an actual 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 result to the case with inflation risk and conclude that the most risk averse agents will now invest all their wealth in the inflation-indexed bond maturing at the end of the investment horizon.

Abstract:Applying a probabilistic causal approach, we define a class of time series causal models (TSCM) based on stationary Bayesian networks. A TSCM can be seen as a structural VAR identified by the causal relations among the variables. We classify TSCMs into observationally equivalent classes by providing a necessary and sufficient condition for the observational equivalence. Applying an automated learning algorithm, we are able to consistently identify the data-generating causal structure up to the class of observational equivalence. In this way we can characterize the empirical testable causal orders among variables based on their observed time series data. It is shown that while an unconstrained VAR model does not imply any causal orders in the variables, a TSCM that contains some empirically testable causal orders implies a restricted SVAR model. We also discuss the relation between the probabilistic causal concept presented in TSCMs and the concept of Granger causality. It is demonstrated in an application example that this methodology can be used to construct structural equations with causal interpretations. JEL: C1

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This paper considers an asset allocation strategy over a finite period under investment uncertainty and short-sale constraints as a continuoustime stochastic control problem. Investment uncertainty is characterised by a stochastic interest rate and inflation risk. If there are no short-sale constraints, the optimal asset allocation strategy can be solved analytically. We consider several kinds of short-sale constraints and employ the backward Markov chain approximation method to explore the impact of short-sale constraints on asset allocation decisions. Our results show that the short-sale constraints do indeed have a significant impact on the asset allocation decisions.