The terminal real wealth optimization problem with index bonds: equivalence of real and nominal portfolio choices for the constant relative risk aversion utility

In this paper, we consider an investment problem where the objective is to maximize the expected utility of terminal real wealth. We demonstrate that, in the market where there exist a risk‐free bond, an index bond and a stock, the problem of maximizing the expected utility of real terminal wealth can be transformed into the problem of maximizing the expected utility of nominal terminal wealth. We find that the optimal real and nominal portfolio choices of an investor with constant relative risk aversion preference are the same when the index bond is available for investment.