Investing in a real world with mean-reverting inflation.

People are concerned about maintaining purchasing power in times of rising inflation. We formulate investment objectives in terms of real wealth, assuming investors derive utility from the number of goods they can buy with their monetary wealth. We derive closed-form solutions for the portfolio choice problem of constant relative risk averse investors, under the assumption that inflation rates are mean-reverting. We consider alternative specifications for the inflation compensation offered by the available assets, in order to study the effect on portfolio choice and welfare. Moreover, we study the added value of inflation-indexed bonds for the investor in our real framework.