Real and Nominal Efficient Sets

Abstract

incorporate the influence of inflation in constructing mean-variance efficient portfolios. He used two different sets of data in deriving the portfolio composition. One was the history of nominal returns of securities; the other was the history of real returns. The efficient portfolios derived from the real data differed in composition from their nominal counterparts and were found to dominate them. Solnik [7] has explored the impact of inflation on the composition of the efficient set. He shows that the real efficient set can be expressed as a combination of the real minimum variance portfolio and a second portfolio common to all investors. Although the second portfolio has no net investment (sum of portfolio investment proportions is zero), the amount of it that is held will vary depending on individual tastes. This paper extends the work of Solnik in that it investigates the difference between the real and nominal efficient sets by showing that every nominal efficient portfolio can be transformed into a real efficient portfolio by the additional purchase of a hedge portfolio. The hedge portfolio requires no net investment, has zero expected return, and its composition does not depend on the composition of the nominal efficient portfolio. The derivations and analysis of this hedge portfolio reveals several interesting facts: (1) If there exists one portfolio that is nominal efficient but not real efficient, then no portfolio can be efficient both in real and nominal terms. Similarly, if there exists one portfolio that is efficient both in nominal and real terms, then all efficient portfolios are both nominal efficient and real efficient; the nominal efficient set and the real efficient set are either identical or disjoint. (2) If the real and nominal efficient sets are identical and the market portfolio is efficient, the risk and expected return of any asset is determined by its covariance with the inflation rate. (3) If the real and nominal efficient sets are disjoint, the real variance of any nominal efficient portfolio can be reduced, with no additional net investment, by acquiring the hedge portfolio. The acquisition of the hedge portfolio will reduce the real variance by an amount equal to the covariance between the hedge portfolio and the inflation rate.