Academic journal article Journal of Money, Credit & Banking

Asset Returns and Measured Inflation

Academic journal article Journal of Money, Credit & Banking

Asset Returns and Measured Inflation

Article excerpt

1. INTRODUCTION

Reports of a "puzzling" inverse relationship between estimates of the real return on assets and the expected rate of inflation have appeared in Fama and Schwert (1977), Jaffe and Mandelker (1975), Body (1976), Nelson (1976), and Lintner (1975). Ely and Robinson (1989) provide evidence that the relationship

holds across long time periods and in many countries. This observation is troublesome because it appears to deny either Irving Fisher's theory of the nominal interest rate or the theory of rational expectations. For example, Fama and Schwert (1977, p. 135) suggest that it may be due to some "as yet unidentified phenomena" or to markets that are "inefficient in impounding available information about future inflation . . ." Modigliani and Cohn (1979, p. 25) think that the puzzle is explained by money illusion.(1) A more recent explanation advanced in Fama (1981), Geske and Roll (1983), Benderly and Zwick (1985), and Kaul (1987) suggests that the inverse relationship is a spurious result of the dual effect that revisions in expected future output growth have on expected future dividends and current inflation.

We think financial markets correctly account for inflation and the puzzling results obtained by others are produced by an inappropriate application of currently published price indices to the problem of measuring asset returns.

Various published price indices differ in terms of their construction, and it is generally recognized that selection of the appropriate index largely depends on the particular problem under analysis.(2) This note shows that using currently published price indices to measure asset returns can produce anomalous results.(3) For the most part, the present technology used to compute price indices is based on the assumption that people's choice sets are restricted to present consumption goods.(4) However, this restriction is clearly violated for problems concerning measurement of asset returns where people necessarily choose between present goods and longer-lived goods.

The problem can be illustrated with a simple example. Suppose there are only three goods: money, apples, and apple trees. Apple trees last forever and yield one hundred apples per year. The price of an apple is $1.00. The observed interest rate is 5 percent and both the actual and expected rates of inflation are initially zero. In this community, an index like the Consumer Price Index measures the money cost of a basket of present apples. If the basket contains one hundred apples, the CPI in the current period is 100. People can purchase this basket each year or they can purchase an apple tree for $2,000 (= $100/.05) which yields a permanent consumption stream of one hundred apples per year. Suppose the money price of apple trees is constant while the interest rate rises to 10 percent due to a blight that reduces the current crop but does not damage the trees. The money cost of the permanent consumption stream does not change but the price of a basket of present apples rises to $200 (= $2,000 x .10). The CPI records an inflation of 100 percent. A naive estimate of the real return on assets that subtracts the rate of inflation in the CPI from the observed interest rate produces an estimated return of -90 percent (= 10 - 100) when, in fact, the real return has risen from 5 percent to 10 percent (= $200/$2,000). There are, of course, an infinite number of combinations of the money prices of apple trees and present apples that are consistent with the new level of the real interest rate. For example, suppose the price of applies is constant while the price of apple trees falls to $1,000 when the interest rate rises. In this case, the naive method of calculating the real rate produces a correct estimate of 10 percent. However, any combination of the price of applies and apple trees that contain a rise of more than 5 percent in the money price of present apples will produce the puzzling relationship between inflation and measured asset returns. …

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