Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-03T08:20:15.896Z Has data issue: false hasContentIssue false
  • English
  • Français

Equilibrium under Uncertain Inflation: A Discrete Time Approach

Published online by Cambridge University Press:  06 April 2009

Haim Levy  and
Azriel Levy
Get access Rights & Permissions [Opens in a new window]

Abstract

Most research dealing with portfolio selection under uncertain inflation is carried out by assuming either one of the following two approximations: a linear or a quadratic approximation. In this paper, we analyze the general case, namely assume that the nominal return is the product of the real return and one plus the rate of inflation. We demonstrate that the general analysis leads to the following results that are not found in the two approximations: (1) even if we assume that nominal returns are independent of inflation, the nominal and real efficient sets will not necessarily coincide. Mean-Variance (M-V) analysis leads to a nominal efficient set, that is, a subset of the real M-V efficient set, whereas the opposite holds assuming investors maximize expected utility of real wealth. (2) Similar results are obtained when real returns are independent of inflation (the Fisher hypothesis). Assuming normality of nominal returns, we derive the CAPM in real terms or its zero beta counterpart.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 22 , Issue 3 , September 1987 , pp. 285 - 297
Copyright
Copyright © School of Business Administration, University of Washington 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Black, F. “Capital Market Equilibrium with Restricted Borrowing.” Journal of Business, 45 (07 1972), 444–445.CrossRefGoogle Scholar
[2]Bodie, Z. “Common Stocks as a Hedge against Inflation.” Journal of Finance, 31 (05 1976), 459–470.CrossRefGoogle Scholar
[3]Brennan, M. “Capital Market Equilibrium with Divergent Borrowing and Lending Rates.” Journal of Financial and Quantitative Analysis, 6 (12. 1971), 1197–1205.CrossRefGoogle Scholar
[4]Chamberlain, G. “A Characterization of the Distributions that Imply Mean-Variance Utility Functions.” Journal of Economic Theory, 29 (02 1983), 185–201.Google Scholar
[5]Chen, A. H. and Boness, J. A.. “Effects of Uncertain Inflation on the Investment and Financing Decisions of the Firm.” Journal of Finance, 30 (05 1975), 469–485.CrossRefGoogle Scholar
[6]Fama, E. F.andSewert, G. W.. “Asset Returns and Inflation.” Journal of Financial Economics, 5 (11 1977), 115–146.Google Scholar
[7]Friend, I.; Landskroner, Y.; and Losq, E.. “The Demand for the Risky Assets under Uncertain Inflation.” Journal of Finance, 5 (12 1976), 1287–1297.Google Scholar
[8]Hanoch, G. and Levy, H.. “The Efficiency Analysis of Choices Involving Risk.” Review of Economic Studies, 36 (07 1969), 335–346.Google Scholar
[9]Levy, H. and Levy, A.. “Ordering Uncertain Options under Inflation.” Journal of Finance, 39 (09 1984), 1223–1229.Google Scholar
[10]Levy, H., and Markowitz, H. M.. “Approximating Expected Utility by a Function of Mean and Variance.” American Economic Review, 69 (06 1979), 308–317.Google Scholar
[11]Lintner, J. “Inflation and Common Stock Prices in a Cyclical Context.” National Bureau of Economic Research Inc., 53 (09 1973), 23–36.Google Scholar
[12]Lintner, J. “Inflation and Security Returns.” Journal of Finance, 30 (05 1975), 259–280.Google Scholar
[13]Long, J. “Stock Prices, Inflation and the Term Structure of Interest Rates.” Journal of Financial Economics, 1 (07 1974), 131–170.Google Scholar
[14]Manaster, S. “Real and Nominal Efficient Sets.” Journal of Finance, 34 (03 1979), 93–102.CrossRefGoogle Scholar
[15]Merton, R. C. “An Analytic Derivation of the Efficient Portfolio Frontier.” Journalof Financial and Quantitative Analysis, 7 (09 1972), 1851–1872.Google Scholar
[16]Mood, A.; Graybill, F.; and Boes, D.. Introduction to the Theory of Statistics, 3rd ed.New York: McGraw Hill (1974).Google Scholar
[17]Roll, R. “Assets, Money and Commodity Price Inflation under Uncertainty: Demand Theory.” Journal of Money Credit and Banking, 5 (09 1973), 903–923.Google Scholar
[18]Roll, R. “A Critique of the Asset Pricing Theory's Tests.” Journal of Financial Economics, 4 (03 1977), 129–176.CrossRefGoogle Scholar
[19]Ross, S. “Mutual Fund Separation in Financial Theory—the Separating Distributions.” Journal of Economic Theory, 17 (04 1978), 254–286.Google Scholar
[20]Sercu, P. “A Note on Real and Nominal Efficient Sets.” Journal of Finance, 36 (06 1981), 721–737.Google Scholar
[21]Sharpe, W. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance, 19 (09 1964), 425–442.Google Scholar
[22]Solnik, B. “Inflation and Optimal Portfolio Choices.” Journal of Financial and Quantitative Analysis, 13 (12 1978), 903–925.Google Scholar