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Some New Variance Bounds for Asset Prices

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  • Engel, Charles

Abstract

When equity prices are determined as the discounted sum of current and expected future dividends, Shiller (1981) and LeRoy and Porter (1981) derived a relationship between the variance of the price of equities, p[subscript t] and the variance of the ex post realized discounted sum of current and future dividends: p[superscript * subscript t]: Var(p[superscript * subscript t]) >= Var(p[subscript t]). The literature has long since recognized that this variance bound is valid only when dividends follow a stationary process. Others, notably West (1988), derive variance bounds that apply when dividends are nonstationary. West shows that the variance in innovations in p[subscript t] must be less than the variance of innovations in a forecast of the discounted sum of current and future dividends constructed by the econometrician, p-hat[subscript t]. Here we derive a new variance bound when dividends are stationary or have a unit root, that sheds light on the discussion in the 1980s of the Shiller variance bound: Var(p[subscript t] - p[subscript t - 1]) >= Var(p[superscript * subscript t] - p[superscript * subscript t - 1])! We also derive a variance bound related to the West bound: Var(p-hat[subscript t] - p-hat[subscript t - 1]) >= Var(p[subscript t] - p[subscript t - 1]).

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Bibliographic Info

Article provided by Blackwell Publishing in its journal Journal of Money, Credit and Banking.

Volume (Year): 37 (2005)
Issue (Month): 5 (October)
Pages: 949-55

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Handle: RePEc:mcb:jmoncb:v:37:y:2005:i:5:p:949-55

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Web page: http://www.blackwellpublishing.com/journal.asp?ref=0022-2879

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  1. Flavin, Marjorie A, 1983. "Excess Volatility in the Financial Markets: A Reassessment of the Empirical Evidence," Journal of Political Economy, University of Chicago Press, vol. 91(6), pages 929-56, December.
  2. Mankiw, N Gregory & Romer, David & Shapiro, Matthew D, 1985. " An Unbiased Reexamination of Stock Market Volatility," Journal of Finance, American Finance Association, vol. 40(3), pages 677-87, July.
  3. Charles Engel & Kenneth D. West, 2005. "Exchange Rates and Fundamentals," Journal of Political Economy, University of Chicago Press, vol. 113(3), pages 485-517, June.
  4. Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
  5. Marsh, Terry A. & Merton, Robert C., 1984. "Dividend variability and variance bounds tests for the rationality of stock market prices," Working papers 1584-84., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  6. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-36, June.
  7. Kleidon, Allan W, 1986. "Variance Bounds Tests and Stock Price Valuation Models," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 953-1001, October.
  8. Gilles, Christian & LeRoy, Stephen F, 1991. "Econometric Aspects of the Variance-Bounds Tests: A Survey," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 753-91.
  9. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-74, May.
  10. Jeffrey A. Frankel and James H. Stock., 1987. "Regression vs. Volatility Tests of the Efficiency of Foreign Exchange Markets," Economics Working Papers 8726, University of California at Berkeley.
  11. Shiller, Robert J, 1988. "The Probability of Gross Violations of a Present Value Variance Inequality," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 1089-92, October.
  12. Charles Engel & Kenneth D. West, 2004. "Accounting for Exchange-Rate Variability in Present-Value Models When the Discount Factor Is Near 1," American Economic Review, American Economic Association, vol. 94(2), pages 119-125, May.
  13. Kleidon, Allan W, 1988. "The Probability of Gross Violations of a Present Value Variance Inequality: Reply," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 1093-96, October.
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