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Some New Variance Bounds for Asset Prices

  • Engel, Charles

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

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  1. 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.
  2. 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.
  3. 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.
  4. Engel, Charles & West, Kenneth D., 2003. "Exchange rates and fundamentals," Working Paper Series 0248, European Central Bank.
  5. Frankel, Jeffrey A. & Stock, James H., 1987. "Regression vs. volatility tests of the efficiency of foreign exchange markets," Journal of International Money and Finance, Elsevier, vol. 6(1), pages 49-56, March.
  6. 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.
  7. 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.
  8. 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.
  9. Marsh, Terry A & Merton, Robert C, 1986. "Dividend Variability and Variance Bounds Tests for the Rationality ofStock Market Prices," American Economic Review, American Economic Association, vol. 76(3), pages 483-98, June.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
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