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Two Trees: Asset Price Dynamics Induced by Market Clearing

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  • John H. Cochrane
  • Francis A. Longstaff
  • Pedro Santa-Clara

Abstract

If stocks go up, investors may want to rebalance their portfolios. But investors cannot all rebalance. Expected returns may need to change so that the average investor is still happy to hold the market portfolio despite its changed composition. In this way, simple market clearing can give rise to complex asset market dynamics. We study this phenomenon in a very simple model. Our model has two Lucas trees.' Each tree has i.i.d.dividend growth, and the representative investor has log utility. We are able to give analytical solutions to the model. Despite this simple setup, price-dividend ratios, expected returns, and return variances vary through time. A dividend shock leads to underreaction' in some states, as expected returns rise and prices slowly adjust, and overreaction' in others. Expected returns and excess returns are predictable by price-dividend ratios in the time series and in the cross section, roughly matching value effects and return forecasting regressions. Returns generally display positive serial correlation and negative cross-serial correlation, leading to 'momentuem,' but the opposite signs are possible as well. A shock to one asset's dividend a.ects the price and expected return of the other asset, leading to substantial correlation of returns even when there is no correlation of cash flows and giving the appearance of contagion.' Market clearing allows the inverse portfolio' problem to be solved, in which the weights of the assets in the market portfolio are inverted' to solve for the parameters of the assets' return generating process.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 10116.

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Date of creation: Nov 2003
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Publication status: published as Cochrane, John, Francis A Longstaff, and Pedro Santa-Clara. "Two Trees." Review of Financial Studies 21 (2008): 247-385.
Handle: RePEc:nbr:nberwo:10116

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  1. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1429-45, November.
  2. He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 6(3), pages 593-617.
  3. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, Econometric Society, vol. 41(5), pages 867-87, September.
  4. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, Elsevier, vol. 22(1), pages 3-25, October.
  5. Tobias J. Moskowitz & Mark Grinblatt, . "Do Industries Explain Momentum?," CRSP working papers 480, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  6. Francis Longstaff & Monika Piazzesi, 2003. "Corporate Earnings and the Equity Premium," NBER Working Papers 10054, National Bureau of Economic Research, Inc.
  7. Cheng, Pao L & Grauer, Robert R, 1980. "An Alternative Test of the Capital Asset Pricing Model," American Economic Review, American Economic Association, American Economic Association, vol. 70(4), pages 660-71, September.
  8. Lo, Andrew W. (Andrew Wen-Chuan) & MacKinlay, Archie Craig, 1955-., 1989. "When are contrarian profits due to stock market overreaction?," Working papers 3008-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  9. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, Elsevier, vol. 3(4), pages 373-413, December.
  10. Fama, Eugene F & Bliss, Robert R, 1987. "The Information in Long-Maturity Forward Rates," American Economic Review, American Economic Association, American Economic Association, vol. 77(4), pages 680-92, September.
  11. Ravi Bansal & Robert F. Dittmar & Christian T. Lundblad, 2005. "Consumption, Dividends, and the Cross Section of Equity Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 60(4), pages 1639-1672, 08.
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  13. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 47(2), pages 427-65, June.
  14. Randolph B. Cohen & Christopher Polk & Tuomo Vuolteenaho, 2001. "The Value Spread," NBER Working Papers 8242, National Bureau of Economic Research, Inc.
  15. Jonathan Lewellen, 2002. "Momentum and Autocorrelation in Stock Returns," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 15(2), pages 533-564, March.
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  17. Tano Santos & Pietro Veronesi, 2001. "Labor Income and Predictable Stock Returns," NBER Working Papers 8309, National Bureau of Economic Research, Inc.
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Cited by:
  1. Theodoros Diasakos, 2008. "Comparative Statics of Asset Prices," Carlo Alberto Notebooks, Collegio Carlo Alberto 72, Collegio Carlo Alberto, revised 2011.
  2. Francis A. Longstaff, 2004. "Financial Claustrophobia: Asset Pricing in Illiquid Markets," NBER Working Papers 10411, National Bureau of Economic Research, Inc.
  3. Frieder, Laura, 2008. "Investor and price response to patterns in earnings surprises," Journal of Financial Markets, Elsevier, Elsevier, vol. 11(3), pages 259-283, August.
  4. Johnson, Timothy C., 2006. "Dynamic liquidity in endowment economies," Journal of Financial Economics, Elsevier, Elsevier, vol. 80(3), pages 531-562, June.

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