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The Term Structure of the Risk-Return Tradeoff

  • John Y. Campbell
  • Luis Viceira

Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. In this paper we propose an empirical model that is able to capture these complex dynamics, yet is simple to apply in practice, and we explore its implications for asset allocation. Changes in investment opportunities can alter the risk-return tradeoff of bonds, stocks, and cash across investment horizons, thus creating a ``term structure of the risk-return tradeoff.'' We show how to extract this term structure from our parsimonious model of return dynamics, and illustrate our approach using data from the U.S. stock and bond markets. We find that asset return predictability has important effects on the variance and correlation structure of returns on stocks, bonds and T-bills across investment horizons.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 11119.

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Date of creation: Feb 2005
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Publication status: published as Campbell, John Y. and Luis Viceira. "The Term Structure of the Risk-Return Tradeoff.” Financial Analysts Journal 61 (January/February 2005): 34-44.
Handle: RePEc:nbr:nberwo:11119
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  1. Chan, Yeung Lewis & Viceira, Luis & Campbell, John, 2003. "A Multivariate Model of Strategic Asset Allocation," Scholarly Articles 3163263, Harvard University Department of Economics.
  2. John Y. Campbell & Motohiro Yogo, 2003. "Efficient Tests of Stock Return Predictability," NBER Working Papers 10026, National Bureau of Economic Research, Inc.
  3. Campbell, John Y., 1987. "Stock returns and the term structure," Journal of Financial Economics, Elsevier, vol. 18(2), pages 373-399, June.
  4. Roberto Rigobon & Brian P. Sack, 2003. "Spillovers across U.S. financial markets," Finance and Economics Discussion Series 2003-13, Board of Governors of the Federal Reserve System (U.S.).
  5. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Robert F. Stambaugh, 1999. "Predictive Regressions," NBER Technical Working Papers 0240, National Bureau of Economic Research, Inc.
  7. Fama, Eugene F. & French, Kenneth R., 1988. "Dividend yields and expected stock returns," Journal of Financial Economics, Elsevier, vol. 22(1), pages 3-25, October.
  8. Campbell, John & Viceira, Luis, 1999. "Consumption and Portfolio Decisions When Expected Returns are Time Varying," Scholarly Articles 3163266, Harvard University Department of Economics.
  9. Yacine Aït-Sahalia, 2001. "Variable Selection for Portfolio Choice," Journal of Finance, American Finance Association, vol. 56(4), pages 1297-1351, 08.
  10. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  11. Samuelson, Paul A, 1969. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 239-46, August.
  12. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
  13. Bekaert, Geert & Hodrick, Robert J. & Marshall, David A., 1997. "On biases in tests of the expectations hypothesis of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 44(3), pages 309-348, June.
  14. John Y. Campbell, 1993. "Why Long Horizons: A Study of Power Against Persistent Alternatives," NBER Technical Working Papers 0142, National Bureau of Economic Research, Inc.
  15. John Y. Campbell & Tuomo Vuolteenaho, 2004. "Inflation Illusion and Stock Prices," NBER Working Papers 10263, National Bureau of Economic Research, Inc.
  16. George Chacko & Luis M. Viceira, 1999. "Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets," NBER Working Papers 7377, National Bureau of Economic Research, Inc.
  17. Goetzmann, William Nelson & Jorion, Philippe, 1993. " Testing the Predictive Power of Dividend Yields," Journal of Finance, American Finance Association, vol. 48(2), pages 663-79, June.
  18. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
  19. Campbell, John, 1991. "A Variance Decomposition for Stock Returns," Scholarly Articles 3207695, Harvard University Department of Economics.
  20. Nelson, Charles R & Kim, Myung J, 1993. " Predictable Stock Returns: The Role of Small Sample Bias," Journal of Finance, American Finance Association, vol. 48(2), pages 641-61, June.
  21. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan Storud, 2004. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," NBER Working Papers 10934, National Bureau of Economic Research, Inc.
  22. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
  23. Brennan, Michael J. & Schwartz, Eduardo S. & Lagnado, Ronald, 1997. "Strategic asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1377-1403, June.
  24. repec:cup:etheor:v:10:y:1994:i:3-4:p:672-700 is not listed on IDEAS
  25. Graham Elliott & James H. Stock, 1992. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," NBER Technical Working Papers 0122, National Bureau of Economic Research, Inc.
  26. Harvey, Campbell R, 1991. " The World Price of Covariance Risk," Journal of Finance, American Finance Association, vol. 46(1), pages 111-57, March.
  27. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  28. Harvey, Campbell R., 1989. "Time-varying conditional covariances in tests of asset pricing models," Journal of Financial Economics, Elsevier, vol. 24(2), pages 289-317.
  29. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, 02.
  30. Hodrick, Robert J, 1992. "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 357-86.
  31. Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
  32. Robert J. Shiller & John Y. Campbell & Kermit L. Schoenholtz, 1983. "Forward Rates and Future Policy: Interpreting the Term Structure of Interest Rates," Cowles Foundation Discussion Papers 667, Cowles Foundation for Research in Economics, Yale University.
  33. Fama, Eugene F., 1984. "The information in the term structure," Journal of Financial Economics, Elsevier, vol. 13(4), pages 509-528, December.
  34. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942, May.
  35. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
  36. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
  37. Avramov, Doron, 2002. "Stock return predictability and model uncertainty," Journal of Financial Economics, Elsevier, vol. 64(3), pages 423-458, June.
  38. Fama, Eugene F. & Schwert, G. William, 1977. "Asset returns and inflation," Journal of Financial Economics, Elsevier, vol. 5(2), pages 115-146, November.
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