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Stocks versus bonds for the long run when a riskless asset is available

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  • Levy, Haim
  • Levy, Moshe

Abstract

Does the famous idiom “stocks for the long run” have an empirical or a theoretical foundation? Bali et al. (2009) show that the cumulative return distributions of stocks and bonds intersect for all investment horizons, implying that stocks do not dominate bonds, regardless of the horizon. This paper shows that adding the riskless asset to the analysis yields a clear-cut dominance of stocks over bonds: for any combination of bonds with the riskless asset, one can find a combination of stocks with the riskless asset that dominates it. This dominance holds for all non-decreasing preferences as long as the investment horizon is 3 years or longer. However, this strong result does not imply that arbitrage opportunities exist.

Suggested Citation

  • Levy, Haim & Levy, Moshe, 2021. "Stocks versus bonds for the long run when a riskless asset is available," Journal of Banking & Finance, Elsevier, vol. 133(C).
  • Handle: RePEc:eee:jbfina:v:133:y:2021:i:c:s0378426621002314
    DOI: 10.1016/j.jbankfin.2021.106275
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    as
    1. Campanale, Claudio & Fugazza, Carolina & Gomes, Francisco, 2015. "Life-cycle portfolio choice with liquid and illiquid financial assets," Journal of Monetary Economics, Elsevier, vol. 71(C), pages 67-83.
    2. Luca Benzoni & Pierre Collin‐Dufresne & Robert S. Goldstein, 2007. "Portfolio Choice over the Life‐Cycle when the Stock and Labor Markets Are Cointegrated," Journal of Finance, American Finance Association, vol. 62(5), pages 2123-2167, October.
    3. Jagannathan, Ravi & Wang, Zhenyu, 1996. "The Conditional CAPM and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 51(1), pages 3-53, March.
    4. Doron Avramov & Scott Cederburg & Katarína Lučivjanská, 2018. "Are Stocks Riskier over the Long Run? Taking Cues from Economic Theory," Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 556-594.
    5. Sharon M. Oster & Daniel S. Hamermesh, 1998. "Aging And Productivity Among Economists," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 154-156, February.
    6. Andrew Ang & Geert Bekaert, 2007. "Stock Return Predictability: Is it There?," Review of Financial Studies, Society for Financial Studies, vol. 20(3), pages 651-707.
    7. Merton, Robert C. & Samuelson, Paul A., 1974. "Fallacy of the log-normal approximation to optimal portfolio decision-making over many periods," Journal of Financial Economics, Elsevier, vol. 1(1), pages 67-94, May.
    8. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    9. Lieven Baele & Geert Bekaert & Koen Inghelbrecht & Min Wei, 2020. "Flights to Safety," The Review of Financial Studies, Society for Financial Studies, vol. 33(2), pages 689-746.
    10. Bodie, Zvi & Merton, Robert C. & Samuelson, William F., 1992. "Labor supply flexibility and portfolio choice in a life cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 427-449.
    11. Ľuboš Pástor & Robert F. Stambaugh, 2012. "Are Stocks Really Less Volatile in the Long Run?," Journal of Finance, American Finance Association, vol. 67(2), pages 431-478, April.
    12. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    13. Levy, Haim, 1973. "Stochastic Dominance Among Log-Normal Prospects," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 601-614, October.
    14. Dammon, Robert M & Spatt, Chester S & Zhang, Harold H, 2001. "Optimal Consumption and Investment with Capital Gains Taxes," The Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 583-616.
    15. Levy, Haim & Levy, Moshe, 2021. "The cost of diversification over time, and a simple way to improve target-date funds," Journal of Banking & Finance, Elsevier, vol. 122(C).
    16. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    17. Fama, Eugene F. & Schwert, G. William, 1977. "Human capital and capital market equilibrium," Journal of Financial Economics, Elsevier, vol. 4(1), pages 95-125, January.
    18. Robert J. Barro, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(3), pages 823-866.
    19. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    20. Gollier, Christian, 2002. "Time diversification, liquidity constraints, and decreasing aversion to risk on wealth," Journal of Monetary Economics, Elsevier, vol. 49(7), pages 1439-1459, October.
    21. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    22. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    23. Bali, Turan G. & Demirtas, K. Ozgur & Levy, Haim & Wolf, Avner, 2009. "Bonds versus stocks: Investors' age and risk taking," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 817-830, September.
    24. Gomes, Francisco & Fugazza, Carolina & Campanale, Claudio, 2015. "Life-Cycle Portfolio choice with Liquid and Illiquid Assets," CEPR Discussion Papers 10369, C.E.P.R. Discussion Papers.
    25. Harry M. Markowitz, 2011. "Investment for the Long Run: New Evidence for an Old Rule," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 35, pages 495-508, World Scientific Publishing Co. Pte. Ltd..
    26. Arditti, Fred D & Levy, Haim, 1975. "Portfolio Efficiency Analysis in Three Moments: The Multiperiod Case," Journal of Finance, American Finance Association, vol. 30(3), pages 797-809, June.
    27. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    28. McDowell, John M, 1982. "Obsolescence of Knowledge and Career Publication Profiles: Some Evidence of Differences among Fields in Costs of Interrupted Careers," American Economic Review, American Economic Association, vol. 72(4), pages 752-768, September.
    29. John W. Payne & Dan J. Laughhunn & Roy Crum, 1980. "Translation of Gambles and Aspiration Level Effects in Risky Choice Behavior," Management Science, INFORMS, vol. 26(10), pages 1039-1060, October.
    30. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 735-765.
    31. Lynch, Anthony W. & Tan, Sinan, 2011. "Labor income dynamics at business-cycle frequencies: Implications for portfolio choice," Journal of Financial Economics, Elsevier, vol. 101(2), pages 333-359, August.
    32. Goetzmann, William N. & Ibbotson, Roger G. & Peng, Liang, 2001. "A new historical database for the NYSE 1815 to 1925: Performance and predictability," Journal of Financial Markets, Elsevier, vol. 4(1), pages 1-32, January.
    33. Levin, Sharon G & Stephan, Paula E, 1991. "Research Productivity over the Life Cycle: Evidence for Academic Scientists," American Economic Review, American Economic Association, vol. 81(1), pages 114-132, March.
    34. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    35. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
    36. Pierre-Olivier Gourinchas & Jonathan A. Parker, 2002. "Consumption Over the Life Cycle," Econometrica, Econometric Society, vol. 70(1), pages 47-89, January.
    37. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    38. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    39. Lieven Baele, 2010. "The Determinants of Stock and Bond Return Comovements," The Review of Financial Studies, Society for Financial Studies, vol. 23(6), pages 2374-2428, June.
    40. Rietz, Thomas A., 1988. "The equity risk premium a solution," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 117-131, July.
    41. Levy, Moshe, 2009. "Almost Stochastic Dominance and stocks for the long run," European Journal of Operational Research, Elsevier, vol. 194(1), pages 250-257, April.
    42. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    43. Robert J. Barro, 2009. "Rare Disasters, Asset Prices, and Welfare Costs," American Economic Review, American Economic Association, vol. 99(1), pages 243-264, March.
    44. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
    45. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    46. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    47. Levy, Haim & Kroll, Yoram, 1978. "Ordering Uncertain Options with Borrowing and Lending," Journal of Finance, American Finance Association, vol. 33(2), pages 553-574, May.
    48. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    49. Yoram Ben-Porath, 1967. "The Production of Human Capital and the Life Cycle of Earnings," Journal of Political Economy, University of Chicago Press, vol. 75, pages 352-352.
    50. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
    51. Bessembinder, Hendrik, 2018. "Do stocks outperform Treasury bills?," Journal of Financial Economics, Elsevier, vol. 129(3), pages 440-457.
    52. Bodie, Zvi & Detemple, Jerome B. & Otruba, Susanne & Walter, Stephan, 2004. "Optimal consumption-portfolio choices and retirement planning," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1115-1148, March.
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    More about this item

    Keywords

    Stocks versus bonds; Investment horizon; First-degree stochastic dominance (FSD); First–degree stochastic dominance with a riskless asset (FSDR);
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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