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The Valuation of Long-Dated Assets

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  • Ian Martin

Abstract

The expected time- and risk-adjusted cumulative return on any asset equals one at all horizons. Nonetheless, I show that a typical asset's realized time- and risk-adjusted cumulative return tends to zero almost surely. As a corollary, the value of a typical long-dated asset is driven by extreme events: either by good news at the level of the individual asset or by bad news at the aggregate level. In the case of the aggregate market, the fact that its Sharpe ratio is higher than its volatility suggests that bad news is the relevant consideration in practice.

Suggested Citation

  • Ian Martin, 2010. "The Valuation of Long-Dated Assets," NBER Working Papers 16219, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:16219
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    References listed on IDEAS

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    1. David Backus & Mikhail Chernov & Ian Martin, 2011. "Disasters Implied by Equity Index Options," Journal of Finance, American Finance Association, vol. 66(6), pages 1969-2012, December.
    2. 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.
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    4. 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..
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    6. William D. Nordhaus, 2011. "The Economics of Tail Events with an Application to Climate Change," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 5(2), pages 240-257, Summer.
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    Cited by:

    1. Gollier, Christian, 2012. "A theory of rational short-termism with uncertain betas," LERNA Working Papers 12.14.371, LERNA, University of Toulouse.
    2. Guerra Vallejos, Ernesto & Bobenrieth Hochfarber, Eugenio & Bobenrieth Hochfarber, Juan & Wright, Brian D., 2021. "Solving dynamic stochastic models with multiple occasionally binding constraints," Economic Modelling, Elsevier, vol. 105(C).
    3. Campbell, John Y. & Sigalov, Roman, 2022. "Portfolio choice with sustainable spending: A model of reaching for yield," Journal of Financial Economics, Elsevier, vol. 143(1), pages 188-206.
    4. Kent D. Daniel & Robert B. Litterman & Gernot Wagner, 2016. "Applying Asset Pricing Theory to Calibrate the Price of Climate Risk," NBER Working Papers 22795, National Bureau of Economic Research, Inc.
    5. Beeler, Jason & Campbell, John Y., 2012. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," Critical Finance Review, now publishers, vol. 1(1), pages 141-182, January.
    6. Ian Martin, 2013. "The Lucas Orchard," Econometrica, Econometric Society, vol. 81(1), pages 55-111, January.
    7. Dutt, Tanuj & Humphery-Jenner, Mark, 2013. "Stock return volatility, operating performance and stock returns: International evidence on drivers of the ‘low volatility’ anomaly," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 999-1017.
    8. Gollier, Christian, 2019. "Valuation of natural capital under uncertain substitutability," Journal of Environmental Economics and Management, Elsevier, vol. 94(C), pages 54-66.
    9. Chabi-Yo, Fousseni & Leisen, Dietmar P.J. & Renault, Eric, 2014. "Aggregation of preferences for skewed asset returns," Journal of Economic Theory, Elsevier, vol. 154(C), pages 453-489.
    10. ARIKAWA Yasuhiro & Vikas MEHROTRA, 2021. "Distribution of Long-run Stock Returns: Evidence from Japan and the US," Discussion papers 21084, Research Institute of Economy, Trade and Industry (RIETI).
    11. Gollier, Christian, 2012. "Asset pricing with uncertain betas: A long-term perspective," TSE Working Papers 12-354, Toulouse School of Economics (TSE).
    12. Martin L. Weitzman, 2012. "Rare Disasters, Tail-Hedged Investments, and Risk-Adjusted Discount Rates," NBER Working Papers 18496, National Bureau of Economic Research, Inc.
    13. Haim Levy, 2016. "Aging Population, Retirement, and Risk Taking," Management Science, INFORMS, vol. 62(5), pages 1415-1430, May.
    14. Koijen, Ralph S.J. & Lustig, Hanno & Van Nieuwerburgh, Stijn, 2017. "The cross-section and time series of stock and bond returns," Journal of Monetary Economics, Elsevier, vol. 88(C), pages 50-69.
    15. Weidong Tian, 2021. "Long Run Law and Entropy," Papers 2111.06238, arXiv.org.
    16. Bessembinder, Hendrik, 2018. "Do stocks outperform Treasury bills?," Journal of Financial Economics, Elsevier, vol. 129(3), pages 440-457.
    17. Anna Battauz & Marzia Donno & Alessandro Sbuelz, 2017. "Reaching nirvana with a defaultable asset?," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 31-52, November.
    18. Arpit Gupta & Stijn Van Nieuwerburgh, 2021. "Valuing Private Equity Investments Strip by Strip," Journal of Finance, American Finance Association, vol. 76(6), pages 3255-3307, December.
    19. van Binsbergen, Jules H. & Boons, Martijn & Opp, Christian C. & Tamoni, Andrea, 2023. "Dynamic asset (mis)pricing: Build-up versus resolution anomalies," Journal of Financial Economics, Elsevier, vol. 147(2), pages 406-431.
    20. Lu, Yueliang (Jacques) & Tian, Weidong, 2023. "An on-line machine learning return prediction," Pacific-Basin Finance Journal, Elsevier, vol. 79(C).
    21. Christian Gollier, 2024. "Evaluating sustainability actions under uncertainty: the role of improbable extreme scenarios," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 49(1), pages 59-74, March.

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    More about this item

    JEL classification:

    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G1 - Financial Economics - - General Financial Markets
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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