IDEAS home Printed from
   My bibliography  Save this article

Hedging downside risk with futures contracts


  • Donald Lien
  • Yiu Kuen Tse


This paper considers a futures hedge strategy that minimizes the lower partial moments; such a strategy minimizes the downside risk and is consistent with the expected utility hypothesis. Two statistical methods are adopted to estimate the optimal hedge ratios: the empirical distribution function method and the kernel density estimation method. Both methods are applied to the Nikkei Stock Average (NSA) spot and futures markets. It is found that, for a hedger who is willing to absorb small losses but otherwise extremely cautious about large losses, the optimal hedge strategy that minimizes the lower partial moments may be sharply different from the minimum variance hedge strategy. If a hedger cares for downside-only risk, then the conventional minimum variance hedge strategy is inappropriate. The methods presented in this paper will be useful in these scenarios.

Suggested Citation

  • Donald Lien & Yiu Kuen Tse, 2000. "Hedging downside risk with futures contracts," Applied Financial Economics, Taylor & Francis Journals, vol. 10(2), pages 163-170.
  • Handle: RePEc:taf:apfiec:v:10:y:2000:i:2:p:163-170 DOI: 10.1080/096031000331798

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. repec:fth:jonhop:390 is not listed on IDEAS
    2. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-1248, September.
    3. Carroll Christopher Dixon, 2001. "Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(1), pages 1-38, April.
    4. Binder, M. & Pesaran, M. H. & Samiei, S. H., 1998. "Analytical and Numerical Solution of Finite-horizon Nonlinear Rational Expectations Models," Cambridge Working Papers in Economics 9808, Faculty of Economics, University of Cambridge.
    5. Neave, Edwin H., 1971. "Multiperiod consumption-investment decisions and risk preference," Journal of Economic Theory, Elsevier, vol. 3(1), pages 40-53, March.
    6. Stephen P. Zeldes, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, Oxford University Press, vol. 104(2), pages 275-298.
    7. Frederick van der Ploeg, 1993. "A Closed-form Solution for a Model of Precautionary Saving," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 385-395.
    8. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    9. Philippe Weil, 1993. "Precautionary Savings and the Permanent Income Hypothesis," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 367-383.
    10. Gabriel Talmain, 1994. "Exact and Approximate Solutions to the Problem of Precautionary Savings," Discussion Papers 94-04, University at Albany, SUNY, Department of Economics.
    11. Miles, David, 1997. "A Household Level Study of the Determinants of Incomes and Consumption," Economic Journal, Royal Economic Society, vol. 107(440), pages 1-25, January.
    12. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-247, April.
    13. Siegel, Jeremy J., 1992. "The real rate of interest from 1800-1990 : A study of the U.S. and the U.K," Journal of Monetary Economics, Elsevier, vol. 29(2), pages 227-252, April.
    14. Caballero, Ricardo J, 1991. "Earnings Uncertainty and Aggregate Wealth Accumulation," American Economic Review, American Economic Association, vol. 81(4), pages 859-871, September.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. repec:eee:eneeco:v:63:y:2017:i:c:p:174-184 is not listed on IDEAS
    2. Donald Lien & Mei Zhang, 2008. "A Survey of Emerging Derivatives Markets," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 44(2), pages 39-69, March.
    3. Chen, Sheng-Syan & Lee, Cheng-few & Shrestha, Keshab, 2003. "Futures hedge ratios: a review," The Quarterly Review of Economics and Finance, Elsevier, vol. 43(3), pages 433-465.
    4. Lien, Donald & Tse, Yiu Kuen, 2001. "Hedging downside risk: futures vs. options," International Review of Economics & Finance, Elsevier, vol. 10(2), pages 159-169.
    5. Fu, Junhui, 2014. "Multi-objective hedging model with the third central moment and the capital budget," Economic Modelling, Elsevier, vol. 36(C), pages 213-219.
    6. Cifarelli, Giulio & Paladino, Giovanna, 2011. "Hedging vs. speculative pressures on commodity futures returns," MPRA Paper 28229, University Library of Munich, Germany.
    7. John Cotter & Jim Hanly, 2012. "Hedging effectiveness under conditions of asymmetry," The European Journal of Finance, Taylor & Francis Journals, vol. 18(2), pages 135-147, February.
    8. Liu, Xiaochun & Jacobsen, Brian, 2011. "The Dynamic International Optimal Hedge Ratio," MPRA Paper 35260, University Library of Munich, Germany.
    9. Cifarelli, Giulio & Paladino, Giovanna, 2015. "A dynamic model of hedging and speculation in the commodity futures markets," Journal of Financial Markets, Elsevier, vol. 25(C), pages 1-15.
    10. repec:spr:empeco:v:53:y:2017:i:3:d:10.1007_s00181-016-1146-9 is not listed on IDEAS
    11. Donald Lien & Mei Zhang, 2008. "A Survey of Emerging Derivatives Markets," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 44(2), pages 39-69, March.
    12. Jonathan Dark, 2005. "A Critique of Minimum Variance Hedging," Accounting Research Journal, Emerald Group Publishing, vol. 18(1), pages 40-49, June.
    13. Chen, Sheng-Syan & Lee, Cheng-few & Shrestha, Keshab, 2008. "Do the pure martingale and joint normality hypotheses hold for futures contracts: Implications for the optimal hedge ratios," The Quarterly Review of Economics and Finance, Elsevier, vol. 48(1), pages 153-174, February.
    14. Ahmedov, Zafarbek & Woodard, Joshua D., 2012. "Do RIN Mandates and Blender's Tax Credit Affect Blenders' Hedging Strategies?," 2012 Annual Meeting, August 12-14, 2012, Seattle, Washington 124980, Agricultural and Applied Economics Association.
    15. Dinica, Mihai Cristian & Armeanu, Daniel, 2014. "The Optimal Hedging Ratio for Non-Ferrous Metals," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 105-122, March.
    16. David Shaffer & Andrea DeMaskey, 2005. "Currency Hedging Using the Mean-Gini Framework," Review of Quantitative Finance and Accounting, Springer, vol. 25(2), pages 125-137, September.
    17. Mattos, Fabio & Garcia, Philip & Nelson, Carl, 2008. "Relaxing standard hedging assumptions in the presence of downside risk," The Quarterly Review of Economics and Finance, Elsevier, vol. 48(1), pages 78-93, February.
    18. Hilal, Sawsan & Poon, Ser-Huang & Tawn, Jonathan, 2011. "Hedging the black swan: Conditional heteroskedasticity and tail dependence in S&P500 and VIX," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2374-2387, September.
    19. Demirer, Riza & Lien, Donald, 2003. "Downside risk for short and long hedgers," International Review of Economics & Finance, Elsevier, vol. 12(1), pages 25-44.
    20. Chevallier, Julien & Ielpo, Florian, 2017. "Investigating the leverage effect in commodity markets with a recursive estimation approach," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 763-778.
    21. repec:eee:eneeco:v:66:y:2017:i:c:p:493-507 is not listed on IDEAS

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:apfiec:v:10:y:2000:i:2:p:163-170. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.