IDEAS home Printed from
   My bibliography  Save this paper

Have your cake and eat it too: increasing returns while lowering large risks!


  • J. V. Andersen

    (NORDITA, Denmark)

  • D. Sornette

    (CNRS/Univ. Nice France and UCLA)


Based on a faithful representation of the heavy tail multivariate distribution of asset returns introduced previously (Sornette et al., 1998, 1999) that we extend to the case of asymmetric return distributions, we generalize the return-risk efficient frontier concept to incorporate the dimensions of large risks embedded in the tail of the asset distributions. We demonstrate that it is often possible to increase the portfolio return while decreasing the large risks as quantified by the fourth and higher order cumulants. Exact theoretical formulas are validated by empirical tests.

Suggested Citation

  • J. V. Andersen & D. Sornette, 1999. "Have your cake and eat it too: increasing returns while lowering large risks!," Papers cond-mat/9907217,
  • Handle: RePEc:arx:papers:cond-mat/9907217

    Download full text from publisher

    File URL:
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    1. Sornette, Didier, 1998. "Large deviations and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 251-283.
    2. Didier Sornette, 1998. "Large deviations and portfolio optimization," Papers cond-mat/9802059,, revised Jun 1998.
    3. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(2), pages 139-140, July.
    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. Alessio Sancetta & Steve E. Satchell, 2007. "Changing Correlation and Equity Portfolio Diversification Failure for Linear Factor Models during Market Declines," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(3), pages 227-242.
    2. Sancetta, A., 2005. "Copula Based Monte Carlo Integration in Financial Problems," Cambridge Working Papers in Economics 0506, Faculty of Economics, University of Cambridge.
    3. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Y. Malevergne & D. Sornette, 2001. "General framework for a portfolio theory with non-Gaussian risks and non-linear correlations," Papers cond-mat/0103020,
    2. Y. Malevergne & D. Sornette, 2003. "VaR-Efficient Portfolios for a Class of Super- and Sub-Exponentially Decaying Assets Return Distributions," Papers physics/0301009,
    3. Huyen Pham, 2007. "Some applications and methods of large deviations in finance and insurance," Papers math/0702473,, revised Feb 2007.
    4. Youngha Cho & Soosung Hwang & Steve Satchell, 2012. "The Optimal Mortgage Loan Portfolio in UK Regional Residential Real Estate," The Journal of Real Estate Finance and Economics, Springer, vol. 45(3), pages 645-677, October.
    5. Stutzer, Michael, 2013. "Optimal hedging via large deviation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3177-3182.
    6. Zhang, Qunzhi & Sornette, Didier & Balcilar, Mehmet & Gupta, Rangan & Ozdemir, Zeynel Abidin & Yetkiner, Hakan, 2016. "LPPLS bubble indicators over two centuries of the S&P 500 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 126-139.
    7. Stutzer, Michael, 2020. "Persistence of averages in financial Markov Switching models: A large deviations approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    8. Sitabhra Sinha, 2006. "The Apparent Madness of Crowds: Irrational collective behavior emerging from interactions among rational agents," Papers physics/0606078,
    9. Provash Mali & Amitabha Mukhopadhyay, 2015. "Multifractal characterization of gold market: a multifractal detrended fluctuation analysis," Papers 1506.08847,
    10. Li, Ming-Xia & Jiang, Zhi-Qiang & Xie, Wen-Jie & Xiong, Xiong & Zhang, Wei & Zhou, Wei-Xing, 2015. "Unveiling correlations between financial variables and topological metrics of trading networks: Evidence from a stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 575-584.
    11. Mahua Barari & Saibal Mitra, 2008. "Power Law Versus Exponential Law in Characterizing Stock Market Returns," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 36(3), pages 377-379, September.
    12. Carvalho, Rui & Penn, Alan, 2004. "Scaling and universality in the micro-structure of urban space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 539-547.
    13. Taisei Kaizoji, 2003. "Speculative bubbles and fat tail phenomena in a heterogeneous agent model," Papers nlin/0312040,
    14. Albrecht Irle & Jonas Kauschke & Thomas Lux & Mishael Milaković, 2011. "Switching Rates And The Asymptotic Behavior Of Herding Models," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 359-376.
    15. Aoki, Masanao, 2002. "Open models of share markets with two dominant types of participants," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 199-216, October.
    16. Lux, Thomas & Sornette, Didier, 2002. "On Rational Bubbles and Fat Tails," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(3), pages 589-610, August.
    17. Stanley, H.Eugene, 2003. "Statistical physics and economic fluctuations: do outliers exist?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(1), pages 279-292.
    18. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Pawe{l} O'swic{e}cimka & Marek Stanuszek, 2018. "Multifractal cross-correlations between the World Oil and other Financial Markets in 2012-2017," Papers 1812.08548,, revised Jun 2019.
    19. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    20. Wei-Xing Zhou, 2012. "Universal price impact functions of individual trades in an order-driven market," Quantitative Finance, Taylor & Francis Journals, vol. 12(8), pages 1253-1263, June.

    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:arx:papers:cond-mat/9907217. 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: (arXiv administrators). 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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.