Financial Markets and Portfolio Management

, Volume 31, Issue 1, pp 27–47 | Cite as

How does the underlying affect the risk-return profiles of structured products?



Regulators of some of the major markets have adopted value at risk (VaR) as the risk measure for structured products. Under the mean-VaR framework, this paper discusses the impact of the underlying’s distribution on structured products. We expand the expected return and the VaR of a structured product with its underlying’s moments (mean, variance, skewness, and kurtosis), so that the impact of the moments can be investigated simultaneously. Results are tested by Monte Carlo and historical simulations. The findings show that for the majority of structured products, underlyings with large positive skewness are preferred. The preferences for the variance and the kurtosis of the underlying are both ambiguous.


Value at risk Structured products Skewness Kurtosis 

JEL Classification

G11 C02 



The author thanks Markus Schmid (the editor), the anonymous referee, Marc Oliver Rieger, Vincent Xiang (discussant), Mohammad M. Mousavi (discussant), conference participants at the 2nd International Conference on Future and Other Derivative Markets (Beijing), the 1st Paris Financial Management Conference, and the 6th IFABS Conference (Lisbon), as well as seminar participants at Xiamen University.


  1. Alexander, G.J., Baptista, A.M.: Economic implications of using a mean-var model for portfolio selection: a comparison with mean-variance analysis. J. Econ. Dyn. Control 26(7–8), 1159–1193 (2002)CrossRefGoogle Scholar
  2. Basak, S., Shapiro, A.: Value-at-risk-based risk management: optimal policies and asset prices. Rev. Financ. Stud. 14(2), 371–405 (2001)CrossRefGoogle Scholar
  3. Benati, S.: The optimal portfolio problem with coherent risk measure constraints. Eur. J. Oper. Res. 150(3), 572–584 (2003)CrossRefGoogle Scholar
  4. Blümke, A.: How to Invest in Structured Products. Wiley, Amsterdam (2009)Google Scholar
  5. Cao, J., Rieger, M.O.: Risk classes for structured products: mathematical aspects and their implications on behavioral investors. Ann. Financ. 9(2), 167–183 (2013)CrossRefGoogle Scholar
  6. Célérier, C., Vallée, B.: What Drives Financial Complexity? A Look into the Retail Market for Structured Products, Research Paper. HEC, Paris (2013)Google Scholar
  7. CESR: CESR’s Guidelines on the Methodology for the Calculation of the Synthetic Risk and Reward Indicator in the Key Investor Information Document. Committee of European Securities Regulators. CESR/10-673 (2010)Google Scholar
  8. Chang, B.Y., Christoffersen, P., Jacobs, K.: Market skewness risk and the cross section of stock returns. J. Financ. Econ. 107(1), 46–68 (2013)CrossRefGoogle Scholar
  9. Consigli, G.: Tail estimation and mean-var portfolio selection in markets subject to financial instability. J. Bank. Financ. 26(7), 1355–1382 (2002)CrossRefGoogle Scholar
  10. Cornish, E.A., Fisher, R.A.: Moments and cumulants in the specification of distribution. Revue de l’Institut International de Statistique 5, 307–322 (1937)CrossRefGoogle Scholar
  11. Cui, X., Zhu, S., Sun, X., Li, D.: Nonlinear portfolio selection using approximate parametric value-at-risk. J. Bank. Financ. 37(6), 2124–2139 (2013)CrossRefGoogle Scholar
  12. El-Jahel, L., Perraudin, W., Sellin, P.: Value at risk for derivatives. J. Deriv. 6(3), 7–26 (1999)CrossRefGoogle Scholar
  13. European Commission: Commission directive 2010/43/eu. Off. J. Eur. Union L. 176, 42–61 (2010a)Google Scholar
  14. European Commission: Commission regulation (eu) no 583/2010. Off. J. Eur. Union L. 176, 1–15 (2010b)Google Scholar
  15. European Structured Investment Products Association: Eusipa derivative map. Published: May. 2012, Accessed 15 Jan 2014
  16. Fisher, R.A., Cornish, E.A.: The percentile points of distributions having known cumulants. Technometrics 2(2), 209–225 (1960)CrossRefGoogle Scholar
  17. Gabrielsen, A., Zagaglia, P., Kirchner, A., Liu, Z.: Forecasting value-at-risk with time-varying variance, skewness and kurtosis in an exponential weighted moving average framework. Working Paper, Dipartimento Scienze Economiche, Universita’ di Bologna (2012)Google Scholar
  18. Hill, G.W., Davis, A.W.: Generalized asymptotic expansions of cornish-fisher type. Ann. Math. Stat. 39(4), 1264–1273 (1968)CrossRefGoogle Scholar
  19. Kraus, A., Litzenberger, R.H.: Skewness preference and the valuation of risk assets. J. Financ. 31(4), 1085–1100 (1976)Google Scholar
  20. Mitton, T., Vorkink, K.: Equilibrium underdiversification and the preference for skewness. Rev. Financ. Stud. 20(4), 1255–1288 (2007)CrossRefGoogle Scholar
  21. Rieger, M.O.: Co-monotonicity of optimal investments and the design of structured financial products. Financ. Stoch. 15(1), 27–55 (2011)CrossRefGoogle Scholar
  22. Santini, L.: Citic pacific sees $2 billion bad-bet hit. Wall Str. J., Published: 22 Oct. 2008, Accessed: 11 June 2013
  23. Scott, R.C., Horvath, P.A.: On the direction of preference for moments of higher order than the variance. J. Financ. 15(4), 915–919 (1980)CrossRefGoogle Scholar
  24. Swiss Structured Products Association: Information about the SSPA risk figure., Published: 31 Jan. 2013, Accessed: 22 Jan 2014
  25. Tsao, C.: Portfolio selection based on the mean-var efficient frontier. Quant. Financ. 10(8), 931–945 (2010)CrossRefGoogle Scholar
  26. Wallace, D.L.: Asymptotic approximations to distributions. Ann. Math. Stat. 29, 635–654 (1958)CrossRefGoogle Scholar
  27. Wallmeier, M.: Beyond payoff diagrams: how to present risk and return characteristics of structured products. Financ. Mark. Portf. Manag. 25(3), 313–338 (2011)CrossRefGoogle Scholar

Copyright information

© Swiss Society for Financial Market Research 2017

Authors and Affiliations

  1. 1.Business SchoolNankai UniversityTianjinChina

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