Skip to main content
Log in

Mean-variance hedging in the presence of estimation risk

  • Published:
Review of Derivatives Research Aims and scope Submit manuscript

Abstract

The mean-variance hedging (MVH) with a significant risk-aversion coefficient is approximately equal to the minimum-variance (MV) hedge. However, how large the risk-aversion coefficient should be in practice? We determine the boundaries of risk-aversion coefficients that significantly distinguish the MV hedge and the MVH based on the different magnitudes of statistical errors in the presence of estimation risk. Based on the hedged variance, hedged return, and hedge ratio, we show that the MV hedge is statistically justified for MVH investor with an extensive range of risk-aversion coefficients. Additionally, the upper bound of the significant risk-aversion coefficient is positively related to the squared information ratio of futures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. Other forms of mean-variance optimization can also approximate the expected utility maximization. Das et al. (2010, p. 316) use the mean-variance utility maximization for this quadratic optimization.

  2. We are grateful to Investing.com for providing the simulation data. Henceforth, we refer to these futures as the FTSE 100 and the S&P 500, respectively.

References

  • Aït-Sahalia, Y., & Lo, A. W. (2000). Nonparametric risk management and implied risk-aversion. Journal of Econometrics, 94, 9–51.

    Article  Google Scholar 

  • Best, M. J., & Grauer, R. R. (1991). On the sensitivity of mean-variance portfolios to change in asset means: Some analytical and computation results, and the structure of asset expected returns. Review of Financial Studies, 4, 315–342.

    Article  Google Scholar 

  • Bliss, R. R., & Panigirtzoglou, N. (2004). Option-implied risk aversion estimates. Journal of Finance, 68, 407–446.

    Article  Google Scholar 

  • Bodnar, T., & Okhrin, Y. (2013). Boundaries of the risk-aversion coefficient: Should we invest in the global minimum variance portfolio? Applied Mathematics and Computation, 219, 5440–5448.

    Article  Google Scholar 

  • Bond, G. E., & Thompson, S. R. (1986). Optimal commodity hedging within the capital asset pricing model. Journal of Futures Markets, 6, 421–431.

    Article  Google Scholar 

  • Brandt, M. W., & Santa-Clara, P. (2006). Dynamic portfolio selection by augmenting the asset space. Journal of Finance, 61, 2187–2217.

    Article  Google Scholar 

  • Cecchetti, S. G., Cumby, R. E., & Figlewski, S. (1988). Estimation of the optimal futures hedge. Review of Economics and Statistics, 70, 623–630.

    Article  Google Scholar 

  • Chang, J., & Shanker, L. (1987). A risk-return measure of hedging effectiveness: A comment. Journal of Financial and Quantitative Analysis, 22, 373–376.

    Article  Google Scholar 

  • Chen, S. S., Lee, C. F., & Shrestha, K. (2003). Futures hedge ratios: A review. The Quarterly Review of Economics and Finance, 43, 433–465.

    Article  Google Scholar 

  • Chiu, W. Y. (2020). The global minimum variance hedge. Review of Derivatives Research, 23, 121–144.

    Article  Google Scholar 

  • Chopra, V. K., & Ziemba, W. T. (1993). The effects of errors in means, variance, and covariance on optimal portfolio choice. Journal of Portfolio Management, 19, 6–11.

    Article  Google Scholar 

  • Černý, A., & Kallsen, J. (2007). On the structure of general mean-variance hedging strategies. Annals of Probability, 35, 1479–1531.

    Article  Google Scholar 

  • Das, S., Markowitz, H., Scheid, J., & Statman, M. (2010). Portfolio optimization with mental accounts. Journal of Financial and Quantitative Analysis, 45, 311–334.

    Article  Google Scholar 

  • Draper, N., & Smith, H. (1981). Applied regression analysis (2nd ed.). Hoboken: Wiley.

    Google Scholar 

  • Duffie, D., & Richardson, H. R. (1991). Mean-variance hedging in continuous time. Annals of Applied Probability, 1, 1–15.

    Article  Google Scholar 

  • Eberlein, E., & Kallsen, J. (2019). Mathematical finance. Berlin: Springer.

    Book  Google Scholar 

  • Ederington, L. H. (1979). The hedging performance of the new futures markets. Journal of Finance, 43, 157–170.

    Article  Google Scholar 

  • Giovannini, A. (1993). Time-series tests of a non-expected-utility model of asset pricing. European Economic Review, 37, 1083–1100.

    Article  Google Scholar 

  • Guisoa, L., Sapienza, P., & Zingales, L. (2018). Time varying risk aversion. Journal of Financial Economics, 128, 403–421.

    Article  Google Scholar 

  • Howard, C., & D’Antonio, L. (1984). A risk-return measure of hedging effectiveness. Journal of Financial and Quantitative Analysis, 19, 101–112.

    Article  Google Scholar 

  • Hsin, C. W., Kuo, J., & Lee, C. F. (1994). A new measure to compare the hedging effectiveness of foreign currency futures versus options. Journal of Futures Markets, 14, 685–707.

    Article  Google Scholar 

  • Khoury, M. T., & Martel, J. M. (1985). Optimal futures hedging in the presence of asymmetric information. Journal of Futures Market, 5, 595–605.

    Article  Google Scholar 

  • Kuo, C. K., & Chen, K. W. (1995). A risk-return measure of hedging effectiveness: A simplification. Journal of Futures Markets, 15, 39–44.

    Article  Google Scholar 

  • Lence, S. H. (1996). Relaxing the assumptions of minimum variance hedging. Journal of Agricultural and Resource Economics, 21, 39–55.

    Google Scholar 

  • Levy, M. (2019). Stocks for the log-run and constant relative risk-aversion preferences? European Journal of Operational Research, 277, 1163–1168.

    Article  Google Scholar 

  • Lien, D., & Shrestha, K. (2008). Hedge effectiveness comparisons: A note. International Review of Economics and Finance, 17, 391–396.

    Article  Google Scholar 

  • Myers, R. J., & Thompson, S. R. (1989). Generalized optimal hedge ratio estimation. American Journal of Agricultural Economics, 71, 858–868.

    Article  Google Scholar 

  • Pham, H. (2000). On quadratic hedging in continuous time. Mathematical Methods of Operational Research, 51, 315–339.

    Article  Google Scholar 

  • Pindyck, R. S. (1988). Risk-aversion and determinants of stock market behavior. The Review of Economics and Statistics, 70, 183–190.

    Article  Google Scholar 

  • Satyanarayan, S. (1998). A note on a risk-return measure of hedging effectiveness. Journal of Futures Markets, 18, 595–605.

    Article  Google Scholar 

  • Schweizer, M. (1992). Mean-variance hedging for general claims. Annals of Applied Probability, 2, 171–179.

    Article  Google Scholar 

  • Schweizer, M. (1996). Approximation pricing and the variance-optimal martingle meansure. Annals of Probability, 64, 206–236.

    Google Scholar 

  • Seber, G. A. F. (1977). Linear regression analysis. Hoboken: Wiley.

    Google Scholar 

  • Shiller, R. J. (2003). From efficient markets theory to behavioral theory. Journal of Economic Perspectives, 17, 83–104.

    Article  Google Scholar 

  • You, L., & Daigleer, R. T. (2013). A Markowitz optimization of commodity futures portfolios. Journal of Futures Markets, 33, 343–368.

    Article  Google Scholar 

Download references

Acknowledgements

The author is thankful to the Editor and a anonymous reviewer for helpful suggestions which have improved the presentation in the paper. The author also gratefully acknowledges partial financial support from the National United University through project 109NUUPRJ-10.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wan-Yi Chiu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chiu, WY. Mean-variance hedging in the presence of estimation risk. Rev Deriv Res 24, 221–241 (2021). https://doi.org/10.1007/s11147-021-09176-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11147-021-09176-6

Keywords

JEL Classifications

Navigation