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Statistical modelling of asymmetric risk in asset returns

Author

Listed:
  • J. L. Knight
  • S. E. Satchell
  • K. C. Tran

Abstract

The purpose of this article is to provide a straightforward model for asset returns which captures the fundamental asymmetry in upward versus downward returns. We model this feature by using scale gamma distributions for the conditional distributions of positive and negative returns. By allowing the parameters for positive returns to differ from parameters for negative returns we can test the hypothesis of symmetry. Some applications of this process to expected utility and semi-variance calculations are considered. Finally we estimate the model using daily UK FT100 index and Futures data.

Suggested Citation

  • J. L. Knight & S. E. Satchell & K. C. Tran, 1995. "Statistical modelling of asymmetric risk in asset returns," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 155-172.
    • Handle: RePEc:taf:apmtfi:v:2:y:1995:i:3:p:155-172
    DOI: 10.1080/13504869500000009
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    Citations

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    Cited by:

    1. Christodoulakis, George A. & Satchell, Stephen E., 1999. "The simulation of option prices with application to LIFFE options on futures," European Journal of Operational Research, Elsevier, vol. 114(2), pages 249-262, April.
    2. Herv¨¦ Ndoume Essingone & Mouhamadou Saliou Diallo, 2019. "Risk and Return: The Case of Securities Listed on the West African Economic and Monetary Union Regional Exchange of Securities (BRVM)," Applied Economics and Finance, Redfame publishing, vol. 6(1), pages 97-108, January.
    3. John Knight & Colin Lizieri & Stephen Satchell, 2005. "Diversification When It Hurts? The Joint Distributions of Real Estate and Equity Markets," Real Estate & Planning Working Papers rep-wp2005-16, Henley Business School, University of Reading.
    4. Sancetta, A., 2005. "Copula Based Monte Carlo Integration in Financial Problems," Cambridge Working Papers in Economics 0506, Faculty of Economics, University of Cambridge.
    5. Hussain, Sultan & Arif, Hifsa & Noorullah, Muhammad & Pantelous, Athanasios A., 2023. "Pricing American Options under Azzalini Ito-McKean Skew Brownian Motions," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    6. Farah, N. & Satchell, S.E., 2003. "A Loss Aversion Performance Measure," Cambridge Working Papers in Economics 0333, Faculty of Economics, University of Cambridge.
    7. Stephen Satchell & David Damant & Soosung Hwang, 2000. "Exponential risk measure with application to UK asset allocation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(2), pages 127-152.
    8. Ba Chu, 2012. "Approximation of Asymmetric Multivariate Return Distributions," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 19(3), pages 293-318, September.
    9. Stefania D'Amico, 2004. "Density Estimation and Combination under Model Ambiguity," Computing in Economics and Finance 2004 273, Society for Computational Economics.
    10. Shaun Bond & Stephen Satchell, 2006. "Asymmetry and downside risk in foreign exchange markets," The European Journal of Finance, Taylor & Francis Journals, vol. 12(4), pages 313-332.
    11. Skouras, Spyros, 2007. "Decisionmetrics: A decision-based approach to econometric modelling," Journal of Econometrics, Elsevier, vol. 137(2), pages 414-440, April.
    12. Davies, G.B. & Satchell, S.E., 2004. "The Behavioural Components of Risk Aversion," Cambridge Working Papers in Economics 0458, Faculty of Economics, University of Cambridge.
    13. Alcock, Jamie & Sinagl, Petra, 2022. "International determinants of asymmetric dependence in investment returns," Journal of International Money and Finance, Elsevier, vol. 122(C).
    14. Hwang, Soosung & Pedersen, Christian S., 2004. "Asymmetric risk measures when modelling emerging markets equities: evidence for regional and timing effects," Emerging Markets Review, Elsevier, vol. 5(1), pages 109-128, March.
    15. Stephen E. Satchell & Shaun A. Bond, 2004. "Asymmetry, Loss Aversion and Forecasting," Econometric Society 2004 Australasian Meetings 160, Econometric Society.
    16. Tae-Hwy Lee & Yong Bao & Burak Saltoğlu, 2007. "Comparing density forecast models Previous versions of this paper have been circulated with the title, 'A Test for Density Forecast Comparison with Applications to Risk Management' since October 2003;," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(3), pages 203-225.
    17. Emmanuel Acar & Stephen Satchell, 1997. "A theoretical analysis of trading rules: an application to the moving average case with Markovian returns," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(3), pages 165-180.
    18. Davies, G.B. & Satchell, S.E., 2004. "Continuous Cumulative Prospect Theory and Individual Asset Allocation," Cambridge Working Papers in Economics 0467, Faculty of Economics, University of Cambridge.
    19. Chu, Ba & Knight, John & Satchell, Stephen, 2011. "Large deviations theorems for optimal investment problems with large portfolios," European Journal of Operational Research, Elsevier, vol. 211(3), pages 533-555, June.
    20. Stefania D'Amico, 2005. "Density selection and combination under model ambiguity: an application to stock returns," Finance and Economics Discussion Series 2005-09, Board of Governors of the Federal Reserve System (U.S.).

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