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Partial moment volatility indices

Author

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  • Zhangxin (Frank) Liu
  • Michael J. O'Neill

Abstract

Forward‐looking partial moment volatility indices are developed using state‐pricing, called the bear index (BEX) and bull index (BUX). Using S&P 500 index (SPX) option prices, we find that BEX and BUX provide superior forecasts for the lower and upper partial moments of future market realised volatility, respectively. We examine the relation between SPX returns and changes in BEX and BUX at the daily level. Results are consistent with the volatility feedback hypothesis. Further, we show that BEX may be more suitable as the ‘investor fear gauge’ than VIX.

Suggested Citation

  • Zhangxin (Frank) Liu & Michael J. O'Neill, 2018. "Partial moment volatility indices," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 58(1), pages 195-215, March.
    • Handle: RePEc:bla:acctfi:v:58:y:2018:i:1:p:195-215
    DOI: 10.1111/acfi.12209
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    as
    1. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    2. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    3. Unser, Matthias, 2000. "Lower partial moments as measures of perceived risk: An experimental study," Journal of Economic Psychology, Elsevier, vol. 21(3), pages 253-280, June.
    4. Anthonisz, Sean A., 2012. "Asset pricing with partial-moments," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2122-2135.
    5. M. S. Feldstein, 1969. "Mean-Variance Analysis in the Theory of Liquidity Preference and Portfolio Selection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(1), pages 5-12.
    6. Cumova, Denisa & Nawrocki, David, 2011. "A symmetric LPM model for heuristic mean-semivariance analysis," Journal of Economics and Business, Elsevier, vol. 63(3), pages 217-236, May.
    7. Francis In & Sangbae Kim & Philip I Ji, 2014. "On timing ability in Australian managed funds," Australian Journal of Management, Australian School of Business, vol. 39(1), pages 93-106, February.
    8. Kim, Sei-Wan & Lee, Bong-Soo & Kim, Young-Min, 2014. "Who mimics whom in the equity fund market? Evidence from the Korean equity fund market," Pacific-Basin Finance Journal, Elsevier, vol. 29(C), pages 199-218.
    9. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Hogan, William W. & Warren, James M., 1974. "Toward the Development of an Equilibrium Capital-Market Model Based on Semivariance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(1), pages 1-11, January.
    11. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    12. Binh Huu Do, 2002. "Relative performance of dynamic portfolio insurance strategies: Australian evidence," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 42(3), pages 279-296, November.
    13. Veld, Chris & Veld-Merkoulova, Yulia V., 2008. "The risk perceptions of individual investors," Journal of Economic Psychology, Elsevier, vol. 29(2), pages 226-252, April.
    14. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    15. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Abstract: Capital Market Equilibrium in a Mean-Lower Partial Moment Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 635-635, November.
    16. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    17. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    18. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
    19. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    20. Wenling Yang & David E. Allen, 2005. "Multivariate GARCH hedge ratios and hedging effectiveness in Australian futures markets," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 45(2), pages 301-321, July.
    21. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    22. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    23. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    24. Estrada, Javier, 2007. "Mean-semivariance behavior: Downside risk and capital asset pricing," International Review of Economics & Finance, Elsevier, vol. 16(2), pages 169-185.
    25. Brailsford, Timothy J. & Faff, Robert W., 1996. "An evaluation of volatility forecasting techniques," Journal of Banking & Finance, Elsevier, vol. 20(3), pages 419-438, April.
    26. Stephen Sault, 2005. "Movements in Australian Stock Volatility: A Disaggregated Approach," Australian Journal of Management, Australian School of Business, vol. 30(2), pages 303-320, December.
    27. K. Borch, 1969. "A Note on Uncertainty and Indifference Curves," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(1), pages 1-4.
    28. Holthausen, Duncan M, 1981. "A Risk-Return Model with Risk and Return Measured as Deviations from a Target Return," American Economic Review, American Economic Association, vol. 71(1), pages 182-188, March.
    29. Jain, Pawan & Jiang, Christine, 2014. "Predicting future price volatility: Empirical evidence from an emerging limit order market," Pacific-Basin Finance Journal, Elsevier, vol. 27(C), pages 72-93.
    30. Ang, James S., 1975. "A Note on the E, SL Portfolio Selection Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(5), pages 849-857, December.
    31. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    32. Price, Kelly & Price, Barbara & Nantell, Timothy J, 1982. "Variance and Lower Partial Moment Measures of Systematic Risk: Some Analytical and Empirical Results," Journal of Finance, American Finance Association, vol. 37(3), pages 843-855, June.
    33. Bondarenko, Oleg, 2003. "Estimation of risk-neutral densities using positive convolution approximation," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 85-112.
    34. Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(2), pages 255-271, June.
    35. Lee, Bong Soo & Paek, Miyoun & Ha, Yeonjeong & Ko, Kwangsoo, 2015. "The dynamics of market volatility, market return, and equity fund flow: International evidence," International Review of Economics & Finance, Elsevier, vol. 35(C), pages 214-227.
    36. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    37. Jun, Xiao & Li, Mingsheng & Shi, Jing, 2014. "Volatile market condition and investor clientele effects on mutual fund flow performance relationship," Pacific-Basin Finance Journal, Elsevier, vol. 29(C), pages 310-334.
    38. Harlow, W. V. & Rao, Ramesh K. S., 1989. "Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 285-311, September.
    39. Mao, James C T, 1970. "Survey of Capital Budgeting: Theory and Practice," Journal of Finance, American Finance Association, vol. 25(2), pages 349-360, May.
    40. Hogan, William W. & Warren, James M., 1972. "Computation of the Efficient Boundary in the E-S Portfolio Selection Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 7(4), pages 1881-1896, September.
    41. Nartea, Gilbert V. & Wu, Ji, 2013. "Is there a volatility effect in the Hong Kong stock market?," Pacific-Basin Finance Journal, Elsevier, vol. 25(C), pages 119-135.
    42. Bawa, Vijay S. & Lindenberg, Eric B., 1977. "Capital market equilibrium in a mean-lower partial moment framework," Journal of Financial Economics, Elsevier, vol. 5(2), pages 189-200, November.
    43. Jahankhani, Ali, 1976. "E-V and E-S Capital Asset Pricing Models: Some Empirical Tests," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(4), pages 513-528, November.
    44. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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