Option-Implied Objective Measures of Market Risk with Leverage
Leverage has been shown to be procyclical and indicative of financial market risk. Here, we present a novel, inherently forward-looking way to estimate market leverage ratios based on derivative prices, option hedging, and the ‘operational’ riskiness measure by Foster and Hart (J Polit Econ 117(5):785–814, 2009). Furthermore, we report option-implied ‘optimal’ leverage levels inferred via the (Kelly, IRE Trans. Inf. Theory 2(3):185–189, 1956) criterion. The resulting measure of leverage exhibits strong procyclicality prior to the Global Financial Crisis of 2008. Finally, we find it to successfully predict large stock market downturns.
KeywordsObjective risk Foster-Hart Leverage Risk-neutral densities
Leiss acknowledges support from the ETH Risk Center and through SNF grant The Anatomy of Systemic Financial Risk, Nax from the European Commission through the ERC Advanced Investigator Grant Momentum (Grant No. 324247).
- Basel Committee on Banking Supervision: Basel III: a global regulatory framework for more resilient banks and banking systems. Technical report, Bank for International Settlements (2010)Google Scholar
- Chicago Board Options Exchange: The CBOE volatility index – VIX. Technical report, White Paper (2009)Google Scholar
- Figlewski, S.: Estimating the implied risk neutral density. In: Bollerslev, T., Russell, J., Watson, M. (eds.) Volatility and Time Series Econometrics. Oxford University Press, Oxford (2010)Google Scholar
- Geanakoplos, J.: The leverage cycle. In: NBER Macroeconomics Annual 2009, vol. 24, pp. 1–65. University of Chicago Press, Chicago (2010)Google Scholar
- Hadar, J., Russell, W.R.: Rules for ordering uncertain prospects. Am. Econ. Rev. 59(1), 25–34 (1969)Google Scholar
- Hildebrand, P.M.: Is Basel II Enough? The Benefits of a Leverage Ratio. Philipp M. Hildebrand, Vice-Chairman of the Governing Board Swiss National Bank, in a Financial Markets Group Lecture at the London School of Economics on December 15, 2008. http://www.ub.unibas.ch/digi/a125/sachdok/2011/BAU_1_5654573.pdf (2008)
- Jackwerth, J.C.: Option-Implied Risk-Neutral Distributions and Risk Aversion. Research Foundation of AIMR Charlotteville (2004)Google Scholar
- Leiss, M., Nax, H.H.: Option-implied objective measures of market risk. Social Science Research Network Working Paper Series, 2690476, Quantitative Economics (2015, submitted)Google Scholar
- Von der Becke, S., Sornette, D.: Toward a unified framework of credit creation. Technical Report 14-07, Swiss Finance Institute Research Paper (2014)Google Scholar