# Conditional dependence in post-crisis markets: dispersion and correlation skew trades

- 10 Downloads

## Abstract

Strengthening of asset return dependence during the 2007–2008 credit crisis highlighted its dynamic and conditional nature. Option prices reflect the market assessment of how dependence between assets varies with price movements and time horizons, yielding the implied correlation surface. Return dependence increases in falling markets and makes correlation a priced risk factor, causing a spread between implied and actual correlation. Order flow pressure from hedging structured products also contributes to the spread. Prior to the crisis, the gap between implied and actual correlation motivated selling dependence between equities—dispersion trading. However, spiking dependence among stock returns during the crisis decimated correlation sellers. Selling at-the-money conditional correlation between NASDAQ-100 components regains an attractive risk-return profile during periods of strong bull market. This may be due to an increasing correlation risk premium caused by greater investor belief heterogeneity. The implied correlation surface enables the construction of strategies with exposures to dependence conditional on various market dynamics. In particular, a long correlation skew trade delivers attractive returns, while hedging the effects of volatility and mitigating exposure to the level of correlation. This suggests segmentation of the options market along the moneyness dimension. As a risk factor, a correlation skew trade is nearly orthogonal to the five Fama–French risk factors, as well as the momentum factor.

## Keywords

Implied correlation Correlation risk premium Conditional dependence Basket options Dispersion trading Market segmentation QQQ## JEL Classification

G11 G13## Notes

### Acknowledgements

The work on this paper was mostly conducted while the author was a faculty member at Rutgers Business School—Newark and New Brunswick, prior to his employment by the Board of Governors of the Federal Reserve System. Only minor revisions were made during the author’s employment by the Board of Governors of the Federal Reserve System. The analysis and conclusions set forth are those of the author and do not indicate concurrence by other members of the research staff or the Board of Governors.

## References

- Andrews DW (1993) Tests for parameter instability and structural change with unknown change point. Econom J Econom Soc 61(4):821–856Google Scholar
- Andrews DW, Ploberger W (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econom J Econom Soc 62(6):1383–1414Google Scholar
- Ang A, Chen J (2002) Asymmetric correlations of equity portfolios. J Financ Econ 63(3):443–494Google Scholar
- Bennett C (2014) Trading volatility: trading volatility, correlation, term structure and skew. In: CreateSpace independent publishing platform. https://books.google.com/books?id=_zPuoAEACAAJ
- Blenman LP, Wang GJ (2012) New insights on the implied and realized volatility relation. Rev Pac Basin Financ Mark Policies 15(01):1250001Google Scholar
- Buraschi A, Kosowski R, Trojani F (2013) When there is no place to hide: correlation risk and the cross-section of hedge fund returns. Rev Financ Stud 27(2):581–616Google Scholar
- Buraschi A, Trojani F, Vedolin A (2014) When uncertainty blows in the orchard: comovement and equilibrium volatility risk premia. J Finance 69(1):101–137Google Scholar
- Byun SJ, Kim S, Rhee DW (2018) Ad hoc black and scholes procedures with the time-to-maturity. Rev Pac Basin Financ Mark Policies 21(01):1850006Google Scholar
- CBOE (2000) Chicago board options exchange margin manualGoogle Scholar
- Cespa G, Foucault T (2014) Illiquidity contagion and liquidity crashes. Rev Financ Stud 27(6):1615–1660Google Scholar
- Chang MC, Wu CF (2012) Who offers liquidity on options markets when volatility is high? Rev Pac Basin Financ Mark Policies 15(04):1250021Google Scholar
- Chen RR, Lee CF, Lee HH (2009) Empirical performance of the constant elasticity variance option pricing model. Rev Pac Basin Financ Mark Policies 12(02):177–217Google Scholar
- Chiu J, Chung H, Ho KY (2014) Fear sentiment, liquidity, and trading behavior: evidence from the index etf market. Rev Pac Basin Financ Mark Policies 17(03):1450017Google Scholar
- Corb H (2012) Interest rate swaps and other derivatives. Columbia Business School Publishing Series, Columbia Business SchoolGoogle Scholar
- Coval JD, Shumway T (2001) Expected option returns. J Finance 56(3):983–1009Google Scholar
- Cox JC (1996) The constant elasticity of variance option pricing model. J Portf Manag 15:15–17Google Scholar
- Deng Q (2008) Volatility dispersion trading. SSRN 1156620Google Scholar
- Diavatopoulos D, Sokolinskiy O (forthcoming) Stochastic volatility models: faking a smile. In: Handbook of financial econometrics, mathematics, statistics, and machine learning, vol 2. World Scientific Publishing, SingaporeGoogle Scholar
- Diks C, Panchenko V, Sokolinskiy O, van Dijk D (2014) Comparing the accuracy of multivariate density forecasts in selected regions of the copula support. J Econ Dyn Control 48:79–94Google Scholar
- Driessen J, Maenhout P (2007) An empirical portfolio perspective on option pricing anomalies. Rev Finance 11(4):561–603Google Scholar
- Driessen J, Maenhout PJ, Vilkov G (2009) The price of correlation risk: evidence from equity options. J Finance 64(3):1377–1406Google Scholar
- Driessen J, Maenhout P, Vilkov G (2013) Option-implied correlations and the price of correlation risk. Netspar discussion paper no 07/2013-061Google Scholar
- Fama EF, French KR (2015) A five-factor asset pricing model. J Financ Econ 116(1):1–22Google Scholar
- Garleanu N, Pedersen LH, Poteshman AM (2008) Demand-based option pricing. Rev Financ Stud 22(10):4259–4299Google Scholar
- Gatheral J (2006) The volatility surface: a practitioner’s guide. Wiley Finance, Wiley, New YorkGoogle Scholar
- Gennotte G, Leland H (1990) Market liquidity, hedging, and crashes. Am Econ Rev 80(5):999–1021Google Scholar
- Gromb D, Vayanos D (2002) Equilibrium and welfare in markets with financially constrained arbitrageurs. J Financ Econ 66(2–3):361–407Google Scholar
- Harikumar T, De Boyrie ME, Pak SJ (2004) Evaluation of black–scholes and garch models using currency call options data. Rev Quant Finance Account 23(4):299–312Google Scholar
- Hitzemann S, Hofmann M, Uhrig-Homburg M, Wagner C (2017) Margin requirements and equity option returnsGoogle Scholar
- Hobbs J, Lee HW, Singh V (2017) New evidence on the effect of belief heterogeneity on stock returns. Rev Quant Finance Account 48(2):289–309Google Scholar
- Ilmanen A, Asness C (2011) Expected returns: an investor’s guide to harvesting market rewards. The Wiley Finance Series, Wiley. https://books.google.com/books?id=WqFf6imwTsUC
- Jacquier A, Slaoui S (2010) Variance dispersion and correlation swaps. arXiv preprint arXiv:10040125
- Lee CF, Sokolinskiy O (2015) R-2gam stochastic volatility model: flexibility and calibration. Rev Quant Finance Account 45(3):463–483Google Scholar
- Lee RW (2005) Implied volatility: statics, dynamics, and probabilistic interpretation. In: Baeza-Yates R, Glaz J, Gzyl H, Hüsler J, Palacios JL (eds) Recent advances in applied probability. Springer, Boston, MA, pp 241–268Google Scholar
- Linders D, Schoutens W (2014) A framework for robust measurement of implied correlation. J Comput Appl Math 271:39–52Google Scholar
- Longin F, Solnik B (2001) Extreme correlation of international equity markets. J Finance 56(2):649–676Google Scholar
- Marshall CM (2009) Dispersion trading: empirical evidence from us options markets. Glob Finance J 20(3):289–301Google Scholar
- Maze S (2012) Dispersion trading in south Africa: an analysis of profitability and a strategy comparisonGoogle Scholar
- McNeil AJ, Frey R, Embrechts P (2015) Quantitative risk management: concepts, techniques and tools-revised edition. Princeton University Press, PrincetonGoogle Scholar
- Muravyev D (2016) Order flow and expected option returns. J Finance 71(2):673–708Google Scholar
- Pástor L, Stambaugh RF (2003) Liquidity risk and expected stock returns. J Polit Econ 111(3):642–685Google Scholar
- Rebonato R (2004) Volatility correlation, 2nd edn. Wiley, New YorkGoogle Scholar
- Santa-Clara P, Saretto A (2009) Option strategies: good deals and margin calls. J Financ Mark 12(3):391–417Google Scholar
- Taleb N (1997) Dynamic heging: managing vanilla and exotic options. The Wiley Finance Series, Wiley, New YorkGoogle Scholar
- Tanha H, Dempsey M (2016) The information content of ASX SPI 200 implied volatility. Rev Pac Basin Financ Mark Policies 19(01):1650002Google Scholar
- Tavella D, Randall C (2000) Pricing financial instruments: the finite difference method. Wiley series in financial engineering, Wiley. https://books.google.com/books?id=E_GPuAEACAAJ
- Walter C, Lopez JA (2000) Is implied correlation worth calculating? Evidence from foreign exchange options and historical data. Federal Reserve Bank of San FranciscoGoogle Scholar
- Wharton Research Data Service (2018a) Compustat. wrds.wharton.upenn.edu
- Wharton Research Data Service (2018b) CRSP. wrds.wharton.upenn.edu
- Wharton Research Data Service (2018c) OptionMetrics. wrds.wharton.upenn.edu
- Wharton Research Data Service (2018d) Pastor–Stambaugh liquidity factors. wrds.wharton.upenn.edu
- Yuan K (2005) Asymmetric price movements and borrowing constraints: a rational expectations equilibrium model of crises, contagion, and confusion. J Finance 60(1):379–411Google Scholar