Decomposing the VIX: Implications for the predictability of stock returns
K. Victor Chow
Chambers College of Business and Economics, West Virginia University, Morgantown, West Virginia
Search for more papers by this authorWanjun Jiang
Guanghua School of Management, Peking University, Beijing, China
Search for more papers by this authorCorresponding Author
Bingxin Li
Chambers College of Business and Economics, West Virginia University, Morgantown, West Virginia
Correspondence
Jingrui Li, GWBC, Room #640, A.B. Freeman School of Business, 7 McAlister Dr., New Orleans, LA 70118.
Email: jli61@tulane.edu
Search for more papers by this authorJingrui Li
A.B. Freeman School of Business, Tulane University, New Orleans, Louisiana
Search for more papers by this authorK. Victor Chow
Chambers College of Business and Economics, West Virginia University, Morgantown, West Virginia
Search for more papers by this authorWanjun Jiang
Guanghua School of Management, Peking University, Beijing, China
Search for more papers by this authorCorresponding Author
Bingxin Li
Chambers College of Business and Economics, West Virginia University, Morgantown, West Virginia
Correspondence
Jingrui Li, GWBC, Room #640, A.B. Freeman School of Business, 7 McAlister Dr., New Orleans, LA 70118.
Email: jli61@tulane.edu
Search for more papers by this authorJingrui Li
A.B. Freeman School of Business, Tulane University, New Orleans, Louisiana
Search for more papers by this authorAbstract
The VIX index is not only a volatility index but also a polynomial combination of all possible higher moments in market return distribution under the risk-neutral measure. This paper formulates the VIX as a linear decomposition of four fundamentally different elements: the realized variance (RV), the variance risk premium (VRP), the realized tail (RT), and the tail risk premium (TRP), respectively. Using an innovative and nonparametric tail risk measure, we find that approximately one-third of the VIX's formation is attributed to the TRP. In addition to VRP, RT and TRP are crucial components for predicting future returns on equity portfolios.
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REFERENCES
- Almeida, C., Ardison, K., Garcia, R., & Vicente, J. (2017). Nonparametric tail risk, stock returns, and the Macroeconomy. Journal of Financial Econometrics, 15(3), 333–376.
- Andersen, T. G., & Bollerslev, T. (1998). Deutsche mark–dollar volatility: Intraday activity patterns, macroeconomic announcements, and longer run dependencies. Journal of Finance, 53, 219–265.
- Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2001). The distribution of realized exchange rate volatility. Journal of the American Statistical Association, 96, 42–55.
- Andersen, T. G., Fusari, N., & Todorov, V. (2015). Parametric inference and dynamic state recovery from option panels. Econometrica, 83, 1081–1145.
- Andreou, E., & Ghysels, E. (2013). What drives the VIX and the volatility risk premium? Working paper, Nicosia, Cyprus: University of Cyprus and Chapel Hill, NC: University of North Carolina.
- Bakshi, G., Kapadia, N., & Madan, D. (2003). Stock return characteristics, skew laws, and the differential pricing of individual equity options. Review of Financial Studies, 16, 101–143.
- Bali, T. G., & Zhou, H. (2016). Risk, uncertainty, and expected returns. Journal of Financial and Quantitative Analysis, 51(3), 707–735.
- Barro, R. J. (2006). Rare disasters and asset markets in the twentieth century. Quarterly Journal of Economics, 121, 823–866.
- Bekaert, G., & Engstrom, E. (2010). Inflation and the stock market: Understanding the “Fed Model.” Journal of Monetary Economics, 57, 278–294.
- Bekaert, G., & Hoerova, M. (2014). The VIX, the variance premium and stock market volatility. Journal of Econometrics, 183, 181–192.
- Bekaert, G., Hoerova, M., & Lo Duca, M. L. (2013). Risk, uncertainty and monetary policy. Journal of Monetary Economics, 60, 771–788.
- Bollerslev, T., Gibson, M., & Zhou, H. (2011). Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities. Journal of Econometrics, 160, 235–245.
- Bollerslev, T., Marrone, J., Xu, L., & Zhou, H. (2014). Stock return predictability and variance risk premia: Statistical inference and international evidence. Journal of Financial and Quantitative Analysis, 49, 633–661.
- Bollerslev, T., Tauchen, G., & Zhou, H. (2009). Expected stock returns and variance risk premia. Review of Financial Studies, 22, 4463–4492.
- Bollerslev, T., & Todorov, V. (2011). Tails, fears, and risk premia. Journal of Finance, 66, 2165–2211.
- Bollerslev, T., & Todorov, V. (2014). Time-varying jump tails. Journal of Econometrics, 183, 168–180.
- Bollerslev, T., Todorov, V., & Xu, L. (2015). Tail risk premia and return predictability. Journal of Financial Economics, 118, 113–134.
- Bondarenko, O. (2014). Variance trading and market price of variance risk. Journal of Econometrics, 180, 81–97.
- Britten-Jones, M., & Neuberger, A. (2000). Option prices, implied price processes, and stochastic volatility. Journal of Finance, 55, 839–866.
- Campbell, J. Y., & Cochrane, J. H. (1999). By force of habit: A consumption-based explanation of aggregate stock market behavior. Journal of Political Economy, 107(2), 205–251.
- Camponovo, L., Scaillet, O., & Trojani, F. (2014). Predictability hidden by anomalous observations. Working Paper, Zurich, Switzerland: Swiss Finance Institute.
- Carr, P., & Madan, D. (1999). Option valuation using the fast Fourier transform. Journal of Computational Finance, 2, 61–73.
10.21314/JCF.1999.043 Google Scholar
- Carr, P., & Wu, L. (2009). Variance risk premiums. The Review of Financial Studies, 22(3), 1311–1341.
- Chow, V., Jiang, W., & Li, J. (2014). Does VIX truly measure return volatility? Working Paper, Morgantown, West Virginia: West Virginia University.
- Cont, R., & Tankov, P. (2003). Financial Modeling with jump-diffusion processes. Boca Raton, FL: Chapman and Hall/CRC Press.
- Corsi, F., Pirino, D., & Reno, R. (2010). Threshold bipower variation and the impact of jumps on volatility forecasting. Journal of Econometrics, 159, 276–288.
- Cremers, M., Halling, M., & Weinbaum, D. (2015). Aggregate jump and volatility risk in the cross-section of stock returns. Journal of Finance, 70, 577–614.
- Demeterfi, K., Derman, E., Kamal, M., & Zou, J. (1999a). More than you ever wanted to know about volatility swaps. Quantitative strategies research notes. New York, NY: Goldman Sachs
- Demeterfi, K., Derman, E., Kamal, M., & Zou, J. (1999b). A guide to volatility and variance swaps. Journal of Derivatives, 6, 9–32.
10.3905/jod.1999.319129 Google Scholar
- Du, J., & Kapadia, N. (2012). Tail and volatility indices from option prices. Working paper, Amherst, MA: University of Massachusetts.
- Drechsler, I., & Yaron, A. (2011). What's vol got to do with it. Review of Financial Studies, 24, 1–45.
- Eraker, B., & Wang, J. (2015). A non-linear dynamic model of the variance risk premium. Journal of Econometrics, 187, 547–556.
- Gabaix, X. (2012). Variable rare disasters: An exactly solved framework for ten puzzles in macro-finance. The Quarterly Journal of Economics, 127(2), 645–700.
- Han, B., & Zhou, Y. (2012). Variance risk premium and cross-section of stock returns. Working paper, Austin, TX: University of Texas at Austin.
- Jiang, G. J., & Oomen, R. C. (2008). Testing for jumps when asset prices are observed with noise—A “swap variance” approach. Journal of Econometrics, 144, 352–370.
- Kelly, B., & Jiang, H. (2014). Tail risk and asset prices. Review of Financial Studies, 27, 2841–2871.
- Klein, R., & Chow, V. (2013). Orthogonalized equity risk premia and systematic risk decomposition. Quarterly Review of Economics and Finance, 53(2), 175–187.
10.1016/j.qref.2013.02.003 Google Scholar
- Li, J., & Zinna, G. (2018). The variance risk premium: Components, term structures, and stock return predictability. Journal of Business and Economic Statistics, 36(3), 411–425.
- Liu, J., Pan, J., & Wang, T. (2005). An equilibrium model of rare-event premia and its implication for option smirks. Review of Financial Studies, 18, 131–164.
- Longstaff, F. A., & Piazzesi, M. (2004). Corporate earnings and the equity premium. Journal of Financial Economics, 74, 401–421.
- Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125–144.
- Naik, V., & Lee, M. (1990). General equilibrium pricing of options on the market portfolio with discontinuous returns. Review of Financial Studies, 3, 493–521.
- Neuberger, A. (1994). The log contract. Journal of Portfolio Management, 20, 74–80.
- Rietz, T. A. (1988). The equity risk premium a solution. Journal of Monetary Economics, 22, 117–131.
- Todorov, V., & Tauchen, G. (2011). Volatility jumps. Journal of Business and Economic Statistics, 29, 356–371.
- Vilkov, G., & Xiao, Y. (2013). Option-implied information and predictability of extreme returns. Working paper, Frankfurt, Germany: Frankfurt School of Finance and Management.
- Wachter, J. A. (2013). Can time-varying risk of rare disasters explain aggregate stock market volatility? Journal of Finance, 68, 987–1035.
