Abstract
Motivated by the research of the variance risk premium (VRP) and MIDAS model, we employ the VRP with different maturities and the ADL-MIDAS regression model to forecast the expected stock return in Standard & Poor 500 market. The VRP is defined as the difference between the realized variance and the implied variance of the options. By using Standard & Poor 500 index options, we provide the empirical tests of the forecasting performance provided by the VRP with different maturities to the expected stock returns in the Standard & Poor 500 stock index market. Based on the empirical results, we know the VRP with 1-month and 2-month maturities can provide the best out-of-sample forecast.
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References
Aiolfi M, Timmermann A (2004) Structural breaks and the performance of forecast combinations. Working Paper
Andersen TG, Bollerslev T, Diebold FX, Labys P (2003) Modeling and forecasting realized volatility. Econometrica 71(2):579–625. https://doi.org/10.1111/1468-0262.00418
Andreou E, Ghysels E, Kourtellos A (2010) Forecasting with mixed-frequency data. Working paper
Andreou E, Ghysels E, Kourtellos A (2013) Should macroeconomic forecasters use daily financial data and how? J Bus Econ Stat 31(2):240–251. https://doi.org/10.1080/07350015.2013.767199
Ang A, Hodrick RJ, Xing Y, Zhang X (2006) The cross-section of volatility and expected returns. J Finance 61(1):259–299. https://doi.org/10.1111/j.1540-6261.2006.00836.x
Aruoba SB, Diebold FX, Scotti C (2009) Real-time measurement of business conditions. J Bus Econ Stat 27(4):417–427
Ba SS, Xia D (2019) Risk management and control of agricultural financial engineering in the process of mortgage securitization in rural areas based on sustainable agricultural development. Revista de la Facultad de Agronomia de la Universidad del Zulia 36(2):417–427
Bai J, Ghysels E, Wright JH (2013) State space models and MIDAS regressions. Econom Rev 32(7):779–813. https://doi.org/10.1080/07474938.2012.690675
Bakshi G, Kapadia N (2003) Delta-hedged gains and the negative market volatility risk premium. Rev Financ Stud 16(2):527–566. https://doi.org/10.1093/rfs/hhg002
Bakshi G, Madan D (2006) A theory of volatility spreads. Manage Sci 52(12):1945–1956. https://doi.org/10.1287/mnsc.1060.0579
Bandi FM, Russell JR (2008) Microstructure noise, realized volatility, and optimal sampling. Rev Econ Stud 75(May):339–369. https://doi.org/10.1111/j.1467-937X.2008.00474.x
Barndorff-Nielsen OE, Neil N (2002) Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J R Stat Soc 64(2):253–280
Bekaert G, Hoerova M (2014) The VIX, the variance risk premium and stock market volatility. J Econom J 183:181–192
Bekaert G, Engstrom E, Xing Y (2009) Risk, uncertainty, and asset prices. J Financ Econ 91(1):59–82. https://doi.org/10.1016/j.jfineco.2008.01.005
Bekaert G, Engstrom E, Grenadier SR (2010) Stock and bond returns with moody investors. J Empir Finance 17(5):867–894
Bollerslev T, Tauchen G, Zhou H (2009) Expected stock returns and variance risk premia. Rev Financ Stud 22(11):4463–4492. https://doi.org/10.1093/rfs/hhp008
Bollerslev T, Gibson M, Zhou H (2011) Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities. J Econom 160(1):235–245. https://doi.org/10.1016/j.jeconom.2010.03.033
Bollerslev T, Marrone J, Xu L, Zhou H (2014) Stock return predictability and variance risk premia: statistical inference and international evidence. J Financ Quant Anal 49(3):633–661. https://doi.org/10.1017/S0022109014000453
Britten J, Neuberger A (2000) Option prices, implied price processes, and stochastic volatility. J Finance 55(2):839–866
Capistrán C, Timmermann A (2009) Forecast combination with entry and exit of experts. J Bus Econ Stat 27(4):428–440
Carr P, Wu L (2009) Variance risk premiums. Rev Financ Stud 22(3):1311–1341. https://doi.org/10.1093/rfs/hhn038
Chen X, Ghysels E (2011) News—good or bad—and its impact on volatility predictions over multiple horizons. Rev Financ Stud 24(1):46–81
Chen X, Ghysels E, Wang F (2011) HYBRID-GARCH: a generic class of models for volatility predictions using mixed frequency data. Stat Sin 25:759–786. https://doi.org/10.2139/ssrn.1815762
Clements MP, Galvão AB (2008) Macroeconomic forecasting with mixed-frequency data. J Bus Econ Stat 26(4):546–554
Clements MP, Galvão AB (2009) Forecasting us output growth using leading indicators: an appaisal using MIDAS models. J Appl Econom 24(7):1187–1206. https://doi.org/10.1002/jae
Clements MP, Hendry DF (2002) Modelling methodology and forecast failure. Econom J 5(2):319–344. https://doi.org/10.1111/1368-423X.00086
Colacito R, Engle RF, Ghysels E (2011) A component model for dynamic correlations. J Econom 164(1):45–59. https://doi.org/10.1016/j.jeconom.2011.02.013
Corsi F (2009) A simple approximate long-memory model of realized volatility. J Financ Econom 7(2):174–196. https://doi.org/10.1093/jjfinec/nbp001
Corte PD, Ramadorai T, Sarno L (2016) Volatility risk premia and exchange rate predictability. J Financ Econ 120(1):21–40
Eklund J, Karlsson S (2007) Forecast combination and model averaging using predictive measures. Econom Rev 26(2–4):329–363
Elliott G, Timmermann A (2004) Optimal forecast combinations under general loss functions and forecast error distributions. J Econometrics 122(1):47–79. https://doi.org/10.1016/j.jeconom.2003.10.019
Elliott G, Timmermann A (2005) Optimal forecast combination under regime switching. Int Econ Rev 46(4):1081–1102
Engle RF, Ghysels E, Sohn B (2013) Stock market volatility and macroeconomic fundamentals. Rev Econ Stat 95(3):776–797
Forsberg L, Ghysels E (2007) Why do absolute returns predict volatility so well? J Financ Econom. https://doi.org/10.1093/jjfinec/nbl010
Ghysels E, Sinko A (2011) Volatility forecasting and microstructure noise. J Econom 160(1):257–271. https://doi.org/10.1016/j.jeconom.2010.03.035
Ghysels E, Santa-Clara P, Valkanov R (2005) There is a risk-return trade-off after all. J Financ Econ 76(3):509–548. https://doi.org/10.1016/j.jfineco.2004.03.008
Ghysels E, Santa-Clara P, Valkanov R (2006) Predicting volatility: getting the most out of return data sampled at different frequencies. J Econom 131(1–2):59–95. https://doi.org/10.1016/j.jeconom.2005.01.004
Ghysels E, Sinko A, Valkanov R (2007) MIDAS regressions: further results and new directions. Econom Rev 26(1):37–41. https://doi.org/10.1080/07474930600972467
Ghysels E, Rubia A, Valkanov R (2009) Multi-period forecasts of variance: direct, iterated, and mixed-data approaches. Working paper
Gonzalez-Urteaga A, Rubio G (2016) The cross-sectional variation of volatility risk premia. J Financ Econ. https://doi.org/10.1016/j.jfineco.2015.09.009
Guidolin M, Timmermann A (2009) Forecasts of US short-term interest rates: a flexible forecast combination approach. J Econom 150(2):297–311
Hendry DF, Clements MP (2004) Pooling of forecasts. Econom J 7(1):1–31. https://doi.org/10.1111/j.1368-423X.2004.00119.x
Hsiao C, Wan SK (2014) Is there an optimal forecast combination? J Econom 178(2):294–309. https://doi.org/10.1016/j.jeconom.2013.11.003
Jiang GJ, Tian YS (2005) The model-free implied volatility and its information content. Rev Financ Stud 18(4):1305–1342. https://doi.org/10.1093/rfs/hhi027
Lemke C, Gabrys B (2010) Meta-learning for time series forecasting and forecast combination. Neurocomputing 73(10–12):2006–2016
Londono JM, Zhou H (2017) Variance risk premiums and the forward premium puzzle. J Financ Econ 124(2):415–440. https://doi.org/10.1016/j.jfineco.2017.02.002
Marcellino M (2004) Forecast pooling for European macroeconomic variables. Oxford Bull Econ Stat 66(1):91–112
Meddahi N (2002) A theoretical comparison between integrated and realized volatility. J Appl Econom 17(5):479–508. https://doi.org/10.1002/jae.689
Pesaran MH, Pick A (2011) Forecast combination across estimation windows. J Bus Econ Stat 29(2):307–318
Stock JH, Watson MW (2001) Vector autoregressions. J Econ Perspect 15(4):101–115
Stock JH, Watson Mark W (2003) Combination forecasts of output growth in a seven-country data set. J Forecast 23(6):405–430
Stock JH, Watson MW (2004) An empirical comparison of methods for forecasting using many predictors. Manuscript
Stock JH, Watson MW (2008) Heteroskedasticity-robust standard errors for fixed effects panel data regression. Econometrica 76(1):155–174
Timmermann A (2006) Forecast combinations. In: Elliott G, Granger C, Timmermann A (eds) Handbook of economic forecasting, vol 1, pp 135–196. https://doi.org/10.1016/S1574-0706(05)01004-9
Wright JH (2009) Forecasting US inflation by Bayesian model averaging. J Forecast 28(2):131–144. https://doi.org/10.1002/for.1088
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Liu, R., Yang, J. & Ruan, C. Expected stock return and mixed frequency variance risk premium data. J Ambient Intell Human Comput 11, 3585–3596 (2020). https://doi.org/10.1007/s12652-019-01528-3
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DOI: https://doi.org/10.1007/s12652-019-01528-3