The ETF market has been growing rapidly in the last two decades as investors looked for ways to passively invest in markets or sectors without an active involvement. ETFs provide a cost-effective alternative in the form of higher liquidity levels, a way to avoid short-sale constraints in the stock market and a better price discovery process than their underlying assets individually. As a result, the financial landscape has seen a steady shift in the market share of the active sector in favor of the passive sector. Therefore, the ability to predict ETF returns has consequently grown in importance. Previous research around ETF return prediction using option information is scarce and its findings are based on the analysis of a few very large ETFs in general. However, the literature around the stock return predictability using measures from the derivative market such as option volume and option implied volatility is rich and actively growing. In this light, I decided to draw a bridge between these fields and investigate whether ETF returns can be predicted using the information in option volume and option implied volatility measures.
Past literature has shown that option volume measures such as the put-call ratio and options-to-shares ratio can negatively predict stock returns. Concerning implied volatility, measures like implied volatility spread and spread in implied volatility innovations have been shown to positively predict stock returns. I challenged these results by analyzing the behavior of these measures with the ETF returns from two standpoints: a portfolio-based analysis and a cross-sectional regression analysis. In the portfolio-based analysis, I single- and double-sorted ETFs into quintiles according to the main independent variables, the put-call ratio and the IV spread, then I analyzed the future returns of various trading strategies. In the second part, I used Fama-MacBeth (1973) regressions with controls to look at the results from a different point of view. The findings
were in favor of the IV spread positively predicting next-day ETF returns, while the put-call ratio did not display any consistent evidence of prediction potential.
In the first robustness check I demonstrated that the double-independent sorts using a continuous sorting process are more appropriate than the same procedure using a categorical sorting process. The results were nevertheless comparable. In consequence of this improved validity, I employed it for the remaining double sorts. In the second set of robustness checks, I used the to-shares ratio as an alternative independent option volume variable. The options-to-shares ratio could negatively predict ETF returns at 5 and 10 days in the future proving that option volume does contain relevant information about future returns if the right measure is investigated. Similarly, in the third alternative method, I used the spread in implied volatility innovations as a proxy for implied volatility and obtained similar results to the main analysis.
Lastly, I checked the analysis for options with 91-day expirations. The results differed in the sense that the IV spread negatively predicted ETF returns at 10 days in the future.
The implications of these results are diverse. First of all, from a technical point of view, this study proves that deviations from the put-call parity in the form of the IV spread can contain significant information about future ETF returns. By this, the positive news is associated with a rise in the popularity of calls and high subsequent ETF returns, and negative news is associated with a rise in the popularity of puts and low subsequent ETF returns, depending on the option expiration used and time horizon of returns.
Second of all, this brings me to the next point that the time to expiration of the options matters and that the timing is of the essence, proving to be two critical factors that draw a line between a profit and a loss in return predictability using option information.
Thirdly, the choice of measure used in the prediction process matters as depicted by the discrepancy between the put-call ratio and the options-to-shares ratio. Moreover, in the economic sense, the options-to-shares ratio significantly increases when negative news about future returns arrives. This shows that the informed investors turn to the options market to trade on that information. Similar implications regarding both types of news can be inferred also from the results of the implied volatility measures. Therefore, my study finds proof, and thu s supports the literature regarding the options market having a lead on the stock market, although this lead is temporary.
Also from the economic spectrum, it can be argued that this paper factually shows ways how the information from the market makes its way up into ETF prices. This process contributes
to a faster price discovery and a more efficient market overall since ETFs represent passive trading vehicles covering a broad, almost market-like, array of securities. This also has implications for policy-makers and global macro investors since being able to predict ETF returns essentially entails trying to predict the movements in the broad market or in specific market sectors. Therefore, the information in the option measures could aid the policy-makers in acting in a timely manner to the macroeconomic events and could motivate global macro investors to initiate or reinforce trading strategies on the market movements.
Nevertheless, I acknowledge that this research has its limitations. First of all, the setting of this analysis does not take into account transaction costs. I consider that further accounting for trading costs such as the bid-ask spreads, brokers’ fees and commissions, and possibly even market impact costs (Pedersen, 2015) could render the predictions unfeasible for trading. Secondly, I only use the IV spread of at-the-money options with expirations of 30 and 91 days as their high trading activity could better reflect information (Stephan & Whaley, 1990; Xing et al., 2010). The analysis could be extended by investigating an aggregate of the implied volatility spreads across all maturities, as Jin et al. (2012) do, or by creating individual implied volatility spreads for different levels of option moneyness as Atilgan et al. (2015) do. Similarly, the insignificant results of the put-call ratio using publicly available volume information strongly indicate that the use of signed option volume data as in the work of Pan and Poteshman (2006) can prove critical for determining its prediction potential. Another limitation stems from the low number of ETFs used in the analysis. As already shown, several factors constrained this outcome such as using ETFs solely from the U.S. market that had traded options available and that were available in the OptionMetrics database. To this end, expanding the sample to include ETFs from other geographic regions could provide additional observations.
Finally, these limitations create interesting avenues for future research to engage in. Further research could analyze the predictive ability of the option measures from this study by also quantifying transaction costs. Also, one could investigate which combinations of option expirations and levels of moneyness offer the highest level of predictability for ETF returns.
Likewise, the relevance of signed option volume data in the case of put-call ratio for ETFs is still a question to be answered. Moreover, future research could also expand this analysis for other ETF markets and other periods in the hopes of finding additional proof concerning the return predictive ability of option volume and option implied volatility. Additionally, one could also investigate the
viability of information in the options of the underlying assets for predicting ETF returns.
Similarly, future research could examine these findings by employing a different methodology than the one I adopt in this paper. In general, future research could also investigate different option measures than the ones I use in the hope of finding other valid predictors of ETF returns, as the evidence presented in this research endeavor clearly indicates that the predictive relation between the options market and ETFs is present and should by no means be neglected.
Reference List
Amihud, Y. (2002). Illiquidity and stock returns: cross-section and time-series effects. Journal of Financial Markets, 5(1), 31-56.
Amin, K. I., & Lee, C. M. (1997). Option trading, price discovery, and earnings news dissemination. Contemporary Accounting Research, 14(2), 153-192.
Amin, K., Coval, J. D., & Seyhun, H. N. (2004). Index option prices and stock market momentum. The Journal of Business, 77(4), 835-874.
An, B. J., Ang, A., Bali, T. G., & Cakici, N. (2014). The joint cross section of stocks and options. The Journal of Finance, 69(5), 2279-2337.
Anthony, J. H. (1988). The interrelation of stock and options market trading‐volume data. The Journal of Finance, 43(4), 949-964.
Atilgan, Y., Bali, T. G., & Demirtas, K. O. (2015). Implied volatility spreads and expected market returns. Journal of Business & Economic Statistics, 33(1), 87-101.
Bali, T. G., & Hovakimian, A. (2009). Volatility spreads and expected stock returns. Management Science, 55(11), 1797-1812.
Ben-David, I., Franzoni, F., & Moussawi, R. (2017). Exchange-traded funds. Annual Review of Financial Economics, 9, 169-189.
Beta Suite (2016). Beta Suite. Wharton Research Database. Retrieved from: https://wrds-www.wharton.upenn.edu/documents/1582/WRDS_Beta_Suite_Documentation_3T4EcS7 .pdf
Bhattacharya, M. (1987). Price changes of related securities: The case of call options and stocks. Journal of Financial and Quantitative Analysis, 22(1), 1-15.
Black, F. (1975). Fact and fantasy in the use of options. Financial Analysts Journal, 31(4), 36-41.
Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. The Journal of Political Economy, 81(3), 637-654.
Blume, L., Easley, D., & O'hara, M. (1994). Market statistics and technical analysis: The role of volume. The Journal of Finance, 49(1), 153-181.
Brennan, M. J., Chordia, T., & Subrahmanyam, A. (1998). Alternative factor specifications, security characteristics, and the cross-section of expected stock returns. Journal of Financial Economics, 49(3), 345-373.
Brown, D. C., Davies, S. W., & Ringgenberg, M. C. (2021). ETF arbitrage, non-fundamental demand, and return predictability. Review of Finance, 25(4), 937-972.
Canina, L., & Figlewski, S. (1993). The informational content of implied volatility. The Review of Financial Studies, 6(3), 659-681.
Cao, C., Chen, Z., & Griffin, J. M. (2005). Informational content of option volume prior to takeovers. The Journal of Business, 78(3), 1073-1109.
Carhart, M. M. (1997). On persistence in mutual fund performance. The Journal of Finance, 52(1), 57-82.
Chakravarty, S., Gulen, H., & Mayhew, S. (2004). Informed trading in stock and option markets. The Journal of Finance, 59(3), 1235-1257.
Chan, K., Chung, Y. P., & Fong, W. M. (2002). The informational role of stock and option volume. The Review of Financial Studies, 15(4), 1049-1075.
Chan, K., Chung, Y. P., & Johnson, H. (1993). Why option prices lag stock prices: A trading‐
based explanation. The Journal of Finance, 48(5), 1957-1967.
Chan, K., Ge, L., & Lin, T. C. (2015). Informational content of options trading on acquirer announcement return. Journal of Financial and Quantitative Analysis, 50(5), 1057-1082.
Chen, J., & Liu, Y. (2020). Bid and ask prices of index put options: Which predicts the underlying stock returns?. Journal of Futures Markets, 40(9), 1337-1353.
Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7(3), 229-263.
Cremers, M., & Weinbaum, D. (2010). Deviations from put-call parity and stock return predictability. Journal of Financial and Quantitative Analysis, 45(2), 335-367.
Diamond, D. W., & Verrecchia, R. E. (1987). Constraints on short-selling and asset price adjustment to private information. Journal of Financial Economics, 18(2), 277-311.
Dong, D., Liu, Q., Tao, P., & Ying, Z. (2021). The pricing mechanism between ETF option and spot markets in China. Journal of Futures Markets, 41(8), 1286-1300.
Easley, D., O'hara, M., & Srinivas, P. S. (1998). Option volume and stock prices: Evidence on where informed traders trade. The Journal of Finance, 53(2), 431-465.
Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383-417.
Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), 3-56.
Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81(3), 607-636.
Fia (2021). Global futures and options trading reaches record level in 2020. Retrieved from:
https://www.fia.org/resources/global-futures-and-options-trading-reaches-record-level-2020
Frazzini, A., & Pedersen, L. H. (2014). Betting against beta. Journal of Financial Economics, 111(1), 1-25.
Ge, L., Lin, T. C., & Pearson, N. D. (2016). Why does the option to stock volume ratio predict stock returns?. Journal of Financial Economics, 120(3), 601-622.
Glosten, L., Nallareddy, S., & Zou, Y. (2021). ETF activity and informational efficiency of underlying securities. Management Science, 67(1), 22-47.
Han, B., & Li, G. (2021). Information content of aggregate implied volatility spread. Management Science, 67(2), 1249-1269.
Han, J., Kim, D. H., & Byun, S. J. (2017). Informed trading in the options market and stock return predictability. Journal of Futures Markets, 37(11), 1053-1093.
Harvey, C. R., Liu, Y., & Zhu, H. (2016). … and the cross-section of expected returns. The Review of Financial Studies, 29(1), 5-68.
Jegadeesh, N. (1990). Evidence of predictable behavior of security returns. The Journal of Finance, 45(3), 881-898.
Jegadeesh, N., & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48(1), 65-91.
Jennings, R., & Starks, L. (1986). Earnings announcements, stock price adjustment, and the existence of option markets. The Journal of Finance, 41(1), 107-125.
Jin, W., Livnat, J., & Zhang, Y. (2012). Option prices leading equity prices: Do option traders have an information advantage?. Journal of Accounting Research, 50(2), 401-432.
Johnson, T. L., & So, E. C. (2012). The option to stock volume ratio and future returns. Journal of Financial Economics, 106(2), 262-286.
Jones, C. S., Mo, H., & Wang, T. (2018). Do option prices forecast aggregate stock returns?. Available at SSRN 3009490.
Karmaziene, E., & Sokolovski, V. (2022). Short-Selling Equity Exchange Traded Funds and Its Effect on Stock Market Liquidity. Journal of Financial and Quantitative Analysis, 57(3), 923-956.
Lee, C. M., & Swaminathan, B. (2000). Price momentum and trading volume. The Journal of Finance, 55(5), 2017-2069.
Lei, Q., Wang, X. W., & Yan, Z. (2020). Volatility spread and stock market response to earnings announcements. Journal of Banking & Finance, 119, 105126.
Lettau, M., & Madhavan, A. (2018). Exchange-traded funds 101 for economists. Journal of Economic Perspectives, 32(1), 135-54.
Li, F. W., & Zhu, Q. (2016). Synthetic shorting with ETFs. Work Pap., Univ. Tex., Austin.
Lin, T. C., Lu, X., & Driessen, J. (2013). Why do options prices predict stock returns?. Network for Studies on Pensions, Aging and Retirement.
Lo, A. W., & Wang, J. (2006). Trading volume: Implications of an intertemporal capital asset pricing model. The Journal of Finance, 61(6), 2805-2840.
Madhavan, A., & Sobczyk, A. (2016). Price dynamics and liquidity of exchange-traded funds. Journal of Investment Management, 14(2), 1-17.
Manaster, S., & Rendleman Jr, R. J. (1982). Option prices as predictors of equilibrium stock prices. The Journal of Finance, 37(4), 1043-1057.
Marshall, B. R., Nguyen, N. H., & Visaltanachoti, N. (2015). ETF liquidity. Work. Pap., Massey Univ.
Mayhew, S., & Mihov, V. (2004). How do exchanges select stocks for option listing?. The Journal of Finance, 59(1), 447-471.
McLean, R. D., & Pontiff, J. (2016). Does academic research destroy stock return predictability?. The Journal of Finance, 71(1), 5-32.
Muravyev, D., Pearson, N. D., & Broussard, J. P. (2013). Is there price discovery in equity options?. Journal of Financial Economics, 107(2), 259-283.
Newey, W. K., & West, K. D. (1987). A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica, 55(3), 703–708.
Ofek, E., & Richardson, M. (2003). Dotcom mania: The rise and fall of internet stock prices. The Journal of Finance, 58(3), 1113-1137.
Ofek, E., Richardson, M., & Whitelaw, R. F. (2004). Limited arbitrage and short sales restrictions:
Evidence from the options markets. Journal of Financial Economics, 74(2), 305-342.
Pan, J., & Poteshman, A. M. (2006). The information in option volume for future stock prices. The Review of Financial Studies, 19(3), 871-908.
Pedersen, L. H. (2015). Efficiently inefficient. In Efficiently Inefficient. Princeton University Press Roll, R., Schwartz, E., & Subrahmanyam, A. (2010). O/S: The relative trading activity in options
and stock. Journal of Financial Economics, 96(1), 1-17.
Scholes, M., & Williams, J. (1977). Estimating betas from nonsynchronous data. Journal of Financial Economics, 5(3), 309-327.
Stephan, J. A., & Whaley, R. E. (1990). Intraday price change and trading volume relations in the stock and stock option markets. The Journal of Finance, 45(1), 191-220.
Stoll, H. R. (1969). The relationship between put and call option prices. The Journal of Finance, 24(5), 801-824.
Wermers, R., & Xue, J. (2015). Intraday ETF trading and the volatility of the underlying. Work.
Pap., Univ. Md.
Xing, Y., Zhang, X., & Zhao, R. (2010). What does the individual option volatility smirk tell us about future equity returns?. Journal of Financial and Quantitative Analysis, 45(3), 641-662.
Zhou, Y. (2022). Option trading volume by moneyness, firm fundamentals, and expected stock returns. Journal of Financial Markets, 58, 100648.
Appendix A Factor Regressions
𝑅𝑡𝑆𝑡𝑟𝑎𝑡𝑒𝑔𝑦= 𝛼𝐶𝐴𝑃𝑀+ 𝛽1𝐶𝐴𝑃𝑀𝑀𝐾𝑇𝑡+ 𝜖𝑡, (A1)
𝑅𝑡𝑆𝑡𝑟𝑎𝑡𝑒𝑔𝑦 = 𝛼𝐹𝐹3+ 𝛽1𝐹𝐹3𝑀𝐾𝑇𝑡+ 𝛽2𝐹𝐹3𝑆𝑀𝐵𝑡+ 𝛽3𝐹𝐹3𝐻𝑀𝐿𝑡+ 𝜖𝑡, (A2)
𝑅𝑡𝑆𝑡𝑟𝑎𝑡𝑒𝑔𝑦= 𝛼𝐹𝐹4+ 𝛽1𝐹𝐹4𝑀𝐾𝑇𝑡+ 𝛽2𝐹𝐹4𝑆𝑀𝐵𝑡+ 𝛽3𝐹𝐹4𝐻𝑀𝐿𝑡+ 𝛽4𝐹𝐹4𝑀𝑂𝑀𝑡+ 𝜖𝑡, (A3) where RStrategyt represents the excess return, α is the expected abnormal return, MKTt is the market excess return, SMBt is the size factor, HMLt is the value factor, MOMt is the momentum factor and ϵt is the residual term, all at day t.
Appendix B
Standardization Procedure of the Continuous Sorting
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑒𝑑 𝑃/𝐶𝑖,𝑡 = −𝑃/𝐶𝑖,𝑡−𝑃/𝐶̅̅̅̅̅𝑖
√𝑣𝑎𝑟(𝑃/𝐶𝑖), (A4)
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑒𝑑 𝐼𝑉𝑆𝑖,𝑡 = 𝐼𝑉𝑆𝑖,𝑡−𝐼𝑉𝑆̅̅̅̅̅𝑖
√𝑣𝑎𝑟(𝐼𝑉𝑆𝑖), (A5)
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑎𝑡𝑖𝑜𝑛𝑖,𝑡 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑒𝑑 𝑃/𝐶𝑖,𝑡+ 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑒𝑑 𝐼𝑉𝑆𝑖,𝑡
2 , (A6)
where Standardized P/Ci,t represents the standardized put-call ratio, P/Ci,t represents the put-call ratio, Standardized IVSi,t represents the standardized IV spread, IVSi,t represents the IV spread, and Average standardizationi,t is the average of the two standardized measures of ETF i in day t.
The Standardized P/Ci,t has a negative sign in equation (A4) in order to reflect a descending sorting in the portfolio formation process.
Appendix C
Fama-MacBeth Regressions over Time
Table 1C
Predictability Over Time using Fama-MacBeth Cross-Sectional Regressions
Variable (1) (2) (3) (4) (5) (6)
Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t
Panel A: 2-day horizon
P/C 0.000 0.8 0.000 1.2 0.000 1.3 0.000 0.6
IVS −0.001 −1.2 −0.001 −0.7 −0.000 −0.6 −0.000 −0.4
Beta −0.000 −0.4 0.000 0.0 −0.000 −0.4 0.000 0.0 0.000 0.0 −0.000 −0.3
Size −0.000 −0.6 −0.000 −1.5 −0.000 −0.2 −0.000 −0.8 −0.000 −1.0 0.000 0.8
Illiq −0.000*** −3.0 −0.000* −1.9 −0.000*** −2.9 −0.000* −1.7 −0.000* −1.6 −0.000 −1.5
Rev −0.005 −0.6 −0.006 −0.7 −0.005 −0.6 −0.005 −0.6
Mom 0.005** 2.0 0.005* 1.9 0.005* 1.9 0.004* 1.7
Rvol 0.041*** 3.2 0.031** 2.4 0.043*** 3.3 0.033*** 2.6 0.032** 2.5
RIvol −0.004*** −4.7
C/P OI −0.000 −0.2 −0.000 −0.0 −0.000 −0.1 −0.000 −0.1 −0.000 −0.1 0.000 0.2
BA 0.000 0.8 0.000* 1.7 0.000 0.4 0.000 1.1 0.000 1.2 −0.000 −0.8
R2 0.22 0.05 0.22 0.05 0.06 −0.04
Panel B: 5-day horizon
P/C 0.000 1.0 0.000 1.5 0.000* 1.6 0.000 0.9
IVS −0.002* −1.8 −0.000 −0.5 −0.000 −0.5 −0.000 −0.0
Beta −0.000 −0.3 −0.000 −0.2 −0.000 −0.3 −0.000 −0.2 −0.000 −0.2 −0.000 −0.3
Variable (1) (2) (3) (4) (5) (6)
Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t
Size 0.000 0.0 −0.000 −0.3 −0.000 −0.1 −0.000 −0.4 −0.000 −0.7 0.000 0.6
Illiq −0.000** −2.2 −0.000 −1.4 −0.000** −2.3 −0.000 −1.3 −0.000 −1.3 −0.000 −1.4
Rev 0.016* 1.9 0.016* 1.8 0.016* 1.9 0.018** 2.2
Mom 0.005* 1.9 0.005* 1.9 0.005* 1.8 0.004* 1.6
Rvol 0.044*** 3.4 0.037*** 3.1 0.045*** 3.6 0.037*** 3.1 0.036*** 3.0
RIvol −0.003*** −4.5
C/P OI −0.000 −0.4 0.000 0.1 −0.000 −0.7 −0.000 −0.2 −0.000 −0.1 −0.000 −0.3
BA 0.000 0.2 0.000 0.5 0.000 0.3 0.000 0.7 0.000 0.8 −0.000 −0.6
R2 0.24 0.26 0.27 0.26 0.26 0.28
Panel C: 10-day horizon
P/C 0.000 0.8 0.000 0.6 0.000 0.8 0.000 0.5
IVS −0.002** −2.3 −0.001 −1.3 −0.001 −1.4 −0.001** −2.0
Beta −0.000 −0.3 −0.000 −0.7 −0.000 −0.3 −0.000 −0.7 −0.000 −0.7 −0.000 −0.7
Size 0.000 0.9 0.000 0.1 0.000 1.1 0.000 0.4 0.000 0.4 0.000 1.0
Illiq −0.000 −1.5 −0.000* −1.7 −0.000* −1.7 −0.000* −1.6 −0.000* −1.7 −0.000** −2.0
Rev 0.011 1.3 0.010 1.1 0.010 1.1 0.009 1.0
Mom 0.003 0.9 0.003 1.0 0.003 0.9 0.003 1.0
Rvol 0.042*** 3.2 0.039*** 3.3 0.042*** 3.3 0.041*** 3.6 0.040*** 3.5
RIvol −0.003*** −4.2
C/P OI −0.000 −0.1 0.000 0.4 −0.000 −0.2 0.000 0.4 0.000 0.6 0.000 0.8
BA −0.000 −0.6 0.000 0.2 −0.000 −0.8 −0.000 −0.1 −0.000 −0.1 −0.000 −0.9
R2 0.24 0.09 0.24 0.11 0.11 0.11
Note. This table presents Fama-MacBeth (1973) cross-sectional daily regressions of future ETF returns on the main independent variables, the put-call ratio (P/C) and the IV spread (IVS), while controlling for the market beta (Beta), lognormal market capitalization (Size), Amihud’s (2002) illiquidity measure (Illiq), short-term reversal (Rev), momentum (Mom), realized volatility (Rvol), realized-implied volatility spread of Bali and Hovakimian (2009) (RIvol), call-put open interest (C/P OI) and the bid-ask spread (BA). Panel A reports the regressions for ETF returns at the 2-day horizon, Panel B reports regressions on ETF returns at the 5-day horizon and Panel C reports regressions on ETF returns at the 10-day horizon. The average slope coefficients and their Newey-West (1987) t-statistics adjusted for time horizons are reported for each regression in the columns “Coeff.” and “t”, respectively. The last row in each panel presents the average R2 of each regression. Significance levels are indicated by *p < .10, **p < .05 and ***p <
.01.
Appendix D
Continuous Double Sorts over Time Robustness Checks
Table 1D
Predictability Over Time using Continuous Double Sorts Return Horizon
Return t-stat.
CAPM FF3 FF4
Alpha t-stat. Alpha t-stat. Alpha t-stat.
D = 2 0.013 1.1 0.012 0.9 0.014 1.1 0.015 1.2
D = 5 −0.015 −1.3 −0.014 −1.1 −0.014 −1.1 −0.014 −1.1
D = 10 −0.021** −2.0 −0.018* −1.7 −0.016* −1.6 −0.017* −1.6
Note. This table reports the performance of the main trading strategy based on double-independent sorts of future ETF excess returns at horizons D = 2, 5 or 10 trading days. ETF excess returns are independently sorted into quintiles based on a continuous sorting procedure on the put-call ratio and the IV spread simultaneously, generating five equal-weighted portfolios on each day. Further details on this continuous sorting aspect of this procedure are given in the methodology section. This table reports the future excess returns of a trading strategy that goes long on the portfolio with the lowest put-call ratio and the highest IV spread and goes short on the portfolio with the highest put-call ratio and the lowest IV spread. Column
“Return” presents the average daily excess ETF return for the strategy. The next three columns report the alphas of the CAPM, Fama and French (1993) three-factor model (FF3), and the four-factor Fama and French (1993) with Carhart’s (1997) momentum (FF4) model. For each estimate, the respective Newey-West (1987) t-statistic is given in the “t-stat.” column to the right. Excess returns are calculated by subtracting the risk-free rate from the ETF returns. Significance levels are indicated by *p < .10. **p < .05.
***p < .01.
Appendix E
Options-to-Shares Ratio Robustness Checks
Table 2E
Correlations Across Variables When using Options-to-Shares Ratio as Option Volume Variable
Variable 1 2 3 4 5 6 7 8
1. Volume calls −
2. Volume puts .96 −
3. O/S .67 .66 −
4. Call implied volatility .02 .01 .01 −
5. Put implied volatility .01 .00 .00 .95 −
6. IVS .02 .02 .02 .17 −.15 −
7. Trading volume .77 .78 .51 .12 .11 .03 −
8. Realized volatility .01 .00 .00 .85 .86 −.03 .08 −
Table 1E
Descriptive Statistics for The Options-to-Shares Ratio
Year
O/S
M SD
2013 13.97 40.33
2014 12.72 36.20
2015 14.48 43.47
2016 13.38 41.87
2017 15.62 49.33
2018 15.71 50.61
2019 16.75 54.07
2020 19.08 63.42
Whole Sample 15.21 48.16
Note. The averages and standard deviations of the options-to-shares ratio (O/S) for the ETFs are reported on a yearly basis from January 2013 to December 2020. The figures are expressed in percentages. The last row reports the average and the standard deviation over the whole sample.
Note. This table reports ETF cross-correlations of the volume of calls and puts, the options-to-shares ratio (O/S), the implied volatilities of calls and puts, the implied volatility spread (IVS), share trading volume and realized volatility.
Table 3E
Portfolios Sorted on Options-to-Shares Ratio Excess
Return
CAPM Alpha
FF3 Alpha
FF4
Alpha O/S IVS Size Rvol
Quintile portfolio
1 (Low O/S) 0.043 −0.009 −0.003 −0.003 0.030 −0.610 21.826 0.914
2 0.048 −0.006 0.001 −0.000 0.277 −0.664 22.509 0.917
3 0.045 −0.008 −0.002 −0.002 1.034 −0.574 22.488 0.965
4 0.056 −0.008 −0.003 −0.004 4.809 −0.656 22.047 1.175
5 (High O/S) 0.046 −0.010 −0.008 −0.009 69.230 −0.491 22.777 1.136
5-1 0.003 −0.001 −0.005 −0.006
t-stat. 0.6 −0.1 −1.0 −1.1
Note. Equal-weighted quintile portfolios are formed daily by sorting next-day ETF returns based on the options-to-shares ratio (O/S). Quintile portfolio 1 (5) contains next-day ETF returns with the lowest (highest) O/S ratio. Column “Excess Return” presents the average daily excess ETF return for each quintile portfolio. The next three columns report the alphas of the CAPM, Fama and French (1993) three-factor model (FF3), and the four factors Fama and French (1993) with Carhart’s (1997) momentum (FF4) model.
Then, the averages of options-to-shares ratio (O/S), IV spread (IVS), Size and realized volatility (Rvol) are reported for each quintile portfolio. These variables are further defined in the methodology section of this paper. The row “5-1” reports the average next-day excess return of a portfolio which takes a long position in the quintile portfolio 5 and a short position in the quintile portfolio 1. Newey-West (1987) t-statistics are given in the “t-stat.” row. The excess returns are obtained by subtracting the risk-free rate from each ETF return for each day. Excess returns, options-to-shares ratio, IV spread and realized volatility are reported in percentages. Significance levels are indicated by *p < .10, **p < .05 and ***p < .01.
Table 4E
Main Trading Strategy from Continuous Double Sorts on Options-to-Shares Ratio and Implied Volatility Spread
Return t-stat. CAPM FF3 FF4
Alpha t-stat. Alpha t-stat. Alpha t-stat.
Main long-short
strategy 0.026* 1.7 0.021 1.2 0.023 1.3 0.023 1.4
Note. The next-day ETF excess returns are independently sorted into quintiles based ona continuous sorting procedure on the O/S ratio and the IV spread simultaneously, generating five equal-weighted portfolios on each day. Further details on this continuous sorting aspect of this procedure are given in the methodology section. This table reports the next-day excess return of a trading strategy that goes long on the portfolio with the lowest O/S ratio and the highest IV spread and goes short on the portfolio with the highest O/S ratio and the lowest IV spread. This trading strategy is named the “main long-short strategy”. Column
“Return” presents the average daily excess ETF return for the strategy. The next three columns report the alphas of the CAPM, Fama and French (1993) three-factor model (FF3), and the four factors Fama and French (1993) with Carhart’s (1997) momentum (FF4) model. For each estimate, the respective Newey-West (1987) t-statistic is given in the “t-stat.” column to the right. Excess returns are calculated by subtracting the risk-free rate from the ETF returns and are reported in percentages. Significance levels are indicated by *p < .10, **p < .05 and ***p < .01.
Table 5E
Predictability Over Time using Continuous Double Sorts on Options-to-Shares Ratio and Implied Volatility Spread
Return Horizon
Return t-stat.
CAPM FF3 FF4
Alpha t-stat. Alpha t-stat. Alpha t-stat.
D = 2 0.011 0.7 0.008 0.5 0.011 0.7 0.013 0.8
D = 5 −0.006 −0.4 −0.006 −0.4 −0.006 0.4 −0.005 −0.3
D = 10 −0.018 −1.4 −0.016 −1.2 −0.013 −1.0 −0.013 −1.0
Note. This table reports the performance of the main trading strategy based on double-independent sorts of future ETF excess returns at horizons D = 2, 5 or 10 trading days. ETF excess returns are independently sorted into quintiles based on a continuous sorting procedure on the O/S ratio and the IV spread simultaneously, generating five equal-weighted portfolios on each day. Further details on this continuous sorting aspect of this procedure are given in the methodology section. This table reports the future excess returns of a trading strategy that goes long on the portfolio with the lowest O/S ratio and the highest IV spread and goes short on the portfolio with the highest O/S ratio and the lowest IV spread. Column “Return”
presents the average daily excess ETF return for the strategy. The next three columns report the alphas of the CAPM, Fama and French (1993) three-factor model (FF3), and the four-factor Fama and French (1993) with Carhart’s (1997) momentum (FF4) model. For each estimate, the respective Newey-West (1987) t-statistic is given in the “t-stat.” column to the right. Excess returns are calculated by subtracting the risk-free rate from the ETF returns. Significance levels are indicated by *p < .10. **p < .05. ***p < .01.
Table 6E
Fama-MacBeth Cross-Sectional Regressions with Options-to-Shares Ratio and Implied Volatility Spread
Variable (1) (2) (3) (4) (5) (6)
Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t
O/S −0.000 −1.5 −0.000 −1.1 −0.000 −1.2 −0.000** −2.3
IVS 0.006*** 6.1 0.004*** 4.4 0.004*** 4.4 0.004*** 4.1
Beta −0.000 −0.3 0.000 0.1 −0.000 −0.3 0.000 0.2 0.000 0.2 −0.000 −0.0
Size −0.000 −0.1 −0.000 −0.5 −0.000 −0.8 −0.000 −1.1 −0.000 −0.7 0.000 0.9
Illiq −0.000** −2.3 −0.000*** −2.7 −0.000*** −2.7 −0.000*** −3.2 −0.000*** −3.2 −0.000*** −2.7
Rev −0.067*** −7.7 −0.065*** −7.5 −0.065*** −7.6 −0.064*** −7.3
Mom 0.006** 2.0 0.006** 2.1 0.006** 2.2 0.005* 1.8
Rvol 0.040*** 3.0 0.026** 2.0 0.041*** 3.2 0.027** 2.2 0.029** 2.2
RIvol −0.003*** −4.3
C/P OI −0.000 −1.1 −0.000 −0.9 −0.000 −1.2 −0.000 −1.1 −0.000 −1.2 −0.000 −0.9
BA 0.000 0.4 0.000 0.8 0.000 1.1 0.000 1.4 0.000 1.0 −0.000 −0.7
R2 0.18 1.22 0.34 1.27 1.27 1.27
Note. This table presents Fama-MacBeth (1973) cross-sectional daily regressions of next-day ETF returns on the independent variables, the options-to-shares ratio (O/S) and the IV spread (IVS), while controlling for the market beta (Beta), lognormal market capitalization (Size), Amihud’s (2002) illiquidity measure (Illiq), short-term reversal (Rev), momentum (Mom), realized volatility (Rvol), realized-implied volatility spread of Bali and Hovakimian (2009) (RIvol), call-put open interest (C/P OI) and the bid-ask spread (BA). The average slope coefficients and their Newey-West (1987) t-statistics are reported for each regression in the columns “Coeff.” and “t”, respectively. The last row presents the average R2 of each regression.
Significance levels are indicated by *p < .10, **p < .05 and ***p < .01.
Table 7E
Predictability Over Time using Fama-MacBeth Cross-Sectional Regressions with Options-to-Shares Ratio
Variable (1) (2) (3) (4) (5) (6)
Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t
Panel A: 2-day horizon
O/S −0.000 −0.7 −0.000 −0.0 −0.000 −0.1 −0.000 −1.3
IVS −0.001 −1.2 −0.001 −0.7 −0.001 −0.7 −0.000 −0.5
Beta −0.000 −0.4 −0.000 −0.0 −0.000 −0.4 0.000 0.0 −0.000 −0.0 −0.000 −0.3
Size −0.000 −0.1 −0.000 −1.0 −0.000 −0.2 −0.000 −0.8 −0.000 −0.6 0.000 1.4
Illiq −0.000*** −3.0 −0.000** −2.0 −0.000*** −2.9 −0.000* −1.7 −0.000* −1.7 −0.000* −1.6
Rev −0.006 −0.7 −0.006 −0.7 −0.006 −0.7 −0.005 −0.6
Mom 0.005** 2.0 0.005* 1.9 0.005* 1.9 0.004* 1.7
Rvol 0.044*** 3.2 0.034*** 2.6 0.043*** 3.3 0.033*** 2.6 0.036*** 2.7
RIvol −0.004*** −5.0
C/P OI −0.000 −0.3 −0.000 −0.1 −0.000 −0.1 −0.000 −0.1 −0.000 −0.1 0.000 0.1
BA 0.000 0.4 0.000 1.3 0.000 0.4 0.000 1.1 0.000 0.8 −0.000 −1.3
R2 0.23 0.06 0.22 0.05 0.06 −0.04
Panel B: 5-day horizon
O/S −0.000** −2.1 −0.000* −1.7 −0.000* −1.7 −0.000** −2.2
IVS −0.002* −1.8 −0.000 −0.5 −0.000 −0.6 −0.000 −0.1
Beta −0.000 −0.4 −0.000 −0.3 −0.000 −0.3 −0.000 −0.2 −0.000 −0.3 −0.000 −0.4
Size 0.000 0.9 0.000 0.7 −0.000 −0.1 −0.000 −0.4 0.000 0.4 0.000* 1.6
Illiq −0.000** −2.2 −0.000 −1.3 −0.000** −2.3 −0.000 −1.3 −0.000 −1.2 −0.000 −1.2
Rev 0.016* 1.9 0.016* 1.8 0.016* 1.9 0.018** 2.2
Variable (1) (2) (3) (4) (5) (6)
Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t Coeff. t
Mom 0.005** 2.0 0.005* 1.9 0.005* 1.9 0.004* 1.6
Rvol 0.050*** 3.7 0.042*** 3.4 0.045*** 3.6 0.037*** 3.1 0.041*** 3.3
RIvol −0.004*** −4.9
C/P OI −0.000 −0.6 −0.000 −0.2 −0.000 −0.7 −0.000 −0.2 −0.000 −0.4 −0.000 −0.5
BA −0.000 −0.6 −0.000 −0.4 0.000 0.3 0.000 0.7 −0.000 −0.1 −0.000 −1.4
R2 0.26 0.28 0.27 0.26 0.28 0.29
Panel C: 10-day horizon
O/S −0.000* −1.8 −0.000 −1.5 −0.000* −1.8 −0.000* −1.7
IVS −0.002** −2.3 −0.001 −1.3 −0.001 −1.3 −0.002** −2.0
Beta −0.000 −0.3 −0.000 −0.7 −0.000 −0.3 −0.000 −0.7 −0.000 −0.8 −0.000 −0.8
Size 0.000 1.5 0.000 0.8 0.000 1.1 0.000 0.4 0.000 1.0 0.000* 1.6
Illiq −0.000 −1.4 −0.000* −1.7 −0.000* −1.7 −0.000* −1.6 −0.000* −1.6 −0.000** −2.0
Rev 0.012 1.3 0.010 1.1 0.011 1.2 0.010 1.1
Mom 0.002 0.9 0.003 1.0 0.002 0.9 0.003 1.0
Rvol 0.045*** 3.4 0.042*** 3.4 0.042*** 3.3 0.041*** 3.6 0.044*** 3.5
RIvol −0.003*** −4.3
C/P OI −0.000 −0.4 −0.000 −0.0 −0.000 −0.2 0.000 0.4 0.000 0.1 0.000 0.4
BA −0.000 −1.1 −0.000 −0.4 −0.000 −0.8 −0.000 −0.1 −0.000 −0.7 −0.000 −1.4
R2 0.25 0.10 0.24 0.11 0.12 0.12
Note. This table presents Fama-MacBeth (1973) cross-sectional daily regressions of future ETF returns on the main independent variables, the options-to-shares ratio (O/S) and the IV spread (IVS), while controlling for the market beta (Beta), lognormal market capitalization (Size), Amihud’s (2002)
illiquidity measure (Illiq), short-term reversal (Rev), momentum (Mom), realized volatility (Rvol), realized-implied volatility spread of Bali and Hovakimian (2009) (RIvol), call-put open interest (C/P OI) and the bid-ask spread (BA). Panel A reports the regressions for ETF returns at the 2-day horizon, Panel B reports regressions on ETF returns at the 5-day horizon and Panel C reports regressions on ETF returns at the 10-day horizon. The average slope coefficients and their Newey-West (1987) t-statistics adjusted for time horizons are reported for each regression in the columns “Coeff.”
and “t”, respectively. The last row in each panel presents the average R2 of each regression. Significance levels are indicated by *p < .10, **p < .05 and
***p < .01.
Appendix F
Spread in Implied Volatility Innovations Robustness Checks
Table 2F
Correlations Across Variables When using The Spread of Implied Volatility Innovations as Implied Volatility Variable
Variable 1 2 3 4 5 6 7 8
1. Volume calls −
2. Volume puts .96 −
3. P/C .08 .10 −
4. Call implied volatility .02 .01 .05 −
5. Put implied volatility .01 .00 .05 .95 −
6. CPV −.00 −.00 .00 .12 −.09 −
Table 1F
Descriptive Statistics forThe Spread of Implied Volatility Innovations
Year CPV
M SD
2013 0.0034 1.9069
2014 0.0097 3.2234
2015 −0.0002 6.0437
2016 −0.0057 5.3363
2017 0.0071 3.7845
2018 −0.0210 4.3513
2019 0.0145 3.4872
2020 0.0003 7.1260
Whole Sample 0.0010 4.6837
Note. The averages and standard deviations of the spread in implied volatility innovations (CPV) for the ETFs are reported on a yearly basis from January 2013 to December 2020. The figures are expressed in percentages. The last row reports the average and the standard deviation over the whole sample.
7. Trading volume .77 .78 .15 .12 .11 −.00 −
8. Realized volatility .01 .00 .03 .85 .86 −.00 .08 −
Note. This table reports ETF cross-correlations of the volume of calls and puts, the put-call ratio (P/C), the implied volatilities of calls and puts, the spread in implied volatility innovations (CPV), share trading volume and realized volatility.
Table 3F
Portfolios Sorted on Spread of Implied Volatility Innovations Excess
Return
CAPM Alpha
FF3 Alpha
FF4
Alpha P/C CPV Size Rvol
Quintile portfolio
1 (Low CPV) 0.040 −0.014 −0.007 −0.007 33.072 −3.824 21.973 1.077
2 0.052 −0.002 0.002 0.002 37.046 −0.899 22.546 0.980
3 0.047 −0.008 −0.005 −0.005 37.269 0.001 22.630 0.972
4 0.051 −0.006 −0.002 −0.002 36.346 0.895 22.543 0.986
5 (High CPV) 0.048 −0.011 −0.005 −0.006 33.648 3.833 21.967 1.083
5-1 0.008 0.003 0.002 0.001
t-stat. 0.5 0.1 0.1 0.0
Note. In Panel B, equal-weighted quintile portfolios are formed daily by sorting ETF returns based on the spread in implied volatility innovations (CPV). Quintile portfolio 1 (5) contains next-day ETF returns with the lowest (highest) spread in implied volatility innovations. Column “Excess Return” presents the average daily excess ETF return for each quintile portfolio. The next three columns report the alphas of the CAPM, Fama and French (1993) three-factor model (FF3), and the four factors Fama and French (1993) with Carhart’s (1997) momentum (FF4) model. Then, the averages of put-call ratio (P/C), the spread in implied volatility innovations (CPV), Size and realized volatility (Rvol) are reported for each quintile portfolio.
These variables are further defined in the methodology section of this paper. The row “5-1” reports the average next-day excess return of a portfolio which takes a long position in the quintile portfolio 5 and a short position in the quintile portfolio 1. Newey-West (1987) t-statistics are given in the “t-stat.” row. The excess returns are obtained by subtracting the risk-free rate from each ETF return for each day. Excess returns, put-call ratio, the spread in implied volatility innovations and realized volatility are reported in percentages. Significance levels are indicated by *p < .10, **p < .05 and ***p < .01.