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Horizon Effect of Options in Predicting Index Returns

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Horizon Effect of Options in Predicting Index Returns Fear of Future: Horizon Effect of Options in Predicting Index Returns David Sun* Kainan University Shuai Qiao† Huazhong University of Science and Technology ABSTRACT Trading in options, as well as futures, has been shown to help forecasting movements in underlying securities. While put-call ratios have been used extensively in gauging the ‘fear’ of market about its further development, the option moneyness used in our study measures that fear more directly. Based on the idea of Fodor, Krieger and Doran (2011), we extend the formula of Bergsma, Csapi, Diavatopoulos and Fodor (2019) to show in this study that option moneyness exhibits a horizon effect, which says that in a longer horizon options forecast equity returns better than futures. Studying the Taiwan’s TXO index option, 5th in volume globally, we find option moneyness provides good information about index returns further in the future. Futures contracts, even as as a collector of information about the immediate future, perform not as good as option moneyness. Information on the longer horizons is only provided by option contracts of various expiration dates. With our analysis, information for longer horizons can be priced better, which elevates market thickness in general. Our results would benefit literature in understanding the price discovery function of options markets. The long horizon forecasting capability of option moneyness would also help investors in constructing effective hedges with options. Keywords: Price discovery, moneyness, forecasting, Kalman filter. JEL Classification: C11, C33, E22, E44, G2, G31 * Correspond author at: Department of Banking and Finance, Kainan University, Taoyuan, Taiwan 33857. † Correspond author at: Department of Economics and Finance, Huazhong University of Science and Technology, China 430074. 1. Introduction Futures, as well as options, markets have been argued to have provided useful information about their underlying markets. Those who have valuable information about future levels of underlying cash markets would prefer to engage trading in the futures markets (Stoll and Whaley, 1990; Antoniou, Koutmos, and Periclic, 2005) or options markets (Manaster and Renleman, 1982; Mihir, 1987; Easley, O’Hara, and Srinivas, 1998). Particularly on the movements of general equity markets, many works were on the relationship between equity indices and their futures (Kawaller, Koch and Koch, 1987; Stoll and Whaley, 1990; Hasbrouck, 2003), as well as the relationship between cash indices and index options (Joseph, 1988, Jens and Robert, 1990; Matthew, 1999), have been studied extensively, what simultaneous relationship lies among futures, options and underlying markets has also been of empirical interests in literature (Fung and Chan, 1994; Frank and Monique, 1998; Booth, So and Tse, 1999). Chakravarty, Gulen, and Mayhew (2004) found that on average, the information share of out-of-the-money (OTM) options is higher than that of at-the-money (ATM) options, suggesting that both leverage and liquidity are important in promoting price discovery. Motivated by the observation above we intend to examine in this study how forecasting future equity index can be improved with the help of an index option’s average moneyness (AM) across all contracts at various exercise prices of a given month. The improvement could be achieved, going through or together with a related index futures contract, either in a nearby or a distant month for the options and futures contract of interest. Observations from options market are also related to the motivation of this study. In general, open-interest based put-call ratio (PCR) is around 30% to 50% higher than the volume based one. Fodor, Krieger and Doran (2011) argued that individual call and 2 put open interest have predicting power about future stock return. Jena, Tiwari and Mitra (2019) found, based on data from the Nifty Index options, most active contract globally and accounting for two thirds of world volume, in India, open interest PCR is an efficient predictor of index return for a horizon of 12 days and volume PCR is only good for 2.5 days. Their results are robust after controlling for information from the futures contract on the same underlying. The structure of the options market in Taiwan supports the argument above in further details. Since the Taiwan Futures Exchange (TAIFEX), whose TXO index option is 5th in volume globally, launched in 2012 weekly expiring options on the side of existing monthly options, the volume for the former has been around 8 to 11 times that for the latter. But the daily open interest for the single-series weekly options is only about 20% higher than the over all open interest for the multi-series monthly options. So the volum-based PCR measure calculated daily is only one primarily gauging a short-horizon measure of ‘fear’. Market-wide open-interest-based PCR would still contain about 45% the kind of long-horizon ‘fear’ represented by figures from the monthly options. For the weekly options the open-interest-based PCR is about 30% higher than the volume-based one, and that difference for the monthly options is about 35%. But the composition of open-interest-based PCR obviously makes it more of a long-horizon ‘fear’ measure. The AM measure captures this exact spirit much better than PCR. One crucial distinction is that while PCR, whichever base is used, for the weekly contracts is higher than that for the monthly contracts, the weekly AM measure is on the contrary much lower than the monthly one. For the spot month put contract of the TAIFEX weekly index option, the open-interest-based AM is only 24.8% that of the corresponding monthly measure in terms of its distance above 1, whereas for the volume-based AM, the distance of weekly measure is 17.8% that of the monthly one. In this comparison, the AM measure seems to have revealed the long-horizon ‘fear’ 3 about market future better than PCR. It is in this regard that we investigate how index option AM can provide long-horizon information about the underlying cash index returns. On the definition of AM, we adopt a modified version from Bergsma, Csapi, Diavatopoulos and Fodor (2020). Our results in this study show that in a longer horizon, index options forecast underlying equity index better than index futures. AM of put options is better than that of call options in forecasting future index returns, and the pattern is more significant for contracts expiring in more distant months. Particularly, option moneyness exhibits a horizon effect, which says that in a longer horizon options forecast equity returns better than futures. we find option moneyness provides good information about index returns further in the future. Futures contracts, even as as a collector of information about the immediate future, perform not as good as option moneyness. Information on the longer horizons is only provided by option contracts of various expiration dates. Along a separate dimension, we place the currently dominant weekly options in the same analysis framework as that for their horizon-rich monthly counterpart. In addition to differences documented by general market statistics, we find that the short-horizon nature of the market, discouraged by the difficulty of taking advantage of leverage benefits, contains little information about long-horizon cash index. Compared with Pan and Poteshman (2006), our study, using AM instead, considers directly the issue of leverage benefits, which rewards information collection, by integrating trading volume or open interest with moneyness of individual strike prices. This construction allows us to compare information revelation across expiration dates and identify the effect of time horizon as suggested by Jena, et al. (2019). Our results would benefit literature in understanding how to price long-horizon information better in the absence of perfect foresight. The market for derivatives 4 expiring more distantly can become more active as it attracts more participants attempting to take advantage of their horizon-dependent information. This improvement elevates eventually market thickness in general and helps investors in constructing effective hedges with derivatives. A brief review of existing literature is given in Section 2, followed by the introduction of our econometric models in Section 3. Empirical results are reported in Section 4, with robustness discussion given in Section 5. Concluding remarks are given in Section 6. 2. Related literature Related to our study is the three-way relationship, among cash, futures and options investigated in literature primarily along a short-horizon approach with one period forecast. PCR is considered primarily as an informative measure, which obviously stresses positions in nearby, at-the-money options contracts. When PCR is used to extract information in the options markets, attention is placed more on short horizon expectations. As Christoffersen and Diebold (1998) particularly indicates that long-horizon forecasts need to be handle differently from near-horizon ones, we attempt to address the three-way relationship along a longer horizon with the help of option moneyness which, available currently, summarizes information on market prospects further into the future. Option moneyness, reflecting the extent of leverage assumed by option traders, was argued by Ge, Lin, and Pearson (2016) as a reason why options could predict stock returns. A number of works find that futures prices lead spot prices and contribute more to the price discovery process (Chan, 1992; Frino et al., 2000). It is often argued that price discovery occurs first in a market where informed traders profit most from their information. Futures markets offer higher leverages, lower trading costs, and fewer short-sale restrictions than spot markets (Black, 1975; Kawaller et al., 1987; Easley et 5 al., 1998). As informed traders prefer futures market for the reasons above, futures market responds to new information ahead of, and therefore can help predicting, spot markets (Finnerty and Park, 1987; Kawaller et al., 1987; Harris, 1989; Stoll et al., 1990; Chan, 1992).
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