Measuring the Disposition Effect on the Option Market: New Evidence

Measuring the Disposition Effect on the Option Market: New Evidence Mi-Hsiu Chiang Department of Money and Banking College of Commerce National Chengchi University Hsin-Yu Chiu Department of Money and Banking College of Commerce National Chengchi University Robin K. Chou Department of Finance and Risk and Insurance Research Center College of Commerce National Chengchi University Address correspondence to Robin K. Chou, Department of Finance, College of Commerce, National Chengchi University, 64 Zhinan Road Sec. 2, Taipei, Taiwan. Tel.: +886-2-29393091; e-mail: rchou@nccu.edu.tw. Robin K. Chou gratefully acknowledges financial support from the Ministry of Science and Technology of Taiwan (No. 101-2410-H-004-067-MY3) and from the National Natural Science Foundation of China (Nos. 71232004, 71373296, 71372137 and 70902030). Mi-Hsiu Chiang gratefully acknowledges financial support from the Ministry of Science and Technology of Taiwan (No. 103-2410-H-004-032-MY2). 1

Measuring the Disposition Effect on the Option Market: New Evidence Abstract We test the disposition effect on the index option markets. We argue that moneyness, the most salient and readily available information for option investors, is a natural reference point for gauging potential gains and losses and likely attracts market participants attention better than traditional disposition measures based on past trading prices. We propose the moneyness-based propensity to sell (MPS) measure and test it along with the adjusted capital gains overhang (ACGO) measure of Grinblatt and Han (2005). We find that a zero-cost strategy formed by buying options with high MPS or ACGO and selling options with low MPS or ACGO generates significant abnormal returns, indicating the presence of the disposition effect. More important, we show that MPS captures the disposition effect on the option market better than ACGO. JEL classification: G02; G14 Keywords: Disposition Effects, Moneyness, Option Markets, Capital Gains Overhang 2

1. Introduction The disposition effect refers to the tendency of individual investors to sell their winning investments (winners) sooner than their losing investments (losers). The strength of the disposition effect depends on investors characteristics. Sophisticated traders, in particular, exhibit a lower disposition effect (Feng and Seasholes, 2005; Dhar and Zhu, 2006; Hur, Pritamani and Sharma, 2010). Although the disposition effect is an empirical phenomenon that is widely observed in many financial settings, such as the stock and real estate markets, and in the exercise of executive stock options, 1 relatively little attention has been paid to the option market, where most informed investors and sophisticated traders gather. 2 The existing literature notes the unlimited upside potential and limited downside risk of call options, which tend to attract investors with skewed preferences (speculative motives). Heath, Huddart, and Lang (1999) find that employees are more likely to exercise their options when stock prices exceed a maximum price over the previous year. Poteshman (2001) examines the option market reaction to the instantaneous variance of the underlying asset and finds that option investors tend to underreact to daily changes in volatility. Poteshman and Serbin (2003) find that option investors engage in irrational early excises of exchange-traded options if the underlying stock price reaches a highest level that exceeds the previous year. 1 Odean (1998) and Grinblatt and Keloharju (2001) find trading patterns of stock investors in the United States and Finland exhibit the disposition effect. Frazzini (2006) analyzes mutual fund holdings from 1980 to 2002 and reports that mutual fund managers also exhibit the disposition effect. Coval and Shumway (2005) find the disposition effect for T-bond futures traders of Chicago Board of Trade. Genesove and Mayer (2001) find sellers are averse to realizing losses in the real estate markets, and Heath, Huddart, and Lang (1999) find evidence of the disposition effect in the exercise of executive stock options. 2 Black (1975) argues that options are more attractive to informed investors than the underlying stocks because the payoff of an option is truncated at the strike price. Chakravarty, Gulen, and Mayhew (2004), Pan and Poteshman (2006) and Ni, Pan, and Poteshman (2008) provide empirical evidence that informed traders use options to trade on directional and volatility information. 3

Bali and Murray (2013) and Boyer and Vorkink (2014) show that low returns of individual stock options are associated with high expected skewness, and option investors exhibit positively skewed preferences. We test whether the disposition effect exists on the option market, and, more important, we propose a moneyness-based disposition measure to determine the disposition effect in option trading. We argue that moneyness is a natural reference point for potential gains and losses and likely attracts option traders attention better than the traditional unrealized capital gains or losses measures based on past trading prices commonly used in the prior literature to test the disposition effect on the stock market. Moneyness is a salient feature of options that is not applicable to the stock market and thus is unique to the option market. To test our hypothesis, we devise a moneyness-based propensity to sell (MPS) measure calculated as the trading-volume weighted average of an option s intrinsic value over the 5-, 10-, and 20-day periods prior to the trading date. We then compare the explanatory power of MPS to that of adjusted capital gains overhang (ACGO), the traditional measure of the disposition effect. Similar to Grinblatt and Han (2005), ACGO uses the trading-volume weighted average of lagged option prices (i.e., cost basis) as the reference price for gain and loss calculations. Although option prices are vital for calculating trading profits and losses, an option s intrinsic value is the most salient and readily available information that is likely to attract market participants immediate attention a scarce cognitive resource (Kahneman, 1973; Hirshleifer and Teoh, 2003; Peng and Xiong, 2006). Our research design mostly follows that of Grinblatt and Han (2005) and Bhootra and Hur (2014). We use daily transactions of S&P 500 index options obtained from OptionMetrics. On a weekly basis, all call or put options on the S&P 500 index are first sorted into an ascending order of five quintiles by MPS and ACGO, respectively. On each 4

quintile, we construct a quintile portfolio with equally weighted call or put options. We then calculate the average weekly return for each MPS and ACGO quintile portfolio. Grinblatt and Han associate the disposition effect to prospect theory and mental accounting. 3 For an asset with higher (lower) capital gains overhang, the disposition effect induces a positive (negative) spread between the asset s fundamental value and its price, which then generates price momentum. 4 As a direct consequence of spread convergence between the asset s fundamental value and its price, the long short strategy of buying the quintile portfolio with the highest MPS or ACGO ranking (i.e., winners) and selling the quintile portfolio with the lowest MPS or ACGO ranking (i.e., losers) should generate abnormal returns. Accordingly, we construct long short portfolios (5 1 portfolios), which buys options in the highest MPS or ACGO quintiles and simultaneously shorts options in the lowest MPS or ACGO quintiles. To test the hypothesis that the disposition effect drives the abnormal returns of the 5 1 portfolios, we regress the portfolio weekly returns on a set of risk factors that are well-known as important determinants of option returns. We allow the quintile portfolios to consist of both call and put options so that the 5 1 portfolios proxy for the difference in the weekly call or put portfolio returns of the winners and losers. Due to the overpriced puts puzzle (Broadie, Chernov, and Johannes, 2009; Bondarenko, 2014), which is particularly pronounced for the 3 Grinblatt and Han (2005) argue that Kahneman and Tversky s (1979) prospect theory and Thaler s (1980) mental accounting framework are the leading explanations for the disposition effect. The prospect theory employs an S-shaped value function that is risk-averse in the domain of gains and risk-seeking in the domain of losses. The domain of gains and losses is measured relative to a reference point. The mental accounting depicts the way in which decision makers set reference points for the accounts that determine gains and losses. 4 Jegadeesh and Titman (1993) report a predictable price pattern that firms with high returns over the past three months to one year continue to outperform firms with low past returns over the same period. Rouwenhorst (1998), Jegadeesh and Titman (2001) and Kang, Liu, and Ni (2002) find that a momentum strategy utilizing the predictable price pattern by buying past winners and selling past losers generates abnormal returns. 5

out-of-the-money (OTM) put options, as a robustness check we remove options with moneyness below 0.98 and above 1.02 and rerun all analyses. 5 The results remain qualitatively the same. Our empirical findings are threefold. First, average returns of the quintile portfolios with calls or puts monotonically increase across all MPS and ACGO quintiles, indicating that options with larger capital gains overhang outperform options with lower capital gains overhang. For example, the returns of the quintile portfolios with call (put) options increase from 9.31% ( 17.52%) in the lowest MPS quintile to 1.12% ( 3.89%) in the highest MPS quintile. Second, the average returns of the 5 1 portfolios are significantly greater than zero, even after controlling for known risk factors, indicating the impact of the disposition effect on the option market. That is, the 5 1 strategy utilizing the disposition effect-induced momentum generates significantly positive abnormal returns. The results are more pronounced for put options than for call options. The results on the returns of the 5 1 option portfolios remain robust even when we only include the options with moneyness ranging from 0.98 to 1.02 and time-to-maturities of less than 30 days. In addition, the abnormal returns generated by the 5 1 portfolios are robust when the quintile portfolios are constructed by delta-hedged option returns. Finally, and most important, the 5 1 portfolio constructed by sorting options with the MPS measure produces a higher abnormal return than that of the ACGO measure. Using double sorting methods, we find that the returns of the 5 1 option portfolio formed using MPS cannot be fully explained by the ACGO measure. This result supports our hypothesis 5 The overprized put puzzle refers to the empirical phenomenon that historic prices of the S&P index puts are overly high and cannot be explained by existing asset-pricing models. 6

that moneyness is a natural reference point for option buying and selling decisions. Given that attention is a limited cognitive resource, it is likely allocated to the most salient information that can be easily recognized and is readily available. Moneyness is easier to calculate than unrealized capital gains and losses. Thus option traders implicitly measure gains and losses based on option moneyness, a salient and readily available feature that is unique to option trading. Accordingly, they are more likely to make decisions based on moneyness than capital gains overhang. The remainder of this paper is organized as follows. Section 2 introduces measures of the disposition effect on the option market. Section 3 describes the data and the methodology for the empirical tests. Section 4 provides an in-depth discussion of the empirical results. Section 5 concludes the paper. 2. Measures of Disposition Effect To measure the disposition effect, we first modify Grinblatt and Han s (2005) capital gains overhang measure by substituting option trading volumes for turnover ratios as the weights for calculating the reference prices, because turnover ratios are not well defined for options that are in zero net supply. We define the reference price,, for the option holder s mental account on date, as 1, 1 where is the lagged option prices on date, and is the lagged option trading volumes on date. Our empirical tests are conducted on lagged time periods of three different lengths in days, namely, 5, 10, and 20. We find that the varying lengths of lagged time periods neither induces significant effects on our empirical findings nor affects our conclusions and 7

present results based on the five-day period. Having established the market s cost basis by the reference price ( ), we then derive the ACGO measure as, 2 where represents the capital gains overhang and is the closing mid-price of option on date. MPS adopts the trading-volume weighted average of an option s intrinsic value over its sampling period. In other words, it is the trading-volume weighted average of the difference between an option s strike price and the price of its underlying asset. The MPS measure is calculated as 1, 3 where denotes the underlying index price on date, and denotes the option strike price. Options moneyness is an appealing reference point for investors mental accounting. Moneyness, which reflects the intrinsic value of an option, is the most readily available information on the option market. Options with an intrinsic value that is in-the-money (ITM) provide potential exercisable gains and likely induce a motive for option holders to exit their positions. OTM options provide no opportunity for realizing immediate gains, and therefore traders are likely to retain their positions in a hope for possible future market reversals. Thus, we posit that holders of ITM options are more likely to sell than those of OTM options. Using past option prices as the reference price is one way of inferring gains or losses for option investors. However, we conjecture that mental accounting also involves a process of attention allocation, which induces option investors to rely on a more intuitive measure of 8

exercisable gains and losses of moneyness. As a limited cognitive resource (Kahneman, 1973; Hirshleifer and Teoh, 2003; Peng and Xiong, 2006), attention is likely allocated to the most salient information that is readily available and can be easily absorbed. Therefore, we argue that such information is more likely to be captured by options moneyness. 3. Data and Empirical Tests The OptionMetrics database contains the end-of-day quotes of European call and put options on S&P 500 index from January 1996 to April 2011. To ensure that our portfolio consists of only options with reliable quotes, we apply several data filters suggested by Constantinides, Jackwerth, and Savov (2013), Bali and Murray (2013), Bondarenko (2014) and Boyer and Vorkink (2014). Table 1 presents the total number of transactions obtained from the OptionMetrics database and the number of observations that are removed after applying these filters. Specifically, we remove options with bids that are missing price information or with prices less than or equal to zero, with a bid ask spread of less than zero or greater than $5, and with deltas less than 1 or greater than 1. We also remove transactions with missing volumes or open interest, with unrealistic trading dates, and with moneyness (S/K for calls and K/S for puts) less than 0.94 or greater than 1.06. 6 Furthermore, we remove trades that violate the arbitrage conditions or have repetitive entries under the same strike/expiration listings on the same date. After filtering, the data set consists of 404,822 observations. <TABLE 1 ABOUT HERE> 6 Constantinides, Jackwerth, and Savov (2013) remove all quotes with moneyness below 0.8 or above 1.2 as these options have thin trading volume and little value beyond their intrinsic value. Broadie, Chernov, and Johannes (2009) and Bondarenko (2014) use a data set that includes only options with moneyness greater than 0.94 and less than 1.06. We remove options with moneyness below 0.94 or above 1.06 to construct the weekly portfolio returns. However, our empirical results remain unchanged when using options with moneyness below 0.8 or above 1.2. 9

We adopt a research design similar to that of Grinblatt and Han (2005) and Bhootra and Hur (2014). Weekly data for call and put options are sorted into five quintiles in ascending order according to the MPS and ACGO measures. We construct a portfolio within each quintile with equally weighted call or put options (the quintile portfolio) and calculate the average weekly returns for all quintile portfolios formed on MPS and ACGO. We then compare the call and the put portfolio returns across different MPS and ACGO quintiles. This step provides us with primitive insights on the impacts of disposition effects on option returns. Next, we construct long short portfolios, denoted as 5 1 portfolios, by buying all calls and puts in the highest MPS and ACGO quintiles and simultaneously selling all calls and puts in the lowest quintiles. We examine the mean, standard deviation, and statistical significance of the long short portfolio return distributions. A significantly positive average return in the 5 1 portfolio indicates that higher a MPS or ACGO measure predicts higher option returns. Therefore, a strategy that buys options in the highest MPS or ACGO quintile and shorts options in the lowest quintile generates positive returns. Returns for the 5 1 portfolio, denoted as,, are formed on option returns on a weekly basis. Using closing mid-prices, the weekly returns of call or put options are approximated by,, 4 where is the option price one week later, and thus equals one week., denotes the option return over the period,. To control for the effect of risk on the 5 1 portfolio returns, we regress the portfolio returns on a set of risk factors. We choose this set of risk factors carefully following prior 10

literature. We include Fama and French s (1993) three factors: market excess returns ( _ ), small-minus-big market capitalization portfolio returns ( ), and high-minus-low book-to-market ratio portfolio returns ( ). We also include the momentum risk factor ( ) suggested by Jegadeesh and Titman (1993) and Carhart (1997). Broadie, Chernov, and Johannes (2009) and Bondarenko (2014) suggest inclusion of jump risk premiums in option returns. Pan (2002), Jones (2006), and Driessen and Maenhout (2013) argue that volatility risk and jump risk premiums are important determinants of option returns. Therefore, to control for the volatility risk and jump risk, we follow Constantinides, Jackwerth and Savov (2013) and include changes in VIX ( ), changes in volatility smirk ( ), and changes in the 30-day realized volatilities ( ). The regression model is as follows:,, 5 where, is the 5 1 portfolio return constructed by buying calls and puts in the highest MPS or ACGO quintile and selling calls and puts in the lowest quintile. Bakshi and Kapadia (2003) find that option portfolios returns are significantly affected by market volatility. Therefore, in equation (5), we consider changes in the VIX and options 30-day realized volatilities. To address this concern further, we adopt changes in the implied volatilities of the ATM call options, denoted as., in place of changes in the VIX for our regression analysis. Both changes in the VIX and ATM option implied volatilities reflect an option investor s expectation about the option s unrealized volatility in the future, whereas changes in the 30-day realized volatilities reflect past volatility estimates. 11

Volatility smirk,, defined as the difference between the implied volatilities of the OTM put options and the ATM call options, represents a negative skewness for the underlying returns. For example, Bates (2000) suggests that volatility smirks capture the crash fears of option investors. Pan (2002) also shows that volatility smirks are primarily due to investors fear of large adverse price jumps. By incorporating both jump and volatility risk premiums, Pan (2002) shows that jump risk premiums can explain up to 80% of the total risk premiums for OTM put options but only 30% for OTM calls. Xing, Zhang, and Zhao (2010) find that stocks with the steepest volatility smirks tend to underperform stocks with the least pronounced volatility smirks. They argue that option investors tend to choose OTM puts to express their concerns about possible future negative jumps. Because our 5 1 portfolio involves long and short positions in calls or puts across different strike prices, controlling for volatility smirks ensures that the abnormal returns of the 5 1 portfolio are not driven by volatility smirks of time-varying magnitudes. To control further for the overpriced puts puzzle (Pan, 2002; Jones, 2006; Driessen and Maenhout, 2013), we incorporate in our regressions a price-jump factor ( ) and a volatility-jump factor (. ), which capture price and volatility jump risks, respectively:,., 6 where is the sum of all daily S&P 500 returns lower than 4% over the past month, and. is the sum of all daily increases in the ATM call implied volatility that are greater than 4% over the past month. 12

As an alternative for controlling for the presence of jump risks in both the price and volatility of options, we introduce and., which are defined as the minimum daily index returns and the maximum daily increase in the implied volatilities of ATM call options over the past month, respectively:,..., 7 The regression tests of equations (5) to (7) for the 5 1 portfolio returns with call or put options are designed to establish empirical evidence of the presence of the disposition effect on the option market. An intercept that is significantly different from zero shows that the disposition effect affects the option market. To test further our hypothesis that MPS is a more salient reference point for inducing the disposition effect than ACGO for investors mental account, we employ a double sorting technique similar to that used by Grinblatt and Han (2005). Specifically, we first sort options into five quintiles according to the ACGO measure. We further sort options within each ACGO quintile into five quintiles by the MPS measure. For each ACGO quintile, we examine the returns of the 5 1 portfolio constructed by buying calls and puts in the highest MPS quintile and selling calls and puts in the lowest MPS quintile. If the returns of the 5 1 portfolio formed by MPS within each ACGO quintile are still significantly different from zero or the intercepts of the regression tests are significant different from zero, we conclude that MPS has a significant explanatory power over the disposition effect, even after controlling for ACGO. 13

Alternatively, we sort all options into five quintiles by the MPS measure and then sort all options in each MPS quintile into five quintiles by the ACGO measure. If the returns of the 5 1 portfolio formed by ACGO within each MPS quintile are insignificantly different from zero or the intercepts of the regression tests are not significantly different from zero, we can conclude that the explanatory power of the ACGO measure over the disposition effect is subsumed by that of the MPS measure. Finally, to check the robustness of our results, we remove those options with moneyness below 0.96 and above 1.04 and, alternatively, those with moneyness below 0.98 and above 1.02. The filters on options moneyness alleviate the impact of the overpriced put option puzzle. We also remove options with maturity that are longer than 30 days to prevent the possibility that the 5 1 portfolio returns are induced by the differences in the sample option maturities. 4. Empirical Findings 4.1 Summary statistics and univariate tests Table 2 reports the summary statistics for the option returns, ACGO, and MPS. Panels A and B present the summary statistics for call and put options, respectively. We include only options with available ACGO and MPS measures at the end of each week. Namely, we require sample options to have transactions for at least five days prior to the trading date. The table also presents the ACGO and MPS results over the past 10- and 20-day periods. Subsequent 1-, 5-, 10-, and 20-day returns are calculated using daily closing mid-prices according to equation (4). <TABLE 2 ABOUT HERE> Table 2 shows that the call and put option returns are, on average, negative. The average five-day returns of calls and puts are 4.45% and 12.68%, respectively. The ACGO and 14

MPS measures are generally negative. Both ACGO and MPS tend to decrease with the length of time, suggesting that options are, on average, traded below the market s cost basis or the average exercise prices. Finally, the average maturities of the call and put options are 58.07 days and 76.09 days, respectively. The average moneyness of the options is 0.99, which is near the money. Table 3 reports the option portfolio returns formed on the ascending ACGO quintiles over the past five days at the end of each week. Panels A and B provide the findings for calls and puts, respectively. Quintile 1 (5) portfolio consists of options in the lowest (highest) ACGO quintile. Changing the benchmark time periods of measuring ACGO does not materially alter our results. <TABLE 3 ABOUT HERE> A couple of interesting empirical findings emerge from Panel A of Table 3. First, the five-day returns of the call portfolios increase with the ACGO measure. The average five-day return in the lowest ACGO quintile is 7.90%, which increases to 1.06% in the highest ACGO quintile. Second, returns of the 5 1 call portfolio are significantly different from zero for the 5-day and 10-day return at the 5% significance level. The results for put options in Panel B of Table 3 are stronger. The patterns across ACGO quintiles for the five-day returns of the put portfolio tend to be monotonic. The average five-day return is 18.62% in the lowest ACGO quintile, which increases to 7.98% in the highest quintile. The returns of the 5 1 put portfolio are more pronounced than those of the call options. All 5 1 put options returns are significantly positive. This finding suggests that ACGO has predictive power for option returns. Next, we sort all options by their past five-day MPS. Panels A and B of Table 4 present the results for the call and put portfolio returns, respectively. The returns of the 5 1 call 15

portfolio in Panel A are all positive and significant at the 1% level except for the 20-day return. The average five-day returns increase monotonically with MPS quintiles from 9.31% to 1.12%. The return differences by MPS quintiles for put options, shown in Panel B, are again, as in Table 3, much stronger than those of call options. The returns of the 5 1 put portfolio are all positively significant at the 1% level. The average returns of the quintile portfolios monotonically increase with the MPS measure except for the 20-day quintile returns. For example, the average five-day returns increase from 17.52% in the lowest MPS quintile to 3.89% in the highest quintile. Finally, the 5 1 put portfolio returns formed on MPS are larger than the 5 1 put portfolio returns formed on ACGO regardless of the return frequencies. <TABLE 4 ABOUT HERE> Overall, Tables 3 and 4 show that the option portfolio returns increase with both the ACGO and MPS measures. In addition, the 5 1 option portfolios generate significantly positive returns, which indicate the existence of significant disposition effects on the option market. More important, the pattern by which the option portfolio returns increase with the measure of disposition effects is more pronounced when options are sorted by the MPS measure compared to the ACGO measure. This finding suggests that the MPS measure is likely a relevant estimate of the disposition effect on the option market. 4.2 Regression tests of the option market disposition effect To control for risk factors that are likely generating part of the differences in the 5 1 portfolio returns, we run several regressions with control variables. Intuitively, if the 5 1 portfolio returns are driven by the disposition effect, the intercept of the linear risk factor model should be significantly different from zero. Namely, if the returns of the 5 1 portfolio cannot be fully explained with the risk factors specified, we can be more confident in drawing the conclusion 16

that the 5 1 portfolio returns formed on the ACGO or the MPS measures are driven by the disposition effect. Table 5 reports our regression results for the 5 1 portfolios by the ACGO measure. In Panel A, the intercepts for the 5 1 call portfolios of Models 1 and 2 are significant at the 5% level and that of Model 3 is only significant at the 10% level. Conversely, in Panel B, the intercepts for the 5 1 put portfolios are all significant different from zero at the 1% level. Consistent with the univariate tests, the momentum returns for the option portfolios formed on ACGO are weaker for the call options. <TABLE 5 ABOUT HERE> Table 5 shows that price jumps and volatility jumps cannot explain the returns of the 5 1 option portfolios; their coefficients are not significantly different from zero. The inclusion of volatility smirks also fails to explain the portfolio returns. These findings suggest that the returns of the 5 1 portfolio constructed by sorting options according to their ACGO are not related to the expected skewness of underlying index and the crash fears (i.e., the jump-related factors) of option investors. Overall, we find that the option market trading exhibits strong disposition effects that cannot be explained by risk factors. Table 6 presents regression results for the 5 1 portfolio formed on the MPS measure. In Panel A, the abnormal returns of 5 1 call portfolios are all positive and consistently significant at the 1% level. For example, the intercept of the call portfolio in Model 1 is 8.73 and significant, which indicates that the abnormal return of the 5 1 call portfolio is 8.73% after controlling for risk factors. In Panel B, the abnormal returns of the 5 1 put portfolios are all positively significant at the 1% level. The general implications of Table 6 are similar to those of Table 5 that the abnormal returns of the 5 1 put portfolios are more significant than those of the 5 1 call portfolios. 17

<TABLE 6 ABOUT HERE> The coefficients of changes in VIX are all significantly negative for the 5 1 call and put portfolios in Table 6. This finding suggests that portfolio returns deteriorate as VIX increases. For example, the coefficient of is 4.98 and significant for the call portfolio in Model 1, suggesting that the portfolio returns decrease by 4.98% as VIX increases by 1%. Since the changes in VIX are positively related to the returns of the call or put options, negative coefficients on VIX suggest that the quintile portfolio returns in the highest ACGO or MPS quintile increases less than those in the lowest quintile when VIX increases. Overall, Tables 5 and 6 indicate that the 5 1 option portfolios exhibit significantly positive returns even after controlling for known risk factors, which indicates the existence of a significant disposition effect on the option market. More important, all intercepts of the call and put portfolios formed on MPS are larger and consistently more significant than those formed on ACGO (as reported in Table 5). These results suggest that MPS captures the disposition effect better than ACGO. MPS is therefore a more salient reference point for option investors buying and selling decisions than ACGO. 4.3 Double sorts We next examine the relative explanatory power of the MPS and the ACGO measures for the disposition effect by applying a double sorting technique to all sample options. We sort all options into quintiles in increasing order by MPS first and then by ACGO into increasing quintiles. We also sort by ACGO first and then by MPS. Panels A and B of Table 7 present the call and put portfolio returns, respectively, sorted by MPS first and then by ACGO. If the effect of MPS subsumes that of ACGO, we expect to find a flat relation between returns and the ACGO measure in each MPS quintile. <TABLE 7 ABOUT HERE> 18

Table 7 shows that the MPS measure does not correlate with the ACGO measure. For example, in the first MPS quintile for put portfolios in Panel B, the average MPS ranges from 57.24% for the lowest ACGO quintile to 59.05% for the highest ACGO quintile and the pattern is almost flat. This finding suggests that the disposition effect represented by the MPS measure is not captured by the ACGO measure. In addition, the call and put portfolio returns almost always increase monotonically with the MPS quintiles, which is consistent with our conjecture that MPS captures the option traders disposition effect. In each MPS quintile of Table 7, the returns of the call and put portfolios are mostly not significantly related to ACGO, and the returns of the 5 1 portfolios formed on ACGO in each MPS quintile are mostly not significantly different from zero. Panel B shows that for put portfolios, although the average returns of the 5 1 portfolio are significant for the first three MPS quintile, the average returns do not increase monotonically with the ACGO measure in each MPS quintile. Table 8 presents regression estimates for the 5 1 portfolio in each MPS quintile. Panel A shows that the 5 1 call portfolio returns in each MPS quintile are not significantly different from zero. This result suggests that the effects of the ACGO are captured by the MPS measure. In Panel B, the intercepts remain statistically significant for the 5 1 put portfolios in the first three MPS quintile, after controlling for risk factors. This result implies that the effects of the ACGO measure remain significant for put options even after we control for the MPS measure. However, as in Table 7, within each MPS quintile the returns of the quintile portfolios formed on ACGO do not increase monotonically with the ACGO measure, suggesting that after sorting on MPS, the predictive power of the ACGO measure decreases noticeably. <TABLE 8 ABOUT HERE> 19

We next sort options by ACGO first and then by MPS. Panels A and B of Table 9 provide the results for call and put portfolios, respectively. In each ACGO quintile, the returns of the 5 1 call and put portfolios are all significantly different from zero. For example, in Panel B, the mean return of the 5 1 put portfolios in the highest ACGO quintile is 4.83% and significantly different from zero. Furthermore, the 5 1 portfolio returns are, on average, more pronounced in Table 9 when options are first sorted by ACGO than those in Table 7 when they are first sorted by MPS. For example, the return of the MPS 5 1 call portfolio in the highest ACGO quintile in Panel A of Table 9 is 9.73% and significant whereas the ACGO 5 1 call portfolio return in the highest MPS quintile is -0.90% and not significant in Panel A of Table 7. These findings suggest that the MPS measure is able to capture the disposition effect better than the ACGO measure. These results are consistent with our hypothesis that option investors have the propensity to sell the options with higher excisable gains. MPS is thus a more relevant measure in capturing option traders disposition effect. <TABLE 9 ABOUT HERE> Table 10 presents the regression estimates of the 5 1 portfolio first sorted by ACGO and then MPS. All 5 1 portfolios in each ACGO quintile generate significant abnormal returns at the 1% level. These results suggest that the effects of the MPS on option returns are not captured by the ACGO measure. This finding further substantiates our argument that MPS is the most salient and readily available measure that attracts market participants immediate attention when making buying and selling decisions. <TABLE 10 ABOUT HERE> 4.4 Robustness checks The returns of the 5 1 option portfolios should be related to the portfolio s greeks. To check the robustness of our results, we include the portfolio s theta and the changes in the square of 20

market excess returns to capture the returns induced by the portfolio s gamma. Having negative coefficients on the changes in VIX risk factor, as reported in Tables 5 and 6, suggests that 5 1 portfolios, on average, generate a negative vega. To provide a better understanding about the composition of the 5 1 portfolio s greeks, Table 11 reports the regression estimates of the 5 1 portfolio returns and the portfolio returns in each MPS quintile. <TABLE 11 ABOUT HERE> Table 11 shows that the coefficients of changes in VIX are positively significant for all option portfolios in each quintile, suggesting that the quintile portfolio returns have positive vegas. However, the coefficients of changes in VIX decrease with MPS. For example, in Panel A, the coefficient for call portfolios is 0.1666 in the lowest MPS quintile and decreases to 0.0523 in the highest quintile, while the coefficient for the 5 1 call portfolio is -0.0310. The pattern that the coefficients of changes in VIX decrease with the MPS quintile in Table 11 explains why the weekly 5 1 portfolio returns are negatively correlated with changes in VIX. (Recall that Tables 5 and 6 report all negative coefficients of changes in VIX when the returns of the 5 1 portfolios are regressed on risk factors.) Overall, we conclude that the abnormal returns of the 5 1 option portfolio are robust when considering a portfolio s theta and gamma. An alternative way to examine the robustness of portfolio returns is to impose restrictions on the maturities of sample options and replicate the results of Table 6. Specifically, we remove options with maturities longer than 30 days, 60 days, and 90 days, respectively, and examine whether the 5 1 portfolio generates abnormal returns. Panels A and B of Table 12 report the regression estimates of the 5 1 call and put option portfolios, respectively. When we include only options with shorter maturities, the abnormal returns 21

generated by the 5 1 portfolio increase. For example, in Panel A, the intercept of the 5 1 call portfolio with maturities less than 30 days (90 days) is 24.18% (10.02%). In Panel B, the results remain significant for put options; that is, that including options only with shorter maturity increases the abnormal returns. We attribute the results to option traders propensity to sell winning options with a shorter maturity to lock in paper gains rather than holding options to maturity. <TABLE 12 ABOUT HERE> Next we test the robustness of our results by putting stricter restrictions on the options strike prices and maturities. We test four constraint scenarios: options must have (i) moneyness between 0.96 and 1.04; (ii) moneyness between 0.96 and 1.04 and maturities of less than 30 days; (iii) moneyness between 0.98 and 1.02; (4) moneyness between 0.98 and 1.02 and maturities of less than 30 days. Panels A and B of Table 13 show the results for call and put options, respectively. The returns of the 5 1 call and put portfolios are significantly different from zero under all scenarios. However, the abnormal returns generated by the 5 1 portfolio seem to be related to the strike prices and the time to maturities. When only near-the-money options are included, the 5 1 portfolio generates less abnormal returns after controlling for risk factors. For example, in Panel B of Table 6, the abnormal return of the 5 1 put portfolio is 11.87% in Model 2, but it decreases to 8.44% when we include only the option with moneyness between 0.96 and 1.04. Overall, when the options are near the money, the portfolio returns remain significantly different from zero, suggesting that the disposition effect is robust. The results of Table 13 are, in general, consistent with our overall findings. <TABLE 13 ABOUT HERE> 22

In addition, we test whether our empirical findings change when the formation of the 5 1 portfolio is allowed to take place on any weekdays, rather than forming at the end of each week. We find that changing the portfolio formation time does not have a significant influence on our findings. We also estimate the ACGO and the MPS measures with option prices and trading volume over the past 10 and 20 days, rather than 5 days. We find that, despite a smaller sample size, our results remain intact. Finally, we use the delta-hedged option portfolio returns to test the robustness of our results. Following Cao and Han (2013), who define the delta-hedged returns as the dollar gains scaled by absolute values of the assets,,, we calculate the delta-hedged option returns as 7,,,, 8 where, is the delta of a call option on date, is the annualized risk-free rate on date, and, denotes the delta-hedged option returns over a period,. Tables 14 and 15 provide the average returns and regression results, respectively, of the quintile portfolios and the 5 1 portfolios formed on MPS. Panels A and B report results for call and put portfolios, respectively. The method in Table 14 is analogous to the method used in Tables 4 and 6 with the exception of using delta-hedged option returns; the results are consistent with those in Table 4. The average returns of the quintile portfolio increase monotonically with the MPS measure for all delta-hedged call and put portfolios and for all return frequencies. For example, in Panel A, the average returns of the call portfolios increase from 0.22% in the lowest MPS quintile to 0.12% in the highest quintile. The returns of the 7 Bakshi and Kapadia (2003) normalize the delta-hedged gains by the index level and the option price. Our empirical findings and implications are qualitatively the same when we use their methods. 23

5 1 portfolio are all positive and significant at the 1% level. In Table 15, the 5 1 delta-hedged call and put portfolios all generate significant abnormal returns for different regression models. The results in Tables 14 and 15 suggest that our results are robust with respect to both the unhedged and delta-hedged option portfolio returns. <TABLE 14 ABOUT HERE> <TABLE 15 ABOUT HERE> 5. Conclusion This study examines the presence of the disposition effects on the option market. Our empirical findings are summarized as follows. First, returns of the option portfolios mostly increase monotonically across the MPS and ACGO quintiles, indicating that options with higher exercisable gains and capital gains overhang outperform options with lower exercisable gains and capital gains overhang. In other words, winners (losers) are likely to continue winning (losing), indicating the existence of the disposition effect. The pattern is more pronounced for the delta-hedged option portfolios. Second, the 5 1 option portfolios constructed by buying winners (options in the highest ACGO or MPS quintile portfolio) and selling losers (options in the lowest ACGO or MPS quintile portfolios) generate significant abnormal returns. The results are robust after including risk factors such as traditional asset pricing risk factors, volatility risk, volatility smirks, price jump risk, and volatility jump risk. Statistical significance of the intercepts remains robust even when we adopt different proxies for the price jump risk and volatility jump risk. The results are also robust after including only near moneyness options and options with short maturities. Hence, we conclude that the abnormal returns of the 5 1 option portfolio are driven by the disposition effect. That is, option traders tend to hold losers too long and sell winners too short. 24

Third, and even more interesting, after controlling for the effect of ACGO, the 5 1 portfolios formed on MPS still generate significant abnormal returns. Conversely, the portfolios formed on ACGO after controlling for the effect of MPS mostly fail to generate significant abnormal returns. This finding indicates that MPS is a better measure for capturing the disposition effect. The rationale is that market participants attention is a scarce limited resource that is allocated only to the most salient and readily available information; for the option market specifically, such information is embedded within our proposed MPS measure. Finally, we find a disposition-induced underreaction to weekly new changes in volatility. Abnormal returns generated by the 5 1 portfolio seem to be related to weekly volatility changes, indicating that the returns of the long positions in the highest MPS and ACGO quintiles increase less than those of the short positions in the lowest quintiles. A closer examination of portfolio returns in each quintile shows that the option portfolio in the higher quintiles exhibit smaller loadings on the changes in VIX. Also, the 5 1 option portfolios with shorter maturities produce higher abnormal returns, indicating that option traders have a greater propensity to sell winning options to lock in the paper gains as expiration nears. 25

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