Option Volume Signals. and. Foreign Exchange Rate Movements

Transcription

1 Option Volume Signals and Foreign Exchange Rate Movements by Mark Cassano and Bing Han Haskayne School of Business University of Calgary 2500 University Drive NW Calgary, Alberta, Canada T2N 1N4

2 Abstract Title: Option Volume Signals and Foreign Exchange Rate Movements Using Deutschmark currency option data from the Philadelphia Stock Exchange, this article examines the signalling quality of option volume measures on movements in the Deutschmark/US Dollar exchange rate. The concept of a volume-weighted strike distribution is proposed. It is demonstrated that measures using the strike distribution are inherently better predictors of both direction and volatility of the exchange rate movements as compared to their more traditional counterparts used in practice, such as the put-call ratio.

3 1 INTRODUCTION The linkage between option volume and spot market (underlying) price movements has been an active area of research. One strand of this literature is motivated by market microstructure theory, as in Easley, O Hara, and Srinivas (1998), where informed traders may choose to trade in either the spot market or the option market. Examples of empirical work along these lines, using equity data, are Anthony (1988), Stephan and Whaley (1990), Vijh (1990), and Chan, Chung, and Fong (2002). These papers find little evidence of information-based trades in option markets. Various measures of total option volume have little incremental predictive significance on price movements of the underlying beyond that of spot market volume. Another strand of empirical work on option volume focuses on the technical sentiment indicators that are used in practice, such as the put-call ratio (PCR). Billingsley and Chance (1988), Chance (1990), and Simon and Wiggins (2001) all find that the PCR has significant predictive power in equity index markets. This paper examines currency option trading volume measurements and foreign exchange rate movements. Besides finding out whether the equity results extend to foreign exchange markets, the central contribution of this paper is to show that the PCR is a blunt and flawed measure of market sentiment. Besides having obvious theoretical problems (described shortly), it is shown below that it performs poorly empirically. A different set of sentiment measurements, based on the strike distri- 1

4 bution defined shortly, does have predictive power. This article proceeds as follows. The section Strike Distribution defines the set of option volume measures that are used in the empirical work of this paper. The description of the data set used, as well as basic summary statistics are presented in the section Data Summary. The section Signalling Quality examines the predictive power of the option volume measures. The last section summarizes the findings. 2 STRIKE DISTRIBUTION The most popular option volume statistic is the put-call ratio (PCR), defined as the ratio of put trading volume to call trading volume. A related measure is the put-call signal (PCS) defined as the volume of puts minus the volume of calls normalized by total volume. These traditional measures are typically used as contrarian indicators in that rises in the PCR/PCS signal a rise in market pessimism as puts are being purchased. If the market is typically wrong, this can be used as a buy signal. Empirical performance aside, the PCR/PCS suffers from several theoretical flaws. An implicit assumption is that the incorrect pessimists/optimists are purchasing options. This precludes the possibility that these naive traders perform such typical strategies as writing covered calls and shorting stocks/writing puts. Even if one accepts unsophisticated and naive traders are typically long options, associating long positions of puts/calls with pessimism/optimism precludes such strategies as 2

5 protective puts and spreads. Finally, put-call parity makes the distinction of puts and calls meaningless. Combined with positions in the underlying and bonds, there is no difference between puts and calls. These reasons make the PCR/PCS imperfect measures of what could be an important measure of market sentiment. If options are non-redundant and are used to complete markets, as in Ross (1976), then buyers and sellers of options are using them to achieve non-linear payoffs. Since options are in zero net supply, these non-linearities are necessarily due to heterogeneities in market participants. Such heterogeneities include risk aversion, wealth, information, background risk, and beliefs. There has been recent theoretical work that tries to explain option positioning and trading volume with these heterogeneities (e.g., Franke, Stapleton, and Subraymanyam, 1998; Carr and Madan, 2001; and Cassano, 2002); however, these models rely on one-period equilibrium modelling and hence are not yet able to provide strong empirical predictions. What can be said is that positions in non-redundant options are the result of non-linear sharing rules. Option trading volume measures may contain important information as to where those non-linearities occur. For the reasons discussed at the beginning of this section, the PCR/PCS are very blunt and imperfect measures of where the non-linearities are occurring. The central question this paper addresses is whether there is a difference in signal qualities between the PCR/PCS and measures based on what this paper terms the strike distribution, defined as follows. 3

6 On a trading day t, denote the trading volume of puts of a given strike K i and time to maturity T j as V p (t, K i,t j ), and that of the calls as V c (t, K i,t j ). For notational convenience,thesumofputvolumesacrossallstrikesandtimestomaturity,v pt, and that of calls, V ct, are written as variables with the functional arguments omitted. Specifically, and V pt = X i V ct = X i X V p (t, K i,t j ) (1) j X V c (t, K i,t j ). (2) j The PCR at time t is simply PCR t = V pt /V ct. The PCS is defined as PCS t = (V pt V ct ) / (V pt + V ct ). Note that this is a non-linear monotone transformation of the PCR since PCS t =(PCR t 1) / (PCR t +1). What is convenient about the PCR (and the PCS) is that as the underlying asset changes, the average strike of puts and calls, in general, move with the asset. In this sense, the PCR takes moneyness into account. In addition, the two measures are volume normalized in the sense that they have little correlation with total trading volume. To begin our discussion of the strike distribution, let S t be the price of the asset on day t. This could be the opening, closing, or mid-day price; for now the difference is unimportant. Define the moneyness of an option on day t by X it K i /S t. Hence at-the-money options have a moneyness parameter close to 1. It is the change in the market s relative demand and supply of options of a given moneyness that is 4

7 of central interest. The strike distribution on day t is a function of the moneyness parameter. It is denoted as φ pt (X i ) for puts, φ ct (X i ) for calls, and φ t (X i ) for the total, where, φ pt (X i ) = φ ct (X i ) = φ t (X i ) = P j V p (t, X it,t j ) V pt (3) P j V c (t, X it,t j ) (4) V ct P j (V p (t, X it,t j )+V c (t, X it,t j )). (5) V pt + V ct These strike distributions (φ pt (X i ), φ ct (X i ), and φ t (X i )) are designed to capture where, in terms of the relative strike price X, the relative option trading volume is occurring. Each trading day, the shape of the distribution changes and such changes possibly convey information on future exchange rate movements. As with probability distributions, the shape can be quantified by its moments, leading to the following definitions of the k-th moments: m kpt X i m kct X i m kt X i X k i φ pt (X i ) (6) X k i φ ct (X i ) (7) X k i φ t (X i ) (8) where k is an integer. For example, m 1t is the average volume-weighted strike price (relative to the spot) of all options (i.e. puts and calls). One would expect large decreases in m 1t signal non-linear sharing at low future underlying prices. Hence m 1t is an alternative to PCR t and this paper addresses the extent to which they differ. 5

8 The multi-dimensionality of the strike distribution leads to a richer set of possible signals than the PCR. For example, κ 2t m 2t m 2 1t would be a measure of the strike dispersion. The second centralized moments for puts and calls, κ 2pt and κ 2ct,are defined similarly. One would conjecture higher dispersion is caused by the greater need for non-linearity in the tails of the future asset price distribution. Hence κ 2t might signal higher future volatility. Other higher order centralized moments could also capture direction and volatility. This paper examines skewness, κ 3t m 3t 3m 1t m 2t +2m 3 1t and (un-normalized) kurtosis κ 4t m 4t 4m 3t m 1t +6m 2t m 2 1t 3m 4 1t. The central question asked here is whether these volume measures help predict exchange rate movements. Denote the daily (continuous) return as y t =ln(s t+1 /S t ). Whether the centralized moments can provide explanatory power on y t,aswellason volatility measures y t and yt 2, is addressed shortly. Before the predictive power of the volume measures on the direction and volatility of the exchange rate is examined, the data used must be described. 6

9 3 DATA SUMMARY This article uses a data set of foreign currency option transactions at the Philadelphia Stock Exchange (PHLX), originated from that exchange. There are three different types of option expiration styles for foreign currency options traded in the Philadelphia Stock Exchange: mid-month, month-end, and long-term. Since most options expire mid-month, the data set studied is chosen to be of options with mid-month expiration only, for all the options on Deutschmark traded in PHLX from February 28, 1983 to December 19, For each trading day during this period, if a particular option is traded on that day, an entry is recorded in the data set, with the date, the symbol of the option, the option type (put or call), expiration month, strike price, number of contracts traded, number of trades in the day, option and spot prices at open, close, day s high, and day s low, and the exact times in the day of these prices. Because the spot exchange rates recorded in the data set vary from day to day according to the time these options were traded, for spot exchange rates in these analyses, a more homogeneous series of rates downloaded from Datastream is used instead. They are daily middle rates originated from Financial Times. Among the entries in the option data set, 862 contain invalid data, usually in the form ofazeroinafield where zeros are not meaningful (strike price, for an example) other than indicating missing data. These 862 entries were omitted from our analyses. Table I presents the univariate summary statistics for the volume measures as 7

10 well as the exchange rate changes. Both the average and the median daily exchange rate change are small; in fact, the returns y t are not statistically different from zero at the 5% level. The average PCR is greater than one and the average PCS is less than zero, suggesting put volume is relatively higher. However, the average volumes of puts and calls reveal calls are typically more popular. This apparent discrepancy is resolved by noting the median and positive skewness of the relative volume measures (PCR/PCS). The high averages are due to relatively few large outliers. In regards to the strike distribution moments, the first moment κ 1 is close to one on average (i.e. at-the-money) and puts have a lower average strike than the calls (0.984 compared to 1.018). Figure 1 shows the time series of the three first moments, κ 1, κ 1p,andκ 1c. There are no large spikes and no apparent trend in any of these series. Figure 2 presents the time series of the total volume moments, i.e. κ 1, κ 2, κ 3, and κ 4.Wecontinuetofind no apparent trend; however, there are large spikes in the third and fourth centralized moments. Referring back to Table I, on average there is negative strike skewness for both option types with puts having relatively more negative strike skewness. Calls have more strike dispersion, as measured by the second and fourth centralized moments, κ 2c and κ 4c. For each of the four centralized moments, the hypothesis test that the average strike moment of the puts is equal to that of the calls (e.g. κ 2p = κ 2c )is rejected at the 99% confidence level. It is shown in the regression analysis of the 8

11 next section that separating puts from calls does indeed affect predictive power of the moments. 4 SIGNALLING QUALITY To explore the general co-movements of the variables, Table II contains their correlation matrix. In regards to directional prediction power, the first row of Table II demonstrates that there is relatively weak correlation between returns (y t )and the option volume statistics. However, the centralized strike moments have stronger correlations (ranging from 1.4% to 3.4% in absolute value) with returns than the standard volume measures (all less than 1% with the exception of V c which is equal to 1%). The first and third centralized moments are negatively correlated with returns; whereas, the second and fourth are positively correlated with returns. For volatility signalling, the squared return y 2 t has correlations over 2% (absolutely) with total volume, put volume, and the first centralized strike moment. The absolute return, y t, is more strongly correlated with the volume statistics, being over 7% correlation with the option volumes (V, V p,andv c ) and the second centralized moment. Although not shown in the table, absolute returns have a 7.5% correlation with the first centralized moment for puts, i.e. κ 1p. The most important feature of these results is that the correlations of the exchange rate movement with the strike moments are much stronger than with the PCR/PCS. This suggests the strike mo- 9

12 ments contain information that is not in the simple PCR/PCS signals. Table II does show that there is fairly strong correlation between the first moment and these traditional signals; κ 1 has correlations of 18.5% and 45.1% with the PCR and PCS respectively. Although not presented in the table, the first moments of the puts and calls (i.e. κ 1p and κ 1c ) have much less correlation with the PCR/PCS signals. In order to examine the behavior of exchange rate movements when the volume variables are abnormally high or low, Table III presents the means of the exchange rate variables (y, y 2,and y ) for the top and bottom deciles of the different volume measures. For example, the average return (y) for the top 10% of the first moment observations (κ 1 )is 0.03% versus an average return of 0.08% for the bottom 10% of the first moment observations. The difference between these two is statistically significant at the 5% confidence level. This suggests κ 1 is a contrarian indicator when it is abnormally high or low. Similarly, abnormally high values of the fourth centralized moment also are associated with significantly lower returns when compared to abnormally low values. The differences in average changes in the bottom versus top deciles of both the PCR and the PCS are insignificant. This suggests, once again, that the strike moments convey more information than these traditional measures. The difference in average returns for the top and bottom deciles of total volume measures is not statistically significant. Table III also presents p-values for the hypotheses that the average of y is zero 10

13 within the top decile and that the average of y is zero within the bottom decile. For the bottom decile, all total volume measures (i.e. V, V p,andv c ) are associated with drops in the exchange rate at very high levels of statistical significance. All other measures are insignificant at the 95% confidence level; however, the average of y is significantly different from zero at a 94.5% level for the bottom decile of the first strike moment. In regards to volatility, for the second, third, and fourth centralized strike moments, as well as for the volume measures, the squared changes and absolute changes (i.e. y 2 and y ) behavemuchdifferently in the top and bottom deciles. Volatility (as measured by y 2 and y ) is higher in the bottom decile than the top decile for the second and fourth centralized moments at very high levels of statistical significance. Volatility is lower in the bottom decile than the top decile for the first and third centralized moments at more modest levels of statistical significance. As one would expect, volatility is significantly higher for the top decile than the bottom of all three option volume measures. The PCR/PCS (which have the same deciles) continues to be a poor predictor of both direction and volatility. The analysis so far suggests that the strike moments capture market sentiment much better than the traditional PCR/PCS measure. The first strike moment behaves in a contrarian manner and that very high/low second and fourth (centralized) strike moments, tend to predict high/low volatility. 11

14 Turning to the statistical significance of these findings, Table IV presents results from univariate regressions of the return variables (y, y 2,and y ) onthedifferent option volume measures. In order to prevent any imperfect synchronization in the data from biasing the outcome, the table also includes results from the same regression using lagged volume measures. For example, y t =ln(s t+1 /S t )isregressedonκ 1t and also regressed on κ 1,t 1. Examining the p-values for the direction regressions (y), the first and second moments (and to a lesser extent the third and fourth) are inherently different from the traditional sentiment measures (PCR/PCS). For example, the PCR and PCS have p- values ranging from 48% to 96%; whereas, κ 1 and κ 2 have p-value ranging from 4.5% to 18.9%. With p-values ranging from 21% to 80%, total volume measures demonstrate little directional power. Once again, the strike moments seem to convey better information than traditional measures. Curiously, the second moment (especially for puts) has strong directional significance (p-values of 4.53% for κ 2 and 1.62% for κ 2p ). The first moment also shows some evidence of being a contrarian indicator as shown by a p-value of 6% for the lagged regression (for κ 1 ) and 5.5% for κ 1p. All of the volume measures have no statistical significance in predicting volatility when measured by y 2. However, if volatility is measured by the absolute change y, the first and second centralized strike moments have strong statistical significance in predicting exchange rate volatility, as do the total volume measures. Once again the 12

15 PCR/PCS are of insignificant statistical power. It should be noted that the R 2 statistics from these regressions are very low; i.e. these measures explain little of the total variations of the changes (relative and absolute) in the exchange rate. This is not surprising; even variables that theoretically should explain exchange rate movements, such as interest rate differentials, do poorly in terms of R 2 in empirical studies (see, for example, Table 1 in Evans and Lyons, 2002). 5 CONCLUSION The central result of this paper is to show that standard sentiment indicators, such as the PCR, are ineffective in signalling future movements in foreign exchange rates. In contrast, measures based on the more theoretically-sound strike distribution are able to provide information on future exchange rate movements. It was also shown that total volume measures provide information on future exchange rate volatility. Whether theseresultsprovideevidenceofpotentiallyprofitable trading strategies and market inefficiencies is beyond the scope of this paper. Besides the obvious problems of implementing such an exercise (e.g. measuring transactions costs, modelling exchange rate risk premia, borrowing/lending rates, etc..), one could argue that these results arise naturally even in an efficient market setting. Just as option implied volatilities predict future spot market volatility (regardless of inefficiencies), the shape in 13

16 the strike distribution should contain economically meaningful data also regardless of inefficiencies. If options are non-redundant, the buyers and sellers of the options are agreeing to non-linear sharing rules, regardless of their reasons which could be as simple as differences in risk aversion. The results here are of central interest to anyone using the more traditional option sentiment indicators (i.e. the PCR and the PCS). Extending this analysis to equity/index assets is the natural next step for future research. BIBLIOGRAPHY Anthony, J. (1988). The interrelation of stock and options market tradingvolume data. Journal of Finance, 43, Billingsley, R. & Chance, D. (1988). Put-call ratios and market timing effectiveness. Journal of Portfolio Management, 15, Carr, P. & Madan D. (2001). Optimal positioning in derivative securities, Quantitative Finance, 1, Cassano, M. (2002). Disagreement and equilibrium option trading volume. Review of Derivatives Research, 5, Chan, K., Chung, Y., & Fong, W. (2002). The informational role of stock and option volume. Review of Financial Studies, 15,

17 Chance, D. (1990). Option volume and stock market performance. Journal of Portfolio Management, 16, Easley, D., O Hara, M., & Srinivas, P. (1998). Option volume and stock prices: Evidence on where informed traders trade. Journal of Finance, 53, Evans, M. & Lyons, R. (2002). Order flow and exchange rate dynamics. Journal of Political Economy, 110, Franke, G., Stapleton, R., & Subrahmanyam, M. (1998). Who buys and who sells options: The role of options in an economy with background risk. Journal of Economic Theory, 82, Ross, S. (1976). Options and efficiency. Quarterly Journal of Economics, 90, Simon, D. & Wiggins, R. (2001). S&P futures returns and contrary sentiment indicators. Journal of Futures Markets, 21, Stephan, J. & Whaley, R. (1990). Intraday price change and trading volume relations in the stock and stock option markets. Journal of Finance, 45, Vijh, A. (1990). Liquidity of the CBOE equity options. Journal of Finance, 45,

18 FIGURE CAPTIONS Figure 1: The values of the first moments (κ 1, κ 1p,andκ 1c ) of the strike distributions (of all options, just puts, and just calls, respectively) from the sample. The horizontal axis is the number of the daily observation (3566 in total). Figure 2: The values of the four centralized moments (κ 1, κ 2, κ 3,andκ 4 )ofthe strike distribution (of all options) from the sample. The horizontal axis is the number of the daily observation (3566 in total). 16

19 Figure κ κ 1p κ 1c

20 Figure κ κ x x 10-3 κ κ

21 Table I Summary statistics for the exchange rate and option volume measures. mean median max min std skew kurtosis y y y V V p V c PCR PCS κ 1p κ 1c κ 2p % % % % % κ 2c % % % % % κ 3p % % % % % κ 3c % % % % % κ 4p % % % % % κ 4c % % % % % κ κ % % % % % κ % % % % % κ % % % % %

22 Table II Correlation coefficients for the exchange rate changes and option volume measures. κ 1 κ 2 κ 3 κ 4 PCR PCS V V p V c y y y κ κ κ κ PCR PCS V V p V c

23 Table III Decile Analysis: The y, y 2, and y values are averages from the bottom and top deciles of the corresponding volume statistics. Volume Statistic y p-value (H1) p-value (H2) y 2 p-value (H2) y p-value (H2) κ 1 κ 2 κ 3 κ 4 PCR/PCS V V p V c Bottom Bottom Bottom Bottom Bottom Bottom Bottom Bottom % % % % % % % % * * * * * % % % % % % % % * * * * * * % % % % % % % % * * * * * * * Top Top Top Top Top Top Top Top % % % % % % % % % % % % % % % % % % % % % % % % p-value (H1): The probability of observing the decile's mean under the null hypothesis that the actual mean of that decile is zero. p-value (H2): The probability of observing the deciles' y, y 2, or y values under the null hypothesis that the actual values of the two deciles are equal. * represents p-values below 5% (Statistical Significance)

24 Estimated ß (upper rows) and p-values (lower rows) for univariate regressions. κ 1 κ 2 κ 3 κ 4 PCR PCS V V p V c κ 1p κ 1c κ 2p κ 2c κ 3p κ 3c κ 4p κ 4c * Significant at the 5% level. Table IV Lagged Regression y y 2 y y y 2 y * * * * * * * * * * * * * * * * * *