# Agriculture Option Returns.

I. IntroductionOptions provide access to volatility speculation in addition to the more traditional motivation of speculating on price movements in the underlying asset. For example, it is clear that equity options offer a relatively low cost venue for highly leveraged speculation on stock prices. However, there is no equivalent leverage argument to be made for futures options. Futures themselves already provide ample leverage (around 10 to 1 notional value to margin) and are the most liquid venue to speculate on commodity price movements. Thus, options on futures are best viewed as pure volatility trading instruments. (1) This leads to a natural desire to understand the (pure) returns to trading volatility. Most importantly, options on agricultural futures offer the ability to speculate on volatility seemingly unconnected to the stock market or its associated volatility. By utilizing over 17-year agriculture futures option data, this research investigates factors that affect option returns on agriculture futures contacts.

Several studies have examined option trading, although this is typically in equities. Analysis focuses on whether option returns are associated with time to expiration or moneyness. Significant work includes Trennepohl and Dukes (1981), which finds that buying longer-term in-the-money options provides the highest returns, with U.S. stock options data. On the other hand, Wilkens (2007) investigates the European equity index option market and argues that option returns are sensitive to option type, moneyness and time to expiration. He finds that call option return increases from in-the-money through out-of-the-money, while put option returns decreases from in-the-money through out-of-the-money. (2) In addition, the difference of the returns is sensitive to the maturity; shorter-term options have higher returns. The literature seems inconclusive regarding how time to expiration and moneyness affect option returns.

Research on commodity option trading is scarce. There is, however, considerable background research on commodity volatilities per se. Samuelson (1965) showed how futures price volatility might increase as the futures contracts approach expiration. There is mixed evidence on the Samuelson effect. (3) However, most of the ambiguities are cleared up when Brooks' (2012) analysis is considered. Brooks (2012) shows how the Samuelson effect is related to the ability to arbitrage the derivative product. This arbitrage issue is relevant for agricultural markets. Markets that are linked by arbitrage should not exhibit the Samuelson effect.

To trade volatility with futures options, the futures price risk must be minimized, such as with a straddle. A straddle involves buying a call option and a put option simultaneously with the same strike price and the same expiration date. There is little sensitivity of the position to asset price movements since, in the short run, the call and put values will move in opposite directions by similar magnitudes as the asset price changes. Both, however, will respond to futures volatility changes in the same way. A long straddle strategy offers positive returns when volatility increases. Doidge and Wei (1998) use Toronto 35 Index options and find that straddle strategy is able to generate positive trading profits. Nadi and Waggoner (2001) utilize S&P 500 Index options and suggest that selling straddles has resulted in substantial losses. They argue that the negative correlation (an empirical, if not theoretical finding) between equity market and implied volatilities could make straddle returns sensitive to the market direction. On the other hand, Wilkens (2007) investigates the European equity index option market and finds that short positions in straddle portfolios yield positive returns. Urcola and Irwin (2011) examine the U.S. agricultural futures contracts and find that buying futures options straddles does not lead to large economic gains. They conclude that the option markets are efficient or that options are priced fairly. The literature seems inconclusive on the straddle returns. In addition, if the Samuelson effect holds, we expect straddles returns to increase when approaching expiration, holding all else constant. As the futures volatility increases, the implied volatilities should rise as well as delivery/expiration approach. Counteracting this will be the time decay. We examine straddle returns and the Samuelson effect.

We use high frequency tick data from corn, soybean and wheat options on futures contracts from January 1995 to Dune 2012. Since the futures price is a major factor in option valuation, the high frequency allows us to capture a simultaneous futures price to match with the option trade, and is used to identify moneyness. Further, to minimize liquidity issues, options are selected based on the last trading price each day for each contract for the most actively traded (most entries in the time and sales record) strike prices. We examine the impact of time to expiration and moneyness on option returns, as well as controlling for the risk free return and equity returns.

Our evidence suggests that time to expiration has a positive effect on call, put and straddle returns, which supports Trennepohl and Dukes (1981), who found that longer-term options have higher returns. The relative strike price has a negative effect on call returns and a positive effect on put returns, indicating that in-the-money calls and puts have higher returns. Again, this result supports Trennepohl and Dukes (1981) that in-the-money options have higher returns. We examine the return volatility and find higher volatility when approaching expiration, which indirectly supports a second order Samuelson effect. If the Samuelson effect holds for volatility uncertainty, we might expect to find higher straddle returns when approaching option expiration as volatility climbs. However, our evidence, consistent with the put and call evidence, shows that the longer-term straddles generate higher returns. We suspect that the time effect dominates the Samuelson effect, which suggests that holding all else constant, American style options decline in value as expiration nears. We also find that interest rates and stock market returns do not seem to have significant effects on these option returns.

This article proceeds as the following. The data and methodology are demonstrated in Section II. Section III presents the empirical results. Section IV concludes.

II. Data and Methodology

We begin with a frequency tick data set for corn, soybean and wheat futures options traded on the Chicago Board of Trade (now part of the CME Group). The sample period spans over 17 years, from January 1995 to lune 2012. The dataset was acquired from the CME Croup. Tick data are time and sales data with a simple history of transaction prices and the time that trades are executed. For our data, these options are traded live as well as electronically via Globex. When trading in pits, traders gather physically around the tiered bowls, known as pits, and have unique access to the physically transacted order flow. Exchange employees record the prices and times. Electronic trading was originally enabled in the 1990s during the hours when pit trading was not occurring. In the 2000s, options began trading electronically simultaneously with pit trading. However, according to the CME Group, on October 19, 2012, for example, options trades were evenly divided, with a little over 1,000,000 contracts traded both in the pits and via Globex. Our sample prices are taken from a merge of time and sales records from both physical and electronic trading environments. There is no information on quantity from the physical time and sales and no indication of who the principals are behind the trade.

Futures options are not as frequently traded as futures, leading to asynchronous issues associated with using settlement prices. The settlement prices are typically adjusted by the exchange to a common option pricing model, diffusing or obscuring potentially important market information. The use of tick data overcomes that issue. In particular, for each option observation we also obtain the most recent futures price (a second or two earlier) to define the option moneyness. For each strike and expiration, we match the last call and put price for the day and then select the strike for that day that has the most entries in the time and sales record. Thus, our put, call and straddle are from the most active strikes for each expiration each day. We calculate daily option returns based on the last trading price each day for each contract, matching the next day's closing prices for the previous day's chosen strikes. We also collect oneyear T-Bill rates from the St. Louis Federal Reserve Bank ("FRED") and the S&P500 index from Yahoo.

Futures options contracts can be highly leveraged, particularly the more frequently traded out-of-the-money options. Out-of-the-money option prices can be quite volatile because of the underlying futures price changes. For example, the futures option price could easily go from $0.01 to $0.10, which generates an outrageous 1,000 percent daily return, on the plus or minus side. As a result, we observe some extreme high and low daily returns because of the underlying futures price volatility. These returns are compounded by general futures option illiquidity. The bid ask spread on out-of-the-money options is quite high. Thus, the inherent volatility due to leverage could be exacerbated by bid ask bounce. For our statistical analysis, we exclude the top five percent and the bottom five percent of returns to overcome this issue.

The futures price for agricultural contracts calls for delivery of a warehouse receipt for 5,000 bushels of corn, wheat or soybeans, respectively. The futures price is quoted in terms of bushels. For wheat and corn, the delivery months are March, May, July, September and December. For soybeans, the delivery months are January, March, May, July, August, September and November. The futures options expire the month before the named futures contract. For example, March soybean future options will expire at the end of February. Futures options are American style, meaning that they can be exercised at any time prior to expiration. The exercise of a futures option results in a futures position. For example, if a call is exercised, the holder obtains a long futures contract, whereas the short call option holder would be given a short futures contract. So if a holder of a March call option exercises the option, he or she obtains a long futures position with a delivery window in March. While the futures contract has an uncertain delivery, due to the window, the futures option has an exact expiration date. The Samuelson effect, as shown by Brooks (2012), means that for the March futures contract, as the time to delivery draws near, the futures price will become more volatile. Because the implied volatility at any point in time prior to expiration will be an average of the expected future volatilities, this value should, on average, rise due to the Samuelson effect, as the option expiration nears. By examining option and straddle returns, we hope to provide indirect evidence towards the Samuelson effect in agricultural futures option markets.

Each agricultural market is unique and has different underlying volatility, which is tied to demand and supply conditions in the market. There are also other factors relevant to each particular market. As a result, we do not combine different agricultural markets in our analysis. Instead, we analyze each agricultural market separately and present the results by these different markets (corn, soybeans and wheat).

III. Empirical Results

We analyze the selected puts and calls separately and then as combined into a straddle. Table 1 presents the average daily returns for call, put and straddle contracts for corn, soybeans and wheat futures contracts, pre filter. For most contracts, the average daily returns appear negative: buying options loses a small amount of money daily. This makes sense. If the futures contract follows something akin to a random walk, the option should, on average, suffer from time decay. In other words, if the futures contract remains fixed from the time the option was purchased, the option would fall in value until expiration. The only exception in our data is the positive average put return for wheat contract. In addition, the average put returns are lower than the average call returns for both corn and soybean contracts. Our evidence on the negative average returns of agriculture straddles should not be seen as surprising, given prior results, such as Urcola and Irwin (2011). Note that we use daily returns, and Urcola and Irwin (2011) use fixed time to expiration returns.

We use a regression model to examine the relationship between the independent variables and option returns. The independent variables include time to expiration and moneyness. We also add interest rate and stock market return as control variables. We have no expectations on the signs of these additional variables and merely add them for completeness. The regression model follows:

[R.sub.it] = [[alpha].sub.i]+[[beta].sub.1,i] (*) [Time.sub.i,t] + [[beta].sub.2,i] (*) [Strike.sub.i,t] + [[beta].sub.3,i] (*) [Interest.sub.t] + [[beta].sub.4,i] (*) [Equities.sub.t] +[[epsilon].sub.i,t], (1)

where [R.sub.i,t] is the daily return on an option or a straddle; [Time.sub.i,t] is the time to expiration, in years, associated with the option or straddle; Strike., is the ratio of the strike price to the most recent futures price associated with the option; [Interest.sub.t] is the daily risk free interest rate; and Equities, is the daily return using S&P 500 Index as proxy for the stock market. High strike ratios (greater than 1) will be associated with out-of-the-money calls and in-the-money puts. Low strike ratios (less than 1) will be associated with in-the-money calls and out-of-the-money puts. We examine how time to expiration and moneyness affect call returns by running the regression with time to expiration and strike price as the independent variables and the daily call returns as the dependent variable. Later, we break the data into quartiles based on time to expiration and moneyness. We also include daily interest rate and stock return as control variables. The same regression is conducted for corn, soybean and wheat call options, respectively.

From the results in Table 2 related to call options, time to expiration is associated with a significant positive effect on wheat call returns. For wheat call options, the longer the time to expiration, the higher the return on the call option. However, a similar effect is not found in corn or soybean call option contracts. The strike ratio has negative effects on call returns in all three contracts, which means that lower strike ratio leadsto higher call returns. In otherwords, more in-the-money call options offer higher returns. In addition, interest rate and stock return do not seem to have significant effects on call returns for most of these contracts.

Next, we examine the relationship between put options and the same independent variables. The regression results are also shown in Table 2. Time to expiration has significant positive effects on put returns in two contracts (corn and soybeans). For corn and soybean put options, longer-term contract generate higher returns. The strike ratio has significant positive effects on put returns across three contracts, which means that higher strike price gives higher put returns. In other words, in-the-money put options offer higher returns. Put options demonstrate the same characteristics as call options that longer-term in-the-money options offer higher returns. Similar to the findings in call returns, interest rate and stock return do not seem to have significant effects on put returns in these contracts. One explanation for the moneyness effect could be that our more in-the-money strikes are actually at the money. These contracts would tend to be more liquid than the out-of-the-money options so that the liquidity effect might take away from the out-of-the-money options.

For straddle returns, time to expiration also has positive effects on returns across all three contracts (corn, soybeans and wheat), as shown in Table 3. Longer-term straddles give higher returns. Since the straddles are composed of the same strike for puts and calls, and these have different returns individually (in-the-money puts would be combined with out-of-the-money calls and out-of-the-money puts would be combined with in-the-money calls), we should not expect much from the strike ratio. Indeed, we have mixed results for the strike ratio, with positive effect from the wheat contracts, negative effect from the corn contracts and insignificance from the soybean contracts. The interest rate does seem to have positive effects on straddle returns, while stock market returns appear unrelated to agriculture futures options.

Our findings support Trennepohl and Dukes (1981) in that longer-term in-the-money options have higher returns. We also find that longer-term straddles also have higher returns. The Samuelson effect argues that price volatility increases as the contracts approach expiration. The straddle strategy offers higher returns when the underlying asset volatility increases. If the Samuelson effect holds, we expect to find higher straddle returns when approaching option expiration, holding all else constant. However, our evidence shows that longer-term straddles generate higher daily returns, which does not provide evidence for the Samuelson effect. This finding leads us to further explore the Samuelson effect.

To investigate the Samuelson effect, we change the dependent variable in the regression models from the daily returns to absolute daily returns and run the regression models again. We still include the same independent variables, such as time to expiration, moneyness, interest rate and stock market return in the models. Since the focus is on the relationship between time to expiration and the absolute returns, we only present the regression results for time to expiration in Table 4, while the complete regression results are readily available from the authors. We find that time to expiration has negative effects on absolute call, put and straddle returns across all three contracts (corn, soybeans and wheat). The absolute returns are higher when approaching expiration. It indicates more volatility in option returns when approaching expiration, which provides indirect support for a second order Samuelson effect.

We next divide our sample into quartiles sorted by the time to expiration. Group One, T1 shown in Table 5, has the lowest 25 percent of time to expiration observations, while Group Four, T4, has the highest 25 percent of time to expiration observations. We compute the average returns and the average absolute returns in each group. Moving from Group One with the shortest time to expiration to Group Four with the longest time to expiration, the average returns increase across all three contracts (corn, soybeans and wheat), which supports our earlier finding that longer-term options and straddles have higher returns. In fact, as most option and straddle returns are negative, on average, for the longest time to expiration (Group Four), the average call option returns are positive for corn and soybeans futures option contracts. To investigate the Samuelson effect, we focus on absolute returns. Moving from Group One to Group Four, the average absolute returns decrease. It means that absolute returns increase when approaching expiration. In other words, there are higher return volatilities when approaching expiration. This offers corroboration to the second order Samuelson effect in option and straddle returns.

To further investigate moneyness, we also conduct similar analysis to divide the observations into four groups based on the strike ratio. As shown in Table 6, Group One, SI, has the lowest 25 percent strike ratio observations, while Group Four, S4, has the highest 25 percent strike ratio observations. We also compute the average returns and the average absolute returns in these groups. For call options, the average returns seem to decrease when we move from Group One with the lowest strike ratio to Group Four with the highest strike ratio. It means that lower strike ratio gives higher call returns, which supports our earlier finding that in-the-money call options have higher returns. For put options, the average returns seem to increase when we move from Group One to Group Four. It means that higher strike ratio gives higher put returns, which also supports our earlier finding that in-the-money put options have higher returns. For straddle returns, the trend is not as significant as those found in call and in put returns. In fact, Group One and Group Four seem to have higher average returns when compared to Group Two and Group Three in straddle returns. This result is not surprising since a straddle contract includes both a call option and a put option. We also examine the absolute returns in these groups but do not find significant difference across different strike ratios. In general, the results, shown in Table 6, support what we discover earlier in the regression models that in-the-money options give higher returns.

IV. Conclusion

We examine agriculture futures option and straddle returns using prices sampled from the high frequency tick data on corn, soybeans and wheat. The sample period spans over 17 years, from January 1995 to Dune 2012. Daily returns are computed based on the last trading price each day for each contract, with tick data used to synchronize the futures and options prices to establish moneyness. The evidence suggests that average daily returns for call, put and straddle contracts are mostly negative for corn, soybeans and wheat futures, which is consistent with previous research. There is an inherent time deterioration in the option value. In addition, the average put returns seem to be lower than the average call returns.

At any time investors can trade different options in terms of time to maturity and moneyness. We examine the effect of time to expiration and moneyness on option returns. We find significant positive relationship between time to expiration and options returns; longer-term option contracts offer higher returns. We use option strike price divided by the futures price as the measurement of moneyness. The strike ratio has a negative effect on call returns and a positive effect on put returns. For call options, a higher strike ratio indicates less moneyness. As a result, higher moneyness call options offer higher returns. On the other hand, for put options, a higher strike ratio indicates more moneyness. Higher moneyness put options also offer higher returns.

A straddle strategy is to buy a call and a put option simultaneously with the same strike price and the same expiration date. The straddle strategy offers higher returns when the underlying asset's volatility increases. According to the Samuelson effect, price volatility increases as the contract approaches expiration. If the Samuelson effect is strong, we expect straddle returns to increase when approaching expiration. However, our empirical evidence suggests a positive relationship between time to expiration and straddles returns, which means that, similar to the underlying options, longer-term straddles offer higher returns. We further divide our sample into subgroups based on time to maturity to investigate the return volatility. We find that groups with shorter time to maturity demonstrate higher return volatility, which supports Samuelson effect. Therefore, we suspect that longer-term straddles have higher returns because the time effect dominates the Samuelson effect.

To conclude, our empirical evidence suggests that time to expiration and moneyness are important factors in option returns. Longer-term in-the-money options give higher returns, both for calls and for puts. We also find higher return volatility when approaching expiration, supporting a second order Samuelson effect. A higher volatility leads to a higher return for straddles. However, the time effect dominates the

Samuelson effect in straddle returns. Prior research seems inconclusive regarding how option and straddle returns are affected by time to expiration and by moneyness. By providing the updated evidence from over 17-year tick data on the U.S. agriculture futures option data, we hope we have shed some light on these issues.

References

Alkeback, P., and N. Hagelin. "Expiration Day Effects of Index Futures and Options: Evidence from a Market with a Long Settlement Period." Applied Financial Economics, vol. 14, no. 6, 2004, pp. 385-396.

Brooks, Robert. "Samuelson Hypothesis and Carry Arbitrage." Journal of Derivatives, vol. 20, no. 2, 2012, pp. 37-65.

Chamberlain, T.W., S.C. Cheung, and C.Y. Kwan. "Expiration-day Effects of Index Futures and Options: Some Canadian Evidence." Financial Analysts Journal, vol. 45, no. 5,1989, pp. 67-71.

Coval, ID., and T. Shumway. "Expected Option Returns." Journal of Finance, vol. 56, no. 3, 2001, pp. 983-1009.

Doidge, C., and J.Z. Wei. "Volatility Forecasting and the Efficiency of the Toronto 35 Index Options Market." Revue Canadienne des Sciences de l'Administration, vol. 15, no. 1, 1998, pp. 28-38.

Galloway, T.M., and R.W. Kolb. "Futures Prices and Maturity Effect." Journal of Futures Markets, vol. 16, no. 7, 1996, pp. 809-828.

Gupta, S.K., and P. Rajib. "Samuelson Hypothesis & Indian Commodity Derivatives Market." Asian- Pacific Financial Markets, vol. 19, no. 4, 2012, pp. 331-352.

Ju, S.E., K.H. Lo, and K. Wang. "Expiration Day Effects: Empirical Evidence from Taiwan." Journal of Global Business Issues, Conference Edition, 2008, pp. 51-62.

Karolyi, G.A. "Stock Market Volatility around Expiration Days in Japan." Journal of Derivatives, vol. 4, no. 2, 1996, pp. 23-43.

Lien, D., and L. Yang. "Availability and Settlement of Individual Stock Futures and Options Expiration-day Effects: Evidence from High Frequency Data." Quarterly Review of Economics and Finance, vol. 45, no. 4, 2005, pp. 730-747.

Nadi, S., and D. Waggoner. "The Risks and Rewards of Selling Volatility." Economic Review--Federal Reserve Bank of Atlanta, vol. 86, no. 1, 2001, pp. 31-39.

Samuelson, P.A. "Proof that Properly Anticipated Prices Fluctuate Randomly." Industrial Management Review, vol. 6, no. 2, 1965, pp. 41-49.

Trennepohl, G.L., and W.P. Dukes. "An Empirical Test of Option Writing and Buying Strategies Utilizing In-the-Money and Out-of-Money Contracts." Journal of Business Finance & Accounting, vol. 8, no. 2, 1981, pp. 185-202.

Urcola, H.A., and S.H. Irwin. "Are Agricultural Options Overpriced?" Journal of Agricultural and Resource Economics, vol. 36, no. 1, 2011, pp. 63-77.

Wilkens, S. "Option Returns Versus Asset-pricing Theory: Evidence from the European Option Market." Journal of Derivatives & Hedge Funds, vol. 13, no. 2, 2007, pp. 170-176.

Xu, C. "Expiration-day Effects of Stock and Index Futures and Options in Sweden: The Return of the Witches." Journal of Futures Markets, vol. 34 no. 9, 2014, pp. 868-882.

Peter Locke

Texas Christian University

Tzu-Man Huang

California State University-Stanislaus

(1) Since a futures contract is linked to the underlying commodity through a cost of carry model, the option on a futures contract is similarly linked to the underlying. Due to arbitrage, the volatility of the futures will mirror the volatility of the underlying, though incomplete arbitrage will allow this to differ. Since we are using futures options, the value or volatility of the underlying itself is not that important. The critical factor is the possibility that the futures price will become more volatile as delivery approaches, hence as options expiration approaches.

(2) Coval and Shumway (2001) also have similar findings in that for the S&P 500 index both call and put option returns increase with strike price. In other words, out-of-the-money calls and in-the-money puts have higher returns.

(3) Supporting literature includes Chamberlain, Cheung and Kwan (1989); Calloway and Kolb (1996; Lien and Yang (2005) and Ju, Lo and Wang (2008). On the other hand, there is also research that does not support the Samuelson effect, including Karolyi (1996), Alkeback and Hagelin (2004), Gupta and Rajib (2012) and Xu (2014).

TABLE 1 Daily Return Statistics Note: Daily returns are calculated for every expiration that yielded a matched pair of put and call for that day. Options from the most active daily strike are selected. Thus, the means presented are cross sectional (across expirations) and time series. Figures are in percentages except for the number of observations. The asterisk (*) indicates statistically significant from zero at five percent level. No. of Mean Std Dev Median Max Min Obs Corn Calls 14621 -0.27 (*) 10.92 0.00 36.00 -32.89 Puts 14621 -0.42 (*) 9.48 0.00 32.69 -31.91 Straddles 14621 -0.20 (*) 4.28 0.00 16.00 -14.95 Soybeans Calls 14021 -0.09 12.36 0.00 40.90 -34.92 Puts 14021 -0.87 (*) 10.82 0.00 35.89 -35.00 Straddles 14021 -0.28 (*) 4.95 -0.26 16.00 -15.00 Wheat Calls 8979 -0.20 12.52 0.00 50.00 -38.98 Puts 8979 0.11 12.19 0.00 50.00 -36.95 Straddles 8979 -0.05 5.29 -0.17 19.89 -15.00 TABLE 2 Relationships between Option Returns, Time to Expiration, Strike, Interest Rate, and Stock Return Note: The asterisk (*) indicates statistically significant at five percent level. Variable Parameter t Value [R.sup.2] Corn calls 0.0203 Intercept -0.189 -14.22 (*) [Time.sub.i,t] 0.003 0.98 [Strike.sub.i.t] -0.201 -15.86 (*) [Interest.sub.t] 39.440 2.19 (*) [Equities.sub.t] -0.088 -1.06 Soybean calls 0.0162 Intercept 0.167 12.22 (*) [Time.sub.i,t] -0.000 -0.05 [Strike.sub.i,t] -0.175 -13.37 (*) Interest, 21.788 0.97 [Equities.sub.t] -0.049 -0.49 Wheat calls 0.0041 Intercept 0.003 0.31 Time,, 0.028 3.51 (*) Strike, t -0.022 -3.09 (*) Interest, -26.774 -0.86 Equities, 0.058 0.40 Corn puts 0.0337 Intercept -0.256 -22.52 (*) Time,, 0.022 8.02 (*) Strike., 0.237 21.90 (*) Interest, 12.114 0.79 Equities, -0.022 -0.31 Soybean puts 0.0239 Intercept -0.217 -18.20 (*) [Time.sub.i,t] 0.045 10.36 (*) [Strike.sub.i,t] 0.177 15.52 (*) [Interest.sub.t] 72.043 3.67 (*) [Equities.sub.t] -0.104 -1.19 Wheat puts 0.0055 Intercept -0.054 -5.85 (*) [Time.sub.i,t] o.on 1.48 [Strike.sub.i,t] 0.040 5.92 (*) [Interest.sub.t] 46.871 1.57 [Equities.sub.t] -0.198 -1.42 TABLE 3 Relationships between Straddle Returns, Time to Expiration, Strike, Interest Rate, and Stock Return Note: The asterisk (*) indicates statistically significant at five percent level. Variable Parameter t Value [R.sup.2] Corn straddles 0.0162 Intercept -0.007 -1.44 [Time.sub.i,t] 0.016 13.05 (*) [Strike.sub.i,t] -0.011 -2.35 (*) [Interest.sub.t] 32.990 4.78 (*) [Equities.sub.t] -0.031 -0.96 Soybean straddles 0.0175 Intercept -0.015 -2.92 (*) [Time.sub.i,t] 0.025 12.97 (*) [Strike.sub.i,t] -0.008 -1.63 [Interest.sub.t] 40.696 4.65 (*) [Equities.sub.t] -0.008 -0.19 Wheat straddles 0.0080 Intercept -0.031 -8.10 (*) [Time.sub.i,t] 0.020 6.35* [Strike.sub.i,t] 0.012 4.16 (*) [Interest.sub.t] 40.266 3.19 (*) [Equities.sub.t] -0.002 -0.04 TABLE 4 Relationships between Absolute Returns and Time to Expiration Note: The asterisk (*) indicates statistically significant at five percent level. Variable Parameter t Value [R.sup.2] Calls Corn -0.051 -25.51 (*) 0.0669 Soybeans -0.075 -24.90 (*) 0.0850 Wheat -0.025 -4.64 (*) 0.0265 Puts Corn -0.051 -28.66 (*) 0.0676 Soybeans -0.079 -28.46 (*) 0.0616 Wheat -0.032 -6.23 (*) 0.0947 Straddles Corn -0.019 -23.04 (*) 0.0457 Soybeans -0.032 -26.69 (*) 0.0605 Wheat -0.040 -20.35 (*) 0.1111 TABLE 5 Returns and Absolute Returns under Different Time to Expirations Note: Figures are in percentages. Calls Puts Straddles Time to Mean Abs Mean Mean Abs Mean Mean Abs Mean Expiration Corn T1 -1.33 12.13 -1.19 10.54 -1.53 4.52 T2 -0.31 10.04 -0.77 7.97 -0.58 3.43 T3 -0.52 8.90 -0.13 7.15 -0.39 3.31 T4 0.24 6.68 -0.55 6.13 -0.01 2.85 Soybeans T1 -1.47 14.20 -2.38 12.35 -1.93 5.50 T2 -0.38 11.95 -1.61 9.95 -0.93 4.37 T3 -0.40 10.06 -0.79 8.52 -0.48 3.86 T4 0.34 7.72 -0.77 7.27 -0.10 3.47 Wheat T1 -1.57 10.04 -0.60 8.91 -0.92 5.37 T2 -1.98 11.63 -0.10 10.79 -1.00 4.72 T3 -0.80 11.13 -0.26 10.91 0.46 4.46 T4 -0.18 9.21 -0.05 8.85 -0.11 3.55 TABLE 6 Returns and Absolute Returns under Different Strike Ratio Note: Figures are in percentages. Calls Puts Straddles Strike Mean Abs Mean Mean Abs Mean Mean Abs Mean Ratio Corn S1 3.34 8.51 -4.48 9.76 0.18 4.07 S2 1.23 8.72 -2.08 7.74 -1.15 3.48 S3 -1.90 9.08 1.05 7.04 -1.10 3.21 S4 -4.58 11.34 2.82 7.20 -0.43 3.33 Soybeans S1 3.23 8.58 -5.13 10.86 0.25 4.70 S2 2.11 10.52 -3.81 10.37 -1.69 4.31 S3 -2.53 11.63 -0.88 9.21 -1.80 4.19 S4 -4.73 13.14 2.47 7.61 -0.20 3.98 Wheat S1 1.25 7.31 -2.43 11.85 0.39 5.90 S2 2.52 11.33 -3.18 12.15 -1.21 4.49 S3 -5.76 13.95 3.47 10.88 -2.03 4.36 S4 -2.54 9.40 1.33 4.58 0.34 3.34

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Author: | Locke, Peter; Huang, Tzu-Man |

Publication: | Quarterly Journal of Finance and Accounting |

Date: | Jun 22, 2019 |

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