This article was downloaded by: [Stony Brook University]On: 05 November 2014, At: 09:05Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Applied Financial EconomicsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/rafe20

How do you straddle hogs and pigs? Ask the Greeks!Andrew McKenzie a , Michael Thomsen a & Josh Phelan aa Department of Agricultural, Economics and Agribusiness , University of Arkansas ,Fayetteville, AR, USAPublished online: 24 Apr 2007.

To cite this article: Andrew McKenzie , Michael Thomsen & Josh Phelan (2007) How do you straddle hogs and pigs? Ask theGreeks!, Applied Financial Economics, 17:7, 511-520, DOI: 10.1080/09603100500428230

To link to this article: http://dx.doi.org/10.1080/09603100500428230

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Applied Financial Economics, 2007, 17, 511–520

How do you straddle hogs and pigs?

Ask the Greeks!

Andrew McKenzie, Michael Thomsen* and Josh Phelan

Department of Agricultural, Economics and Agribusiness, University of

Arkansas, Fayetteville, AR, USA

Evidence of distortions is found in commodity options premiums around

informational events. Option Greeks are used to uncover the nature of

these distortions in terms of underlying factors. Both changes in underlying

futures prices and implied volatility are mispriced.

I. Introduction

A common approach used to empirically test stock

options market efficiency (see Whaley, 1982, p. 35)

has been to evaluate the profitability of simulated

trading strategies generated by identifying mispriced

option premiums. Typically, an option valuation

model is used to identify overvalued or undervalued

observed (call) option premiums, which are sold or

bought against a delta-hedged position in the under-

lying asset. Theoretically, if a market is efficient the

trading strategy should generate an appropriate rate

of return commensurate with its associated risk and

transaction costs. For example, a riskless hedge

portfolio should earn the risk-free rate of return. In

general, most stock options studies using this kind of

trading approach support options market efficiency

(Black and Scholes, 1972; Galai, 1977; Whaley, 1982;

Gemmill and Dickens, 1986; Harvey and Whaley,

1992; Joo and Dickinson, 1993). That is, these studies

find that options based trading strategies fail to yield

statistically significant profits after taking into

account transaction costs. Noh et al.’s (1994) study

of the S&P 500 Index options market represents a

notable exception to this body of literature. They

found evidence of market inefficiency after incorpor-

ating GARCH volatility forecasts into an option

valuation model. However, Corredor and Santamaria

(2004) using a similar modelling approach found the

Spanish Ibex-35 index options market to be efficient.

Recent research with respect to foreign currency

options indicate potential inefficiencies, depending

upon transaction cost assumptions (Chen and Leung,

2003; Chong, 2004).Hauser and Liu (1992) and Simon (2002) used such

an option valuation model approach to examine the

efficiency of options markets for futures on agricul-

tural commodities. The findings of these studies are

consistent with conclusions from research on stock

options in that they find little evidence of inefficiency.

Hauser and Liu (1992) evaluated live cattle futures

options efficiency over the period November 1984 to

September 1987, while Simon’s (2002) more recent

study addressed the issue of corn futures options

efficiency for the January 1988 through September

1999 period. Both studies identified mispriced options

by comparing various volatility forecasts with Black

model generated implied volatility measures. When

implied volatility measures exceeded (were less than)

volatility forecasts by a certain threshold level it was

assumed this indicated that observed options pre-

miums were overpriced (underpriced). Hauser and

Liu (1992) found that in general arbitrage opportu-

nities using delta-hedged portfolios containing the

theoretically mispriced options did not exist. In a

similar vein Simon (2002) found insignificant profits

from short-straddle positions implemented using

theoretically overpriced call and put options.However, a fundamental problem associated with

this type of efficiency test is that it assumes some

model of market equilibrium. In other words, it is in

fact a joint test that: (a) the option valuation model is

*Corresponding author. E-mail: mthomsen@uark.edu

Applied Financial Economics ISSN 0960–3107 print/ISSN 1466–4305 online � 2007 Taylor & Francis 511http://www.tandf.co.uk/journalsDOI: 10.1080/09603100500428230

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14

correctly specified; and (b) the options market isefficient. An alternative way to empirically test foroptions market efficiency, that circumvents the jointhypothesis problem, is to use an event study typeapproach. In this case the generation of tradingstrategies do not rely upon a theoretical optionvaluation model but are instead unambiguouslyimplemented in event time. In this sense theimplementation of event induced trading strategiesare predetermined. The existence of a trading strategygenerating systematic profits, implemented aroundknown (scheduled) events, would indicate a degree ofmarket inefficiency by failing to take into account allrelevant price sensitive information. In spite of itsinherent advantages, few studies using the eventinduced trading strategy approach exist, and empiri-cal evidence of options markets efficiency using thistype of event approach is mixed. For exampleMonroe (1992) found evidence of efficiency in theTreasury bond futures options market. In Monroe’s(1992) study various simulated trading strategiesestablished around the announcement of majoreconomic series, such as money supply, failed togenerate significant profits net of transaction costs.In contrast, Hemler and Miller (1997) found thata box spread strategy implemented with S&P 500index (SPX) options yielded arbitrage profit oppor-tunities immediately following the 1987 stock marketcrash, and that market inefficiency prevailed for threeweeks following the Crash.

In light of the above studies, one objective of thisstudy is to present the first known empirical applica-tion of the event induced trading strategy approachwith respect to an agricultural commodity futuresoptions market. In the empirical application the studytests the efficiency of the hog futures options marketsurrounding the release of quarterly United StatesDepartment of Agriculture (USDA) Hogs and PigsReports (HPRs) over the 1985 to 2000 period. Thistime period is chosen because it provides the largestwindow over which a continuous and uninterruptedset of reports coincides with hog options market data.Hog options began trading in 1985. Beginning in 2001and continuing through August 2003, the USDAswitched from a quarterly to a monthly releaseschedule. In September 2003, USDA reverted backto the quarterly release schedule. The market for hogoptions offers fertile ground for such an exercisebecause extensive previous research has investigated –using futures price data – whether or not HPRscontain unanticipated information (Carter andGalopin, 1993; Mann and Dowen, 1996, 1997), andif hog futures markets react efficiently to unantici-pated information contained in the reports(Koontz et al., 1984; Colling and Irwin, 1990; and

Schroeder et al., 1990). Two modal conclusions of

these studies are that: (a) large futures price move-

ments are observed around the reports’ release date;

and (b) the hog futures market appears to be efficient

at impounding new information. The market effi-

ciency conclusion stems from the fact that even

though futures prices tend to react to HPRs,

a systematic speculative futures strategy set up prior

to the report, would result in trading profits that are

insignificantly different from zero. In other words

there is no systematic movement in futures prices

following HPRs.An event study is used to empirically test efficiency

in the hog futures options market by assessing the

profitability of long straddle positions established

around the release of HPRs. The long straddle is a

trading strategy that involves the simultaneous

purchase of an equal number of put and call options

with the same strike price. Straddles have been used

in several previous studies to test for options market

efficiency (Noh et al., 1994; Simon, 2002; Chen and

Leung, 2003; Chong, 2004). In particular, see Chen

and Leung (2003) for a review of literature involving

straddle strategies. The results, assuming half tick

transaction costs, suggest pricing inefficiencies

because evidence is found of systematic profits from

long straddle positions. However, the results (like

previous research) are sensitive to the assumed level

of transaction costs. Once higher levels of transaction

costs of a full tick are considered, systematic profits

from long straddle positions were no longer possible.

In this case, the existence of a significant no-arbitrage

transaction cost band would be consistent with

market efficiency and would not imply that mispri-

cing had occurred in the hog futures options market.What constitutes a reasonable level of transaction

costs is somewhat subjective, and hence while the

results show the possibility of earning systematic

speculative returns, no definitive conclusions may be

reached as to whether or not these returns translate

into pricing inefficiencies per se, only that options

prices may exhibit misalignment around the reports

within a given transaction cost band. Regardless of

whether the observed misalignments are indicative of

option market inefficiency, of equal importance is an

understanding of what might be causing misalign-

ments around release dates. The behaviour of options

markets is of particular interest because options

prices must reflect both changes in the first moment

(mean price) and second moment (volatility) of the

ex-ante price probability distribution (McNew and

Espinosa, 1994). In short, markets for options on

futures have higher informational requirements than

would markets for futures.

512 A. McKenzie et al.

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14

This leads to the second objective of the study,which is to demonstrate a method for decompos-ing returns to a portfolio of options in such amanner that allows the researcher to distinguishbetween returns attributable to changes in volati-lity, changes in underlying futures prices, or any ofseveral other factors that affect options returns.Such methods would be useful in empirical studiesbecause when evidence of option market ineffi-ciency or pricing misalignments are observed theresearcher could shed further light on the under-lying causes.

The decomposition of portfolio returns usesGreek terms derived from a binomial option pricingmodel. Greeks are used to determine the relativecontribution of changes in underlying factors –implied volatility (Vega), futures price changes(Delta), time to maturity effects (Theta), andinterest rate changes (Rho) – to movements instraddle returns. The dynamic decomposition ofstraddle returns in this manner, and subsequentanalysis of the time paths of the various compo-nents, allows one to shed light on the source ofoption price distortions. Previous research (e.g.,Hauser and Neff, 1985) has attempted to quantifythe impact of factors such as implied volatility onoptions premiums using traditional regression tech-niques. However, such an approach is more staticin nature (only measuring the average impact of afactor over a period of time) and is limited bylinearity assumptions. In contrast, the ‘Greeksapproach’ is dynamic in nature and allows for anonlinear relationship between changes in optionpremiums and movements in the underlying factorsthat drive those changes.

At first glance results from the event study usingactual options premiums suggest the market wasfailing to fully incorporate volatility changesaround the reports. The Greek decompositionsconfirm this but indicate that distortions couldnot be attributed solely to volatility. Changes inunderlying futures prices also explained a signifi-cant portion of the systematically positive portfolioreturns.

The remainder of the paper proceeds as follows:The next two sections describe the event inducedtrading strategy approach the Greek decomposi-tions, and data. The final two sections of thepaper present the results and concludingcomments.

II. Approach

As noted earlier, a long straddle is a position in theoptions market that involves the simultaneouspurchase of an equal number of put and call optionswith the same strike price. It is useful to briefly justifywhy a long straddle position is suited to test forpersistent profitability around the release of HPRs.Figure 1 presents average measures of impliedvolatility and average percentage price changes (inabsolute value) for the live/lean hogs futures contractover a ten-day interval surrounding the release of anHPR1 In the figure, day t¼ 0 refers to the releasedate. Figure 1 presents averages for release dates overthe period 1985 to 2000.

HPRs are released after the market has closed onday 0. The first opportunity for the market toincorporate information contained in the report isday 1. Prior to release of the report, Fig. 1 showsstable futures price changes and an upward trend inimplied volatility. Implied volatility peaks on the

report release day. On the first day after the report,implied volatility drops precipitously and the averageabsolute futures price change is large. These trendsare consistent with findings reported in earlier studiesexamining hog futures responses to report releases.Colling and Irwin (1990) note that over their studyperiod, hog futures experienced limit moves on 40%of the days following the release of a report. Thetrend in implied volatility is also consistent withearlier findings that HPRs contain new informationabout market conditions. New information wouldnot only cause traders to revise their price expecta-tions but would also reduce uncertainty with regardto these expectations. Ederington and Lee (1996) andFornari and Mele (2001) provide empirical evidencethat implied volatility declines after scheduledannouncements. Moreover, on days without sched-uled announcements these authors found higherimplied volatilities. These earlier findings are con-sistent with the general pattern of implied volatilityshown around HPR releases.

Given the observed average patterns in absoluteprice changes and implied volatility, a speculatormight enter into a long straddle some days prior tothe release of a report and offset the position on thereport day. This would exploit the observed patternin implied volatility because value of both optionswould be expected to increase as implied volatilityincreased. Alternatively, establishing a long straddle

1Data on closing prices for nearby live/lean hog futures contracts, closing put and call options premiums, and impliedvolatility were obtained from Bridge CRB. The implied volatility measure is derived from Black’s option pricing model and isan average implied volatility based on premiums for the two nearest the money call options and the two nearest the money putoptions. Release dates for HPRs are from the USDA Agricultural Marketing Service.

Hog option price behaviour 513

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14

position on any day prior to day 1 and offsetting theposition on day 1 or day 2 could be profitable becausethe large change in price will move one of the optionsinto the money and thereby increase its value. In thissense, the strategy is non-directional in nature.In other words, it requires no forecast about thedirection of futures price movements. It should alsobe noted that a long straddle position has limiteddownside risk. Losses are strictly limited to thepremiums paid to open the position.

In an efficient market, options premiums wouldaccurately reflect patterns in price and impliedvolatility around HPRs and systematic profits froma strategy such as the long straddle would not bepossible. Thus, a formal test for the efficiency ofoptions markets around HPRs can be stated as:

Hypothesis 1

H0: Rðt1, t2Þ ¼ 0

HA: Rðt1, t2Þ > 0

where Rðt1, t2Þ is the average return from establishinga long straddle on day t1 and offsetting the positionon day t2.

This hypothesis is examined by calculating thereturns to long straddle positions consisting of one atthe money put option and one at the money call optionaround each HPR released between 1985 and 2000.

In these calculations, values of t1 range from �5(five days before the report release) to þ4 (four daysafter the report is released). The position is kept openfor at least one trading day and is closed by offsettingthe position at closing premiums on day t2, wheret1þ 1� t2� 5. Returns to the long straddle positionare computed in percentage terms as

Rðt1, t2Þ ¼�PCðt1, t2Þþ�PPðt1, t2Þ� 4C

PCðt1ÞþPPðt1Þþ 2C� 100 ð1Þ

where PC(t1) and PP(t1) are put and call premiums onday t1; �PCðt1, t2Þ and �PPðt1, t2Þ are the changepremiums between days t1 and t2; and C is thetransaction cost per trade.

In computing transactions costs we consider a floortrader. Such an individual will not pay a commissionbut will face liquidity cost (bid-offer spread) in thatthey would need to offer an incentive for anothertrader to make a market. An assumption used in otherstudies is that setting transactions costs equal to one-half tick, can approximate these costs (Simon, 2002;Noh et al., 1994; Harvey and Whaley, 1992). A tick isthe minimum unit by which the price of a commoditycan fluctuate, as established by the Exchange and isequal to $10 per contract (0.025 cents per pound) forlean hog futures. Establishing a long straddle positionand then offsetting this position involves a total offour transactions.2 Although half tick may be a

0.00

0.50

1.00

1.50

2.00

2.50

−5 −4 −3 −2 −1 0 1 2 3 4 5Day

Mea

n a

bso

lute

% p

rice

ch

ang

e

0.20

0.21

0.21

0.22

0.22

0.23

0.23

0.24

0.24

0.25

0.25

Mea

n im

plie

d v

ola

tilt

y

Absolute percent price change Implied volatility

Day of report

Fig. 1. Price and volatility trends surrounding HPR release dates

2 The Exchange charges half tick to liquidate an option that is deep out of the money. This is another precedent forapproximating transactions costs in this manner.

514 A. McKenzie et al.

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14

reasonable transaction cost assumption under normalmarket conditions, the possibility remains that a floortrader may face higher transaction costs to liquidatepositions prior to the release of HPRs because ofhigher than normal levels of volatility and lower thannormal levels of trading volume. Tomek and Peterson(2001) note that although option premium mispricingis thought to be arbitraged quickly away, if a market isthin, the adjustment may take longer, and the price-effect of entering and exiting positions could be large.We investigate this issue further by considering highertransaction costs up to a full tick.

Two series of options premiums are used togenerate the returns series defined by equation 1:

Returns series 1. Equation 1 uses actualpremiums generated by market activity over thestudy period. It is assumed that the positionswere opened at the closing premiums for optionswith strike prices nearest the money on day t1 andthat the positions are offset at the closingpremiums on day t2. Data needed to calculatereturns consist only of closing option premiumson days t1 and t2.Returns series 2. Equation 1 uses premiumsgenerated through binomial option pricingmodels for American put and call options withstrike prices nearest the money on day t1.

3 Datarequired are closing prices for live/lean hogfutures, implied volatility, time to option expira-tion, and risk free interest rates for days t1 and t2.

Because the first return series is based on actualmarket activity, a test of H1 based on this series isideal for drawing conclusions about the efficiency ofoptions markets. It does not require equilibriumassumptions inherent in an options pricing model andavoids the joint hypothesis problem alluded to in theintroduction. The second returns series is hypothe-tical in that it supposes that a model rather than amarket determined premiums over the study period.However, this second series is potentially useful.Greek terms derived from the model provide evidenceabout the extent to which volatility patterns orpatterns in futures price changes explain returnsbehaviour around HPR release dates.

The Greek terms are: DELTA¼ @P/@F is the rateof change in the options value with respect to thefutures price; THETA¼ @P/@T is the rate of change inthe options value with respect to time remaining toexpiration; VEGA¼ @P/@� is the change in the

options value with respect to volatility; andRHO¼ @P/@r is the change in the options premiumwith respect to the risk free rate. Because the longstraddle position is a portfolio consisting of one putand one call option, let �¼PC

þPP represent thevalue of this portfolio. The portfolio Greeks can becomputed as simple sums, e.g., DELTA�

¼

DELTACþDELTAP, and the change in value of

the portfolio can be approximated by:

�� � DELTA��Fþ VEGA��� þ THETA��T

þRHO��r ð2Þ

Each term on the right hand side of Equation 2represents the change in portfolio value attributableto the change in one of the factors. For instance,DELTA��F is the change in portfolio valueattributable to a change in the underlying futuresprice. Note that initially a long straddle consistingof one at the money put and one at the moneycall is delta neutral. Given put-call parity,DELTAC

¼�DELTAP so DELTA�¼ 0. In the

present study, the position is established as a buy-and-hold strategy and is not rebalanced over theholding period. Therefore, DELTA� can becomepositive or negative as the futures price changes andmoves one of the options into the money.

The Greek terms are not constants and arethemselves functions of factors affecting the optionsvalues. Empirically, the Greek terms are pointestimates derived from the options pricing modelgiven data at the close of the trading day.Furthermore, �F, ��, etc. reflect changes from theclose of one day to the next, not infinitesimalchanges. For these reasons, we implementEquation 2 using an average of Greek terms thatcorresponds to the periodicity of the data. Forexample, because �F¼Ft�Ft�1, DELTA�

¼

ðDELTA�t þDELTA�

t�1Þ=2. If the changes weretruly infinitesimal, Equation 2 would be a Taylorseries expansion including higher order terms.

III. Results

Table 1 presents average returns based on actual(market determined) options premiums, and assum-ing transaction costs of half tick, over the studyperiod. The primary result in Table 1 is that positionsoffset on the release date (t2¼ 0) show evidence of

3An exhaustive discussion of the binomial model is available in most textbooks on options. The models are dynamicprograms solved by backwards recursion through a lattice (tree). Computer code for the models used in this study was writtenin SAS IML and is available from the authors.

Hog option price behaviour 515

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14

persistent profit opportunities from a long straddle

strategy. The strongest evidence is for positions

opened two and three days prior to the report

(t1¼�2 or t1¼�3). There is also marginal evidence

for positions opened four to five days prior to the

report. Another result that is interesting in light of the

trends in Fig. 1 is that there is no statistical evidence

of systematic profits resulting from positions that are

offset on the day after the report (t2¼ 1), despite the

large average change in price that occurred on this

day. Table 1 shows statistically significant losses for

long straddles established after the report (positions

opened on days t1¼ 1 through t1¼ 4).4

These findings provide strong evidence of a

systematic pattern in portfolio returns surrounding

HPR releases. With transactions costs of half tick,

there is evidence that a long straddle opened two or

three days prior to the report and offset on the report

day would have been profitable over the study period.

The evidence for persistent profitability, however,

depends heavily on assumptions about transactions

costs. Table 2 provides average returns for positions

offset on the release day under varying transaction

cost assumptions. Table 2 shows profits that are highly

significant at transactions costs lower than the base-

line costs of half tick. When transactions costs are

Table 1. Mean percentage returns to options portfolio calculated from market premiums (N^ 59)a

t2

t1 Statistic �4 �3 �2 �1 0 1 2 3 4 5

�5 mean �1.487 �0.638 �0.748 0.456 2.463 0.858 �0.097 0.423 �1.309 �3.462�5 p value 0.057 0.552 0.460 0.703 0.101 0.819 0.981 0.922 0.766 0.398�4 mean �0.946 �0.303 �0.115 2.025 �2.483 �2.457 �2.242 �3.960 �5.425�4 p value 0.101 0.715 0.900 0.072 0.410 0.474 0.556 0.308 0.131�3 mean �0.569 �0.084 2.392 1.675 2.241 2.057 0.112 �1.980�3 p value 0.460 0.925 0.029 0.595 0.524 0.599 0.976 0.558�2 mean �0.687 2.834 0.838 0.944 1.294 �0.660 �2.526�2 p value 0.186 0.006 0.779 0.774 0.722 0.855 0.432�1 mean 1.089 �0.508 0.479 1.185 �0.445 �2.342�1 p value 0.181 0.843 0.874 0.726 0.896 0.4210 mean �3.014 �2.896 �2.744 �3.968 �5.8280 p value 0.133 0.261 0.369 0.199 0.0331 mean �3.447 �3.730 �4.487 �6.0151 p value 0.001 0.005 0.004 0.0012 mean �2.962 �4.032 �4.5532 p value 0.001 0.001 0.0003 mean �2.687 �3.2903 p value 0.001 0.0014 mean �1.7204 p value 0.021

Note: a p values are for a two tailed t test of the null hypothesis that mean returns are zero.

Table 2. Mean percentage returns to positions offset on day t2^ 0 under different transaction cost assumptions (N^ 59)a

Zero costs Costs¼Quarter tick Costs¼Half tick Costs¼Three quarter tick Costs¼Full Tick

t1 mean p value Mean p value mean p value mean p value mean p value

�5 3.959 0.011 3.208 0.035 2.463 0.101 1.725 0.244 0.993 0.498�4 3.528 0.003 2.773 0.016 2.025 0.072 1.281 0.248 0.544 0.620�3 3.921 0.001 3.153 0.005 2.392 0.029 1.637 0.127 0.888 0.398�2 4.374 0.000 3.602 0.001 2.834 0.006 2.074 0.039 1.321 0.180�1 2.606 0.003 1.845 0.028 1.089 0.181 0.339 0.671 �0.404 0.609

Note: a p values are for a two tailed t test of the null hypothesis that mean returns are zero.

4One might conclude that the negative and significant returns for positions after the report are indicative of profits to be hadby taking a position opposite that of the long straddle (i.e., a short straddle). Drawing such a conclusion from Table 1 wouldbe inappropriate. Results (not shown) indicate no statistical evidence of persistent profitability from short straddle strategiesaround HPR releases. It should also be noted that the short straddle, unlike, the long straddle has unlimited downside risk.

516 A. McKenzie et al.

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14

increased to three-quarters of tick, profits remainsignificant only for positions opened two days prior tothe report release date. At transactions costs of a fulltick, there is no evidence of statistically significantprofits. The results in Table 2 suggest that at highertransactions costs – costs that might face someoneother than a floor trader or that floor traders mightface in the presence of liquidity constraints –systematic profits over the study period were notpossible.

The evidence in support of unexploited profitpotential does not warrant a conclusion that optionsmarkets were inefficient. As already noted, thestatistical significance of systematic profits thatindicate inefficiency depends largely on the transac-tions cost assumptions. A conclusion of marketinefficiency can be supported only if one is willingto assume very low transactions costs. While percen-tage returns are fairly impressive at low transactionscosts, market inefficiency would imply the ability tomake large profits in dollar terms rather than inpercentage terms. To make large profits in dollarterms, a trader would need to be long in a largenumber of straddle positions, which would likelyincrease transactions costs.

Even if we cannot reject the efficient markethypothesis, option premiums do not fully reflect

anticipated volatility and/or underlying price changesprior to the HPR release dates. In this sense theprice discovery role played by the options market iscompromised and pricing signals distorted.Transactions costs preclude traders from exploitingthis distortion. Given the trends in absolute pricechanges and implied volatility shown in Fig. 1, it istempting to conclude that options markets failed toaccurately incorporate the increase in volatility priorto report releases but do a fairly good job ofincorporating expected large price swings that occurafter the report. Such a conclusion is, after all,consistent with the evidence that portfolio returnswere largest on the report day when implied volatilityis at its peak. This conclusion also makes sense giventhe smaller returns for positions offset one or twodays after the report when large price swings have thepotential to drive one of the options deep into themoney.5 However, Greek terms from the optionspricing model indicate that such a conclusion ispremature. A decomposition of portfolio value interms of the Greeks provides evidence that pricechanges and volatility changes are each responsible,in part, for the increase in portfolio value prior to dayzero.

Consider first the role of price changes presented inTable 3. This table shows the average day to day

Table 3. Daily contribution (cents/lb) of price change to portfolio value (N^ 59)a

t2

t1 Statistic �4 �3 �2 �1 0 1 2 3 4 5

�5 mean 0.027 0.025 0.000 0.039 0.039 0.132 0.160 0.093 0.041 �0.020�5 p value 0.014 0.159 0.999 0.009 0.023 0.003 0.001 0.017 0.211 0.450�4 mean 0.024 0.009 0.015 0.029 0.099 0.149 0.094 0.025 �0.017�4 p value 0.019 0.427 0.220 0.036 0.004 0.001 0.013 0.351 0.531�3 mean 0.005 0.021 0.030 0.175 0.189 0.106 0.010 �0.008�3 p value 0.593 0.101 0.002 0.000 0.000 0.011 0.757 0.762�2 mean 0.016 0.054 0.147 0.162 0.098 0.018 �0.021�2 p value 0.022 0.000 0.000 0.000 0.010 0.526 0.451�1 mean 0.036 0.163 0.181 0.098 0.016 �0.012�1 p value 0.000 0.000 0.000 0.004 0.555 0.7060 mean 0.138 0.170 0.093 0.008 0.0010 p value 0.000 0.000 0.008 0.761 0.9711 mean 0.099 0.071 0.043 0.0111 p value 0.000 0.003 0.055 0.6472 mean 0.056 0.035 0.0282 p value 0.000 0.045 0.1493 mean 0.041 0.0353 p value 0.001 0.0344 mean 0.0554 p value 0.000

Note: a p values are for a t test of the null hypothesis that mean price contribution is zero.

5 Even under the assumption of zero transactions costs results (not shown) provide no evidence of profits from long straddlepositions offset on any day other than day 0.

Hog option price behaviour 517

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14

changes in portfolio value attributable to changes inthe price of the underlying live/lean hog futurescontract, DELTA��F. The price contribution afterday t2¼ 0 is almost uniformly positive and statisti-cally significant. This is consistent with the fact that alarge price move increases the value of the portfolio.However, the price contribution is also significant onday t2¼ 0, and in some cases, is significant for earlierdays as well. These results suggest that prior toreceiving the information contained in the report, thefutures market is positioning itself in anticipation ofthe report release. Price changes, though smallrelative to those observed after the report, appear tobe making significant contributions to portfolio valueprior to the market having an opportunity to adjustits price expectation based on new information in thereport.

It may appear at first glance that a positive pricecontribution, DELTA��F, is a simple artefact of thelong straddle established with at the money put andcall options. If underlying futures prices move ineither direction the price contribution to portfoliovalue will be unambiguously positive. However, asnoted earlier, the portfolio is not rebalanced to bedelta neutral throughout the holding period. Asfutures prices move over the holding period oneoption moves into the money and one moves out. Theportfolio delta is no longer zero and the pricecontribution could be positive or negative.

Table 4 presents contributions to portfolio valueattributable to changes in volatility, VEGA���.Results are as would be expected given the volatilitytrend in Fig. 1, prior to and including the release date,the increase in implied volatility makes a positive andstatistically significant contribution to the portfoliovalue. After the release date, the drop in volatilityresults in statistically significant negative contribu-tions to portfolio value. Changes in portfolio valueresulting from changes in time to expiration,THETA��T, and interest rate changes, RHO��r,are not reported. The contribution from change intime is always negative, of roughly the samemagnitude regardless of which day is considered,and is statistically significant. This merely reflects thefact that the time value of the options in the longstraddle portfolio declines as expiration nears. For allpractical purposes, the contribution to portfolio valueresulting from changes in the interest rate is zero. Thisis not surprising given the short holding periodsexamined here.

Figure 2 summarizes portfolio value over theholding period in terms of cumulative factor con-tributions. Note that prior to the release day, bothchanges in implied volatility and changes in priceincrease the portfolio’s value. This increase more thanoffsets the reduction in portfolio value resulting fromthe passage of time. After the report, the drop involatility has a negative effect on portfolio value.

Table 4. Daily contribution (cents/lb) of volatility change to portfolio value (N¼ 59)a

t2t1 Statistic �4 �3 �2 �1 0 1 2 3 4 5

�5 mean 0.048 0.044 0.046 0.034 0.045 �0.249 �0.063 �0.033 �0.028 �0.003�5 p value 0.029 0.002 0.006 0.002 0.005 0.000 0.000 0.001 0.030 0.772�4 mean 0.045 0.046 0.036 0.044 �0.248 �0.068 �0.035 �0.028 �0.002�4 p value 0.002 0.006 0.002 0.007 0.000 0.000 0.001 0.034 0.831�3 mean 0.046 0.035 0.044 �0.248 �0.064 �0.034 �0.026 �0.002�3 p value 0.007 0.002 0.007 0.000 0.000 0.001 0.043 0.877�2 mean 0.036 0.046 �0.245 �0.070 �0.035 �0.028 0.001�2 p value 0.002 0.006 0.000 0.000 0.001 0.029 0.939�1 mean 0.047 �0.244 �0.069 �0.035 �0.024 0.000�1 p value 0.007 0.000 0.000 0.001 0.060 0.9680 mean �0.245 �0.075 �0.038 �0.022 �0.0010 p value 0.000 0.000 0.001 0.082 0.9621 mean �0.079 �0.041 �0.028 �0.0011 p value 0.000 0.001 0.043 0.9572 mean �0.042 �0.029 �0.0012 p value 0.001 0.042 0.9073 mean �0.030 �0.0023 p value 0.044 0.8574 mean �0.0024 p value 0.852

Note: a p values are for a t test of the null hypothesis that mean volatility contribution is zero.

518 A. McKenzie et al.

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14

The decline attributable to reduced volatility incombination with reduced time value of the optionsportfolio counteracts the positive contribution of thelarge price move that occurs after the report. In thissense, options markets efficiently adjust to informa-tion contained in the reports after it is known. It isbefore release, when the information contained in thereport is unknown, that there is evidence of optionprice distortions.

IV. Conclusions

One reason that the efficiency of commodity optionsmarkets is an interesting topic is that options pricesmust reflect changes in the mean futures price levelalong with the volatility of futures prices. In thisrespect, options markets must meet a higher standardof efficiency than would the market for the under-lying futures contract that needs only to accuratelyreflect the mean price. The behaviour of price changesand implied volatility around HPR releases is whatwould be expected given that HPRs are scheduledevents and provided they contain unanticipatedinformation (McNew and Espinosa, 1994;Ederington and Lee, 1996; Fornari and Mele, 2001).Market participants know that upon release of areport, new information may alter price expectationsand this is reflected by the gradual increase in impliedvolatility. The large price move on the day after the

report and reduction in implied volatility is evidencethat reports contain information that affects priceand removes uncertainty from the market.

This study found evidence of options price distor-tions prior to the release of reports. Given transac-tions costs, these distortions probably would not haveled to systematic profits and hence do not warranta rejection of the market efficiency hypothesis.However, these distortions are interesting becauseit is after the report, not before, when there is thelargest mean absolute price change and the largestchange in implied volatility. Long straddle positionsclosed after the report show no evidence of systematicreturns, only those closed on the report day. At firstblush this suggests that prior to the report optionsmarkets are failing to accurately reflect the gradualincrease in implied volatility. The problem though isthat returns to an option position are affected both bychanges in implied volatility and changes in theunderlying futures price. Hence, one cannot conclu-sively say that volatility is the only thing leading todistortions. The study sought to overcome thisempirical dilemma through a decomposition basedon the Greek terms. In the present case, theconclusion reached was that options markets couldbe inaccurately reflecting a combination of bothfutures price changes and volatility changes. Theempirical evidence suggests that small but unidirec-tional price moves occurring in anticipation of thereports was also making a significant contribution tothe long straddle returns.

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

−4 −3 −2 −1 0 1 5

Day

Cen

ts/lb

Cumulative price contribution Cumulative volatility contributionCumulative time contribution Cumulative change in portfolio value

2 3 4

Fig. 2. Cumulative factor contributions to long straddle returns for positions opened 5 days prior to release dates

Hog option price behaviour 519

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14

In future studies, Greek decompositions of optionsportfolios could provide useful insight into thebehaviour of options markets around a variety ofevents. The most common use of Greek terms is byprofessional traders where they are used to determinethe risk exposure of holding various options posi-tions. As shown here, they can also be used inempirical research to examine the contribution ofchanges in underlying factors, such as futures pricesand implied volatility, to option portfolio returns.The decompositions allow the researcher to gauge thecontribution of volatility to option returns separatefrom changes in the price of the underlying securityand hence measure the value of new information interms of both lower uncertainty and adjustments toprice expectations. In this sense Greek decomposi-tions can be used to infer when and why marketsrespond to an event.

References

Black, F. and Scholes, M. (1972) The valuation of optioncontracts and a test of market efficiency, Journal ofFinance, 27, 399–418.

Carter, C. A. and Galopin, C. A. (1993) Informationalcontent of government Hogs and Pigs Reports,American Journal of Agricultural Economics, 75,711–8.

Chen, A. and Leung, M. T. (2003) Option straddle trading:financial performance and economic significance ofdirect profit forecast and conventional strategies,Applied Economic Letters, 10, 493–8.

Chong, J. (2004) Options trading profits from correlationforecasts, Applied Financial Economics, 14, 1075–85.

Colling, P. R. and Irwin, S. H. (1990) The reaction of livehog futures prices to USDA Hogs and Pigs Reports,American Journal of Agricultural Economics, 72, 84–94.

Corredor, P. and Santamaria, R. (2004) Forecastingvolatility in the Spanish option market, AppliedFinancial Economics, 14, 1–11.

Ederington, L. H. and Lee, J. H. (1996) The creation andresolution of market uncertainty: The impact ofinformation releases on implied volatility, Journal ofFinancial and Quantitative Analysis, 31, 513–39.

Fornari, F. and Mele, A. (2001) Volatility smiles and theinformation content of news, Applied FinancialEconomics, 11, 179–86.

Galai, D. (1977) Tests of market efficiency and the ChicagoBoard Options Exchange, Journal of Business, 50,167–97.

Gemmill, G. and Dickins, P. (1986) An examination of theefficiency of the London Traded Options market,Applied Economics, 18, 995–1010.

Harvey, C. and Whaley, R. E. (1992) Market volatilityprediction and the efficiency of the S&P 100 IndexOption Market, Journal of Financial Economics, 31,43–73.

Hauser, R. J. and Neff, D. (1985) Pricing options onagricultural futures: Departures from traditionaltheory, The Journal of Futures Markets, 5, 539–77.

Hauser, R. J. and Liu, Y. (1992) Evaluating pricing modelsfor options on futures, Review of AgriculturalEconomics, 14, 23–32.

Hemler, M. L. and Miller, T. W. (1997) Box spreadarbitrage profits following the 1987 market crash: Realor illusory? Journal of Financial and QuantitativeAnalysis, 32, 71–90.

Joo, T. W. and Dickinson, J. P. (1993) A test of theefficiency of the European Options Exchange, AppliedFinancial Economics, 3, 175–81.

Koontz, S. R., Hudson, M. A. and Purcell, W. D. (1984)The impacts of Hog and Pig Reports on live hogfutures prices: An event study of market efficiency,Staff Paper SP-84-11, Department of AgriculturalEconomics, Virginia Polytechnic Institute and StateUniversity.

Mann, T. L. and Dowen, R. J. (1996) Are Hog and PigReports informative? The Journal of Futures Markets,16, 273–87.

Mann, T. L. and Dowen, R. J. (1997) The impact ofproprietary-public information on pork futures, TheJournal of Futures Markets, 17, 417–32.

McNew, K. P. and Espinsosa, J. A. (1994) The informa-tional content of USDA crop reports: Impacts onuncertainty and expectations in grain futures markets,The Journal of Futures Markets, 14, 475–92.

Monroe, A. M. (1992) The profitability of volatility spreadsaround information releases, The Journal of FuturesMarkets, 12, 1–9.

Noh, J., Engle, R. and Kane, A. (1994) Forecastingvolatility and option prices of the S&P 500 Index,Journal of Derivatives, 2, 17–30.

Schroeder, T., Blair, J. and Mintert, J. (1990) Abnormalreturns in livestock futures prices around USDAInventory Report releases, North Central Journal ofAgricultural Economics, 12, 293–304.

Simon, D. P. (2002) Implied volatility forecasts in thegrains complex, The Journal of Futures Markets, 22,959–81.

Tomek, W. G. and Peterson, H. H. (2001) Risk manage-ment in agricultural markets: a review, Journal ofFutures Markets, 21, 953–85.

Whaley, R. E. (1982) Valuation of American call optionson dividend-paying stocks: Empirical tests, Journal ofFinancial Economics, 10, 29–58.

520 A. McKenzie et al.

Dow

nloa

ded

by [

Ston

y B

rook

Uni

vers

ity]

at 0

9:06

05

Nov

embe

r 20

14