Investors With Too Many Options?∗
Daniel Dorn†
This draft: October 22, 2011
Abstract
Markets for over-the-counter derivatives have flourished during the last decade, especially in Europe and Asia. As in many markets for retail financial products, investors face
a choice among several instruments that differ only slightly from one another. Examining
retail trades in call options on the German DAX index, this paper documents economically
meaningful price dispersion across securities that are close substitutes. The observed product proliferation imposes a substantial search cost on investors even though the market is
transparent, products are homogenous, and product pricing is well understood. Investors
rely on behavioral search heuristics based on low nominal prices, advertising, and the status
quo, which costs them an average of 1.2% of the amount invested or EUR 50 per one-week
roundtrip trade.
JEL codes: G11, G13, D83
Keywords: Price dispersion, investor behavior, search, status quo bias, nominal prices,
advertising, OTC derivatives
∗
I thank Michael Boldin, James Choi, Anne Dorn, Frank Fehle, Mark Kamstra, Lisa Kramer, Oleg Rytchkov,
Alex Schober, and an anonymous ECB referee, as well as seminar participants at Maastricht University, Temple
University, and participants at Queen’s University’s Behavioral Finance Conference and the European Retail
Investor Conference in Stuttgart for comments. I also thank Charles Bergquist for his Perl programming help,
Philipp Dorn and Tu Nguyen for their help downloading option quotes, and Torsten Lüdecke for answering
questions about the data from the Karlsruher Kapitalmarktdatenbank (KKMDB). This paper has been prepared
by the author under the Lamfalussy Fellowship Program sponsored by the European Central Bank. Any views
expressed are only those of the author and do not necessarily represent the views of the ECB or the Eurosystem.
†
LeBow College of Business, Drexel University; 101 North 33rd Street, Room 208; Philadelphia, PA 19104;
Email: dd79@drexel.edu
1
I
Introduction
This paper examines the choices of retail investors in the fast-growing market for over-thecounter (OTC) derivatives, also known as bank-issued or covered warrants. Over the past
decade, these markets have grown rapidly in Europe and Asia, in part because they give retail investors easy access to option-like payoffs. The trading activity in OTC derivatives is
remarkable, both in absolute terms and relative to traditional derivatives exchanges. Germany
provides a good illustration of this market because it is host to Eurex, one of the world’s largest
traditional derivatives exchanges, as well as to the European Warrant Exchange (Euwax), one
of the world’s largest exchanges for OTC derivatives. For 2007, Euwax reported aggregate
premium trading volume of EUR 128 billion, or roughly 30% of Eurex volume. According to
Bergstresser (2008), the DAX 30 – the index of the 30 largest and most liquid German stocks
– was the most popular underlying for OTC derivatives worldwide between 1995 and 2008;
Bartram and Fehle (2007) estimate that, in terms of Euwax trading volume in DAX options,
the DAX would have ranked among the top five underlying assets on the Chicago Board Options Exchange. OTC derivatives are popular among German retail investors, a sample of
whom are studied in this paper. One out of four sample investors trade these instruments
and the observed option premium trading volume rivals aggregate mutual fund flows. Moreover, retail investors in OTC derivatives place big bets. The average sample option purchase
of EUR 9,000 corresponds to taking a position of EUR 90,000 in the underlying German stocks.
In addition to their size and importance for retail investors, markets for these instruments
offer several features that make them an attractive field laboratory to study investor choices.
Relative to other retail financial products, the OTC market is transparent in that prices and
product features are publicly available in electronic databases. Moreover, products are homogenous and product pricing is well understood, at least in the case of the plain-vanilla
instruments examined in this paper. Despite these features, markets for OTC derivatives are
characterized by product proliferation and price dispersion. In 2000, for example, there were
four times as many OTC call options on the DAX index as there were Eurex-listed DAX calls;
2
the number of OTC call options on the DAX has risen from 50 in 1992 to more than 4,000
in 2007. Figure 1 shows that, at the same time, the implied volatilities of OTC calls on the
DAX were much more dispersed than the implied volatilities of their Eurex-listed counterparts.
The paper considers three hypotheses to explain the observed price dispersion and investor
behavior. Under the rational null, investors costlessly identify attractive alternatives; economically meaningful price dispersion across instruments reflects genuine product differentiation.
Since information about product features and prices is readily available, this null hypothesis
is not unrealistic. Under the alternative hypothesis of costly search, prices can be dispersed
even among homogenous products and investors with lower search costs or greater search incentives make better choices. Finally, the alternative hypothesis of behavioral search admits
the possibility that investors make inferior choices, on average. Unlike rational searchers, who
may choose to stay uninformed and pick an alternative at random, behavioral searchers may
rely on choice heuristics that systematically steer them into inferior alternatives.
To discriminate between these hypotheses, the paper combines data on retail trades in DAX
call options made at a large German discount broker and intraday quotes for the population
of DAX calls listed on the Euwax during the period November 1999 to May 2000.
The results fail to support the rational null. The options actually chosen by the investors
significantly underperform similar available options, that is, options with a similar price elasticity with respect to changes in the DAX. The difference between the roundtrip return of similar
options that could have been bought and the return of the options actually bought averages
0.4%; the duration of a roundtrip averages about one week. Actual choices fare even worse
when compared with similar options that are predicted to outperform based on information
available to investors at the time of purchase, such as spreads. Options bought underperform
similar such options by 1.2% per one-week roundtrip, on average. To put these numbers into
perspective: investors lose an average of EUR 50 per trade and the average investor loses EUR
3
350 during the sample period relative to similar options.
Why do investors underperform, on average? The paper identifies two mechanisms. The
first, and more important, mechanism is based on variation in nominal prices. Issuers of OTC
derivatives vary the nominal price scale of their issues and investors prefer options with low
nominal prices, controlling for implied volatility and absolute spread. As in the case of stocks –
where a retail investor preference for low prices has been noted by Kumar and Lee (2006) and
Green and Hwang (2009), for example – low nominal prices are associated with high trading
costs. Weld et al. (2009) and Baker et al. (2009) report that firms actively manage their nominal share price. The market for OTC derivatives offers an ideal setting to examine the role
of nominal prices since one can identify options with different nominal prices, but otherwise
similar features. The second mechanism driving underperformance appears to be based on
persuasive advertising. Investors exhibit a preference for options issued by more aggressive
advertisers, controlling for other option attributes such as liquidity, and such options tend to
be more expensive. Cronqvist (2006) notes a similar effect of advertising on the mutual fund
purchases in the Swedish public pension system. A strong status quo bias reinforces these
choice heuristics. Once an investor has chosen an option, he is likely to stick with it for subsequent purchases; such status-quo purchases perform particularly poorly.
A detailed examination of investor performance yields further support for the alternative
hypotheses of costly and behavioral search. Investors who submit larger trades and those who
have already traded with different issuers have presumably greater incentives to search, face
lower search costs, or are less susceptible to behavioral biases. Such investors perform better.
Investors also perform better when they choose from a smaller menu of options (the number of
listed options varies substantially during the sample period). Sethi-Iyengar et al. (2004) note
the benefits of smaller menus in the context of defined contribution retirement plans. Variation
in counterparty risk and liquidity across instruments fail to explain variation in performance,
and controlling for risk and liquidity does not affect the results. This is perhaps not surprising
4
since the issuers – large banks such as Citigroup and Goldman Sachs – have similar credit
ratings and options are only held for brief periods; moreover, as part of the Euwax listing,
issuers commit to making a market in their options and to maintain certain levels of liquidity.
Product proliferation and price dispersion characterize many markets for retail financial
products. The documented dispersion of prices for homogenous equity index options is reminiscent of the price dispersion in the municipal bond market reported by Green et al. (2007)
and the dispersion of expense ratios among S&P 500 index funds reported by Hortacsu and
Syverson (2004). Based on aggregate quantities and prices, Hortacsu and Syverson (2004)
attribute the dispersion of expense ratios to search costs, nonportfolio differentiation (such as
differential tax exposures of the fund) and switching costs. Elton et al. (2004) report that variation in nonportfolio attributes fails to explain much of the variation in S&P 500 index fund
flows. In experiments with Harvard staff, Wharton MBAs, and Harvard college students, Choi
et al. (2010) report that subjects overwhelmingly fail to identify the lowest cost alternative
when faced with a hypothetical choice of four S&P 500 index funds stripped of any nonportfolio
differences. The present paper adds a perspective based on microdata from the field. This
perspective affords a clean examination of different hypotheses about investor behavior using
actual choices with large stakes.
Prior research on OTC derivatives has focused on the “average” pricing of these instruments, especially of complex instruments. Bartram and Fehle (2007) and Ter Horst and Veld
(2008) report substantial price deviations between OTC options and comparable standardized options traded in Germany and the Netherlands; consistent with their findings, Euwaxlisted DAX calls have higher implied volatilities than Eurex-listed DAX calls, on average,
as illustrated in Figure 1. Wilkens et al. (2003), Muck (2006), Ter Horst and Veld (2008),
and Henderson and Pearson (2010) report deviations between market and model prices for
OTC derivatives traded in Germany, the Netherlands, and in the U.S., especially at the time
of issue. Bergstresser (2008) reports poor performance of a comprehensive global sample of
5
structured equity products, especially before 2005. Bernard and Boyle (2008) report that the
popularity of structured equity products with local caps and global floors is consistent with
investors overweighing the probability of certain rare events that feature prominently in the
selling prospectus. The tenor of these papers is that issuers use the complexity of certain
OTC derivatives to extract rents from unsophisticated or biased retail investors. In contrast
to the focus of earlier papers on the difference between market and model prices of complex
derivatives, the focus here is on the dispersion of market prices across simple instruments that
are close substitutes and how investors choose among those instruments.
The paper does not address why retail investors trade or hold options in the first place.
The combined evidence reported in Glaser and Schmitz (2007), Lakonishok et al. (2007), Dorn
and Sengmueller (2009), and Bauer et al. (2009) suggests that speculating on directional price
movements as well as gambling and entertainment motives drive most of the observed activity;
in contrast, hedging does not seem to be an important rationale for trading derivatives. The
interpretation of the paper’s results, however, is unlikely affected by the particular motivation
behind the trades.
The paper is organized as follows. The next section develops the hypotheses about investor
behavior and price dispersion. Section III describes the data used to test the hypotheses.
Section IV examines what makes retail investors choose a particular option from a pool of
similar options. Section V evaluates the quality of the investors’ choices. Section VI concludes.
The Appendix describes features of the market for OTC derivatives in Germany and reflects
on the results in light of more recent developments in this market.
II
Hypothesis Development
The paper considers three candidate hypotheses to explain investor choices and performance.
Under the rational null hypothesis of effortless information acquisition and processing, investors’ choices are purely driven by value-relevant criteria such as trading costs. If there is
6
a performance gap between options chosen and similar options, it is economically small and
does not vary systematically as a function of trader or trade characteristics. Economically
meaningful price dispersion across instruments reflects genuine product differentiation. The
assumptions underlying the null are strong, but not unrealistic. The pricing of plain-vanilla
index options is well understood. The sample investors have free access to up-to-date information on option attributes provided in searchable online databases by the broker, the options
exchange Euwax, and third-party providers such as OnVista – essentially the same information used in this paper. Rational investors at full-service brokers might buy more expensive
options because the option trades are bundled with advice or because they get some form of
consideration; since the paper’s sample consists of self-directed clients at a discount broker,
however, bundling or switching costs should not distort observed choices.
The alternative hypothesis of rational costly search, pioneered by Stigler (1961), acknowledges that comparing all the different investment options may not be a trivial task for all
investors and that prices can be dispersed even when products are homogeneous. This hypothesis predicts that variation in investor performance is a function of the magnitude of search
costs and incentives to search. For example, newcomers may face higher search costs than
experienced investors; investors who place larger orders or expect to trade repeatedly have
stronger incentives to search. Even investors who face high search costs or have little incentives to search, however, should not consistently make poor choices since they can randomly
sample from the available options as in Salop and Stiglitz (1977). A variant of this hypothesis
recognizes that search frictions induce at least some firms to advertise. Nelson (1974) argues
that advertising credibly signals product quality; only more efficient issuers are able to recoup
the cost of advertising with revenues from repeat customers. Robert and Stahl (1993) develop
a sequential search model for a homogenous good in which firms either advertise a low price or
charge a high price which is not advertised. One might thus expect that buyers are influenced
by their experience and by the visibility of an issuer or particular issue; moreover, buyers of
more aggressively advertised options should not systematically underperform.
7
Costly search can also give rise to a behavioral alternative that can be detected if investors
rely on choice heuristics that lead them to systematically focus on expensive options. (It is
challenging to distinguish between the rational and behavioral search stories on the basis of
investor attributes alone; for example, a less experienced investor might make worse choices
because he faces higher search costs or because he is more susceptible to behavioral biases.)
Suppose that retail investors pay attention to nominal securities prices as suggested, for example, by Green and Hwang (2009), Weld et al. (2009), and Kumar (2009). Such a heuristic
is potentially harmful as the desirable attributes of low nominal prices (such as low implied
volatilities or spreads) tend to be outweighed by their undesirable attributes (high trading
costs). There is no minimum quantity trading requirement in German OTC derivatives and
hence no reason for rational traders to prefer options with low nominal prices, other things
equal. Issuer marketing is another channel that can systematically steer investors towards
expensive options. According to the persuasive view of advertising, as summarized in Bagwell
(2007), issuers can use advertising to create spurious product differentiation and brand loyalty
which allows them to extract higher prices from a captive clientele. Choice consistency may
also be associated with a status quo bias as reported by Samuelson and Zeckhauser (1988) for
a variety of economic settings; once an investor has decided on particular issuer or issue, he is
likely to stick with his decision in subsequent trades even if the status quo is suboptimal.
III
The Data
This paper focuses on OTC options, specifically on call options on the DAX 30 Performance
Index traded on the Euwax between November 22, 1999 and May 31, 2000. The sample period
is determined by the availability of Euwax quotes (available from November 22, 1999, onwards)
and retail transaction records from one of the three largest German discount brokers (available until May 31, 2000). This broker is not affiliated with any of the major issuers of OTC
derivatives during the sample period and does not provide any investment advice. Appendices
A and B describe the market for OTC derivatives in Germany in detail and contrast it with
8
the Eurex, a traditional derivatives exchange.
DAX options are chosen because the DAX is the most common underlying asset for OTC
derivatives in Germany. Glaser and Schmitz (2007) report that transactions in DAX options
account for more than one third of all transactions in a sample of option trades made by a sample of German discount brokerage clients between 1997 and 2001. The population of DAX calls
is identified using a register of securities listed on German stock exchanges obtained from the
Karlsruher Kapitalmarktdatenbank (KKMDB) which makes data feeds from Deutsche Börse
available to academics at cost. The register provides the security’s International Securities
Identification Number (ISIN), the name of the issuer, the name of the underlying, and the
expiration date. Frequently, the nature of the option (call or put) and the strike price can
also be inferred. The ISIN can then be used to verify the static option features and obtain
additional information from records maintained by the Börsen-Zeitung, the official publication
of the German stock exchanges. A total of 726 DAX calls that are alive at some point during
the sample period can thus be identified. The KKMDB also provides the daily trading volume
separately for each option and German stock exchange; this does not include volume handled
by the issuer on his own platform, however.
Intraday Euwax quotes for 610 of these options, posted by the corresponding issuer in his
role as market maker, are available from the Euwax website.1 The difference between the
total number of DAX calls and the number with Euwax quotes is mainly due to some issuers
(notably WestLB) choosing to list their derivatives on the Frankfurt Stock Exchange or one of
the other regional exchanges, but not on Euwax. For a small subset of issues, it is impossible
to verify static features since their ISIN has been reassigned. Moreover, the paper requires
valid Euwax quotes at different times on all transaction dates. Conditioning on options with
valid Euwax quotes does not affect the size of the sample in terms of trading volume, however.
1
The data was downloaded at
https
:
//www.boerse − stuttgart.de/de/toolsundservices/euwaxarchiv/gesamt − archiv.html.
As of October 19, 2011, the data can be downloaded from https
:
//www.boerse −
stuttgart.de/de/toolsundservices/euwaxarchiv/euwax − archiv.html.
9
The resulting sample of 610 DAX calls accounts for 97% of the total EUR trading volume in
all DAX call options across all German exchanges during the sample period, as reported by
the KKMDB.
This data can be merged with daily transaction records available for a large sample of
German discount brokerage clients for the period January 1995 to May 2000. Dorn and Sengmueller (2009) provide a more detailed description of this sample which constitutes a non-trivial
portion of the population of German discount brokerage customers. Such customers tend to
be younger, better educated, and earn higher incomes than the typical German investor. A
comparison of the sample investors who trade options and those who do not reveals that the
groups are similar in terms of age, experience, and account size as well as self-reported educational attainment, income, and net worth. One significant difference is that option investors
are more aggressive traders; they turn over their portfolio at three times the rate of their peers.
The focus of this paper is the intersection of the data sets described above. The sample
investors trade a total of more than EUR 100 million in DAX call options during the sample
period; 96% of the trading volume occurs in DAX call options that are quoted on Euwax. The
final data set consists of more than 7,000 DAX call purchases (plus subsequent sales) made by
1,000 investors in 250 different DAX calls between November 22, 1999, and May 31, 2000. The
difference between the number of calls with Euwax quotes and the number of calls traded by
the sample investors is not due to trading restrictions; in principle, the sample investors could
trade all the DAX calls listed on the Euwax.
Table I summarizes trade size, holding period, and performance as a function of the holding
period. The table reports statistics for three different returns. The investor’s actual return,
ractual , is only calculated for completed roundtrips using buy and sell prices gleaned from the
trading records. A roundtrip is deemed complete if an investor sells at least part of a previously established position; in most cases, a sale closes out the entire position. rEuwax is the
10
hypothetical return from buying at the Euwax ask in effect at 9:20am on the actual day of
the purchase and selling at the Euwax bid at 5:30pm on the actual day of the sale (trading
at these times corresponds to the baseline trading strategy considered in Sections IV and V).
rEuwax is calculated for incomplete roundtrips assuming that all open positions at the end of
the sample period are sold at the Euwax closing bid on May 31, 2000, the last day of the
sample period. rEU W AX,net is the corresponding return adjusted for trading commissions; the
selling commissions are calculated as if the investor had closed out the entire position and are
adjusted for issuer rebates, when necessary.
More than two out of five observations are intraday trades; the average holding period
across all observations is 6 days. Given the option’s implied leverage, the average trade size
of EUR 9,200 roughly corresponds to trading EUR 90,000 in the shares of the underlying
DAX stocks; trade size decreases in the holding period. Roundtrip returns average 4.6% which
reflects the appreciation of the DAX during the sample period. However, the median roundtrip
results in zero profit after transaction costs. Returns on incomplete roundtrips are very poor –
investors sit on losses averaging 50% – primarily because of the DAX’s negative performance
during the last third of the sample period.
IV
How Do Investors Choose Among Similar Options?
This section presents a panel logit model of option choice. The model answers the question
“given that an investor buys a call on the DAX, what makes him choose that particular call
from a set of similar DAX call options?” The modelling strategy is similar to that of Grinblatt
and Keloharju (2001) who explore, given an investors’ decision to sell a stock from his portfolio, what makes the investor sell that particular stock rather than another stock in his portfolio.
The three hypotheses – rational choice, costly search, and behavioral search – differ in their
predictions about which option attributes matter for decisions. According to the rational null,
choices should only be influenced by value-relevant attributes such as the cost of trading an op11
tion and its implied volatility. Under the costly and behavioral search alternatives, attributes
that capture the investor’s familiarity with an option or the option’s visibility may matter as
well. The data set offers a variety of proxies for familiarity and visibility, for example, whether
an investor has already traded a particular option and how much issuers spend on advertising.
In general, the alternative hypotheses of costly and behavioral search make similar predictions,
with one important exception. If investors use a low-price search heuristic, variation in nominal prices should be negatively associated with the purchase probability. In contrast, rational
searchers should prefer options with higher nominal prices – controlling for implied volatility
and absolute spread – because they are cheaper to trade.
Given a particular option bought, what constitutes a similar option? The paper considers
three definitions. First, for a given DAX call actually traded by a sample investor, one can
think of all DAX calls that could have been bought on the actual purchase date (and sold on
the actual date it was sold by the sample investor) as similar alternatives in the sense that
their payoffs are highly correlated.
This correlation, however, masks substantial differences in return levels. For example,
the price of an out-of-the-money option close to expiry will be much more sensitive to price
changes in the underlying than the price of a deep-in-the-money option. The second definition
recognizes this by matching options in terms of their price elasticity, defined as:
Elasticity =
∂C S ∗ ratio
·
∂S
C
(1)
where C is the option price, S is the value of the DAX, and ratio is the option’s conversion
ratio. Given a particular option bought, an option is considered similar in this narrower sense
if its price elasticity is within 10% of that of the option actually bought and it can be traded
on both the actual purchase date and the actual sale date. Presumably, elasticity or leverage
is one of the primary features sought by retail investors in options which makes it a natural
matching criterion. Moreover, matching by leverage is essential when comparing the perfor12
mance of different options as done in Section V.
The third, and narrowest, definition of similarity focuses on options with similar price elasticities that can be traded directly with the issuer (in addition to the Euwax, where the issuer
also serves as the market maker). Issuer platforms are prominently featured on the sample
broker’s website which could be interpreted as an endorsement. One potential advantage of
these platforms is the convenience of being able to trade outside the normal exchange trading
hours. Euwax hours are 9am to 5:30pm; issuer platforms typically remain open until 8pm or
later. One disadvantage relative to Euwax is that investors trading on issuer platforms lack
systematic information about quotes. The transaction records identify the venue on which
the orders are executed. During the sample period, about 85% of the trades go through the
issuer’s platform as opposed to an exchange.
For each purchase of a call, one can record the characteristics of the call bought as well as
the characteristics of other similar calls quoted on Euwax. Given n similar calls on a particular
day, an investor’s decision to purchase one of these calls that day generates n observations –
one “bought” observation (dependent variable equal to one) and n − 1 “not bought” observations (dependent variable equal to zero), each with its associated options characteristics. The
resulting panel logit specification is
P (Option Purchased = 1) = Λ(β1 X1 + β2 X2 + controls)
(2)
where Λ is the logistic cumulative distribution function, X1 is a vector of attributes that could
affect performance and hence choices of rational investors, and X2 is a vector of attributes that
should not affect rational investors, but might have explanatory power under the alternative
hypotheses of costly and behavioral search. Table II contrasts the attributes of options actually
bought with those of similar options not bought; these attributes are discussed below in more
detail.
13
In principle, investment banks have discretion over the pricing and attributes of the options they issue. As a result, the model has several variables that could be endogenous, that is,
correlated with unobserved demand components. Related econometric models of differentiated
demand for products – see Berry et al. (1995) for a widely cited study of the U.S. car market –
typically treat product characteristics other than price as exogenous; the formal treatment of
multiple endogenous variables is a current research topic in econometrics, as summarized by
Ackerberg and Crawford (2009). Unlike goods such as cars, however, options have a theoretically correct price that can be calculated via the no-arbitrage argument of Black and Scholes
(1973) and Merton (1973); given the underlying idealized assumptions, prices of options would
actually be exogenous. In the OTC derivatives market, of course, these assumptions are likely
violated because of trading frictions and counterparty risk. When trading frictions are present,
option demand can affect prices as noted by Bollen and Whaley (2004) and Garleanu et al.
(2009). This gives rise to an identification problem: the observed absence of a negative relation
between demand and price attributes could be due to price proxying for desirable attributes
that are omitted from the regression, demand causing price pressure, or suboptimal choices by
investors, for example.2
The paper addresses this identification problem in several ways. The model of investor
choice includes a wide range of option attributes that may be correlated with prices, including
proxies for option liquidity and counterparty risk. As discussed below, the resulting models fit
the data well; the pseudo-R2 ranges between 40% and 60%, depending on model specification.
Since investors’ individual choices are known, one can restrict the analysis to options with
similar expected payoffs which should also alleviate endogeneity concerns. Moreover, Section
V considers the possibility that the observed option purchases exert or proxy for price pressure.
Without adjustments, the model’s errors will be correlated across investors and over time.
The primary source of error correlation in the cross section is that the number of options
2
In the case of suboptimal choices, investors pick options that are expensive to begin with; in the case of
price pressure, investors’ picking particular options makes them temporarily expensive.
14
varies over time. Adding the inverse number of options available to trade on a given day – the
unconditional probability of buying any available option that day – as a regressor addresses
this problem. (Alternatively, one could add a full set of time dummies. The results using time
dummies are similar to those reported below and thus omitted.) In addition, the coefficient
standard errors are adjusted to allow same-investor errors to be arbitrarily correlated across
time, using the adjustment recommended by Williams (2000). To prevent tiny trades from
driving the results, the observations associated with the smallest 1% of the purchases are
dropped (70 purchases of less than EUR 200). Not surprisingly, these trades tend to earn the
lowest returns, especially after subtracting trading costs.
A
Rational Option Attributes
Three option attributes, in particular, are expected to influence the choices of rational investors: the option’s absolute spread, its conversion ratio, and its implied volatility. There are
a number of other attributes that might have a bearing on the decisions of rational investors
although, in practice, their performance effects are expected to be small: trading commissions,
past aggregate trading activity in an option, the past frequency with which the issuer updated
his quotes, and the issuer’s credit risk.
The absolute spread for an option ranges between EUR 0.01 and EUR 0.05 per unit; in
two out of three observations, the absolute spread is EUR 0.02. The absolute spread stays
constant over the life of an option and tends to be the same for all options from a particular
issuer. The median unit price for an option bought by the sample investors is EUR 2.48 which
renders even a one cent difference in absolute spreads economically meaningful.
The issuer determines the relative spread by setting the absolute spread and by setting
a particular conversion ratio. For each unit of the option held at expiry, an investor gets
an amount in Euro equal to the product of the conversion ratio and the positive difference
between the DAX level and the strike price. The conversion ratio ranges between 1:100 and
15
1:1000; in three out of four observations, the conversion ratio is 1:100. The relative spread of
an option with a conversion ratio of 1:1000 is ten times the relative spread of an option that
has a conversion ratio of 1:100 but otherwise identical attributes. Since there is no minimum
number of units that need to be traded, rational investors should prefer higher conversion
ratios, other things equal. Even the smallest traders in the sample can “afford” options with
high conversion ratios. The maximum unit price of an option traded in the sample is EUR
27 which is below the minimum purchase amount observed. Moreover, fixed transaction costs
on the order of EUR 10 would render such small transactions uneconomical. Option exercise
is typically subject to a minimum of 100 units. Since the underlying is a performance index
that reflects reinvested dividends, however, investors should sell rather than exercise before
maturity.
The implied volatility is the standard deviation σ that solves the Black and Scholes (1973)
equation
C = SN (d1 ) − Xe−rT N (d2 ), where
ln(S/X) + (r + σ 2 /2)T
√
, and
σ T
√
= d1 − σ T
(3)
d1 =
(4)
d2
(5)
where S is the value of the DAX 30 Performance Index at the close on the trading day before
the purchase and C is the midpoint of the Euwax quote in effect at the same time. DAX
intraday data as well as static option features such as strike price X and time to maturity T
come from the KKMDB and are checked against the option record in the Börsen-Zeitung, the
official publication of the German stock exchanges. Datastream provides the daily German
treasury yield curve at discrete points in time such as one week, one month, three months, and
so on. The interest rate r for a given expiry date is the spot on the yield curve that is closest
to that expiry date.
16
Trading commission schedules are generally similar across trading venues. One-way commissions average 0.9% of the traded amount and decline in trade size. Occasionally, issuers
offer rebates for trades directed to their platforms during one-week promotions; one or more
issuers run promotions in 5 out of the 27 weeks in the sample. Such rebates are captured by
a reduced fee dummy variable.
Since Euwax requires market makers to honor posted quotes up to a depth of EUR 3,000
or 10,000 units, liquidity is unlikely to be an issue for smaller trades. Liquidity may be a more
important consideration for larger option traders. During the sample period, only 3 out of
10 DAX call options trade on any given day on any of the German exchanges (this, however,
does not include trading that takes place on issuer platforms). The model considers three
proxies for liquidity: the fraction of aggregate market volume in DAX calls across all German
exchanges captured by a given call during the previous trading day, the fraction of brokerage
volume in DAX calls captured by the call during the previous trading day, and the logarithm
of the number of times the issuer updated the call’s Euwax quotes during the previous trading
day. A higher update frequency may indicate more aggregate trading volume on the issuer’s
platform. On average, issuers update their quotes roughly every 30 seconds, but the update
interval ranges from less than 10 to more than 60 seconds.
An issuer’s credit rating might also affect the attractiveness of an option since any payoff
at expiry is conditional on the issuer being able to meet his obligation. Based on a Factiva
search for the issuers’ S&P long-term counterparty risk rating one year before and during the
sample period (Subject “Corporate/Industrial News”/“Funding/Capital”/“Corporate Credit
Ratings”), the paper uses a nine-point scale representing all the issuer ratings from 1 (A) to
9 (AA+ with a stable outlook). The one issuer without an S&P rating has a Fitch rating
of “A” which is coded as a 1. Another issuer undergoes a ratings change during the sample
period which is reflected in an updated risk rating. The short average holding period and the
homogeneity of issuers in terms of credit risk suggest that it should have a negligible effect on
17
choices and performance.
B
Search and Behavioral Option Attributes
Attributes that should have no bearing on choices under the rational null, but may matter
under the alternative hypotheses of costly and behavioral search, include: whether or not investors have traded securities from the same issuer before, the issuer’s market share during the
year before the sample period, the distance between the investor and the issuer’s headquarters,
and the issuer’s related advertising activity.
Since the data set contains all the trades placed by the sample investors at the broker, not
just trades in DAX call options during the sample period, one can ask whether familiarity with
a security or an issuer affects subsequent choices. Three dummy variables model different levels
of familiarity with a given DAX call option. The first dummy recognizes whether an investor
has already traded that DAX call option (possibly before the start of the sample period). The
second dummy recognizes whether an investor has traded other derivatives from the same bank
that issued the DAX call in question. Finally, the third dummy recognizes whether an investor
has traded the associated issuer’s stock or mutual funds managed by that issuer or one of its
subsidiaries.
An institution’s market share is calculated as the number of sample brokerage trades in
options issued by that institution divided by the number of all sample brokerage trades in
options during the year before the sample period. Citigroup has the largest market share
with 68% of all trades, followed by UBS with 11%. According to Glaser and Schmitz (2007),
Citigroup accounted for 52% of total trading volume in bank-issued derivatives in Germany
in 2000. Issuers that offer trading on their own platforms account for more than 90% of all
trades prior to November 1999. An institution’s number share, a related explanatory variable,
is calculated as the number of DAX call listings by a given issuer divided by the total number
of active DAX call listings on a given day.
18
Given latitude (lat) and longitude (lon) coordinates for investor i and issuer j, the distance
between i and j can be calculated as
di,j = earth radius · acos (sin(latj )sin(lati ) + cos(latj )cos(lati )cos(lonj − loni ))
(6)
The distance between issuers and investors who reside abroad is set to the average distance
between issuers and domestic investors.
Nielsen Germany provides advertising expenditure for each issuer at the placement level.
During the sample period, Nielsen classifies OTC derivatives as “other financial instruments” –
as opposed to stocks, mutual funds, mortgages, credit cards, and other consumer credit products which are identified as separate categories. Placements that do not advertise a specific
product category are classified as image advertising. In addition, Nielsen sometimes provides
a short description of the advertisement’s contents. After a manual review of 26,000 placements, advertisements of “other financial instruments” and image advertisements are classified
as related advertising, unless the content description suggests otherwise.3 The large German
universal banks are the most aggressive advertisers in terms of expenditures. Deutsche Bank,
for example, spent almost EUR 50 million on image and product-related advertising between
January and November 1999. During the same period, the largest four issuers of OTC derivatives in the sample in terms of trading volume – Citigroup, UBS, HSBC, and Société Generale
– spent only EUR 10 million combined.
C
Regression results
The three pairs of columns in Table III present the regressions results for the different definitions of similar options. The first column in each pair reports estimates of the logit coefficients
along with the corresponding standard errors. The second column reports the change in the
3
Nielsen does not provide information on the direct mailing activities. Also, the category of “other financial instruments” includes products other than OTC derivatives such as high-interest savings accounts. Such
advertising is excluded when it can be identified.
19
purchase probability associated with a one-standard deviation increase in significant continuous variables and a switch from zero to one in significant dummy variables, evaluated at the
mean of the other regressors (in other words, these are differences in estimated purchase probabilities, not marginal effects). Since the results have a similar thrust regardless of the definition
of similarity used, the discussion focuses on the results for elasticity-matched options, reported
in Columns (3)-(4).
The results offer little support for the rational view. Other things equal, options chosen
do have significantly lower implied volatilities and have been traded more actively both at
the market and the broker level. However, the economic magnitudes of these coefficients are
small. A one-standard deviation increase in implied volatilities, for example, is associated with
a 0.2% reduction in the purchase probability relative to an unconditional purchase probability of 5.4%. In contrast to the rational null, but consistent with the behavioral alternative,
investors systematically opt for options with low nominal prices which are more expensive to
trade. Variation in nominal prices has a meaningful effect on choices. The purchase probability
for an option with a below-median conversion ratio is 1.6% higher than for otherwise similar
options – roughly one-third of the unconditional purchase probability.
Variation in search and behavioral attributes is more successful in explaining investor
choices. Among these attributes, past experience is the most important determinant of option
purchases. Other things equal, investors are almost 30% more likely to buy an option they
have bought before – five times the unconditional purchase probability. Having traded another
option by the same issuer also increases the purchase probability significantly, but the effect is
necessarily much smaller. Other dimensions of familiarity with an issuer such as having traded
the issuer’s stock or mutual funds, living close to issuer headquarters, or the issuer’s market
share are not systematically related to the probability of purchase, other things equal. The
association between the pre-sample advertising expenditures of an issuer and the purchases of
his options is positive and significant. A one-standard deviation of pre-sample advertising is
20
associated with a 1.4% increase in the purchase probability. The importance of prior experience, by itself and relative to advertising, is consistent with studies of household purchase
behavior in other settings as summarized by Bagwell (2007), for example (Chapter 8.1). It is
possible that the existence of issuer platforms, which is prominently featured on the broker’s
web site, serves as another advertising channel; the effect of advertising becomes stronger in
the model that focuses on options that can be traded on issuer platforms, reported in Columns
(5) and (6) of Table III.
The results are qualitatively similar to unreported variations in variable definitions such as:
replacing implied volatility calculated at the previous day’s close with the implied volatility at
9:20am on the day of purchase, replacing the reduced fee dummy with several dummy variables
(recognizing that temporary fee reductions range from a commission discount of 25% to a
full reimbursement of both commission and spread), replacing the time-varying credit rating
score with a credit score dummy, and replacing advertising expenditures manually classified as
related with all advertising expenditures reported by Nielsen Germany.
V
How Well Do Investors Choose?
Given the size of the OTC derivatives market and the average size of observed positions,
investor performance is interesting in its own right. Perhaps more importantly, investor performance further helps discriminate between the three different hypotheses about investor
behavior and price dispersion – the rational null hypothesis, the alternative of costly search,
and the alternative of behavioral search. This section estimates the performance gap – the
difference between the returns of the options chosen and the returns of similar options – and
examines how the performance gap varies with investor and trade attributes.
A
Performance Gap – Baseline Results
One can compare the returns of the options actually bought with the returns available from the
subset of DAX calls that are similar to those chosen by the investor. A particularly interesting
21
subset consists of similar DAX calls that are ex ante judged superior to the call actually chosen
based on option attributes such as absolute spread, conversion ratio, and implied volatility.
Since the trading records are date-stamped, but not time-stamped, such a comparison requires
assumptions about when exactly traders get their orders executed. Any particular set of assumptions implies little loss of generality as long as differences in the attractiveness of options
persist over time. Such persistence can be conjectured in part because absolute spreads and
conversion ratios remain fixed over the entire life of a given option. Robustness checks reported
below will verify this conjecture.
The main trading strategy considered here assumes that the investors buys at the Euwax
ask in effect at 9:20am (that is, twenty minutes after the market opens) on the day of the
actual purchase and sells at the Euwax closing bid on the day of the actual sale. This trading
strategy is feasible for orders that are small enough because the broker quickly relays orders
to Euwax and because the Euwax market maker is obliged to honor publicly posted quotes
up to a maximum of EUR 3,000 or 10,000 units. Another straightforward trading strategy
consists of buying at the Euwax opening ask on the day of the actual purchase and selling at
the Euwax closing bid on the day of the actual sale. The issue with this hypothetical trading
strategy, however, is that there is relatively more variation in the timing of the first quote after
9am across options. The first quote is typically posted at 9:15, with an interquartile range
from 9:11 to 9:18. In contrast, the quotes in effect at 9:20am are typically posted at 9:19:40,
with an interquartile range from 9:19:10 to 9:19:50. Of course, assuming 9:20am as the time
of purchase and 5:30pm as the time of sale is fairly arbitrary; Section V.B below examines the
robustness of these assumptions.
Table IV summarizes the performance gap associated with the purchase of a given option
i, defined as
Gap =
1 X
(retj,Euwax
) − reti,Euwax
t,t+T
t,t+T
||S||
(7)
j∈S
where reti,Euwax
is the return from buying option i at the Euwax ask in effect at 9:20am on day
t,t+T
22
t and selling at the closing Euwax bid on day t + T , T = 0, 1, 2, ..., after trading commissions.
The different columns of Table IV report performance gap statistics for different definitions
of similarity. Options are considered similar in Column (1) if they could have been bought
and sold on the dates the actual option was bought and sold and their price elasticities are
within 10% of the chosen option. In addition to conditioning on trading dates and elasticity,
Column (2) considers only options that can be traded on issuer platforms. The remaining
columns consider options that can be ex ante classified as better because they have weakly
lower spreads (Column 3), weakly lower spreads and higher conversion ratios (Column 4), and
weakly lower spreads, higher conversion ratios, and lower implied volatilities (Column 5) –
as well as being available on trade dates and having similar price elasticities. Since spreads
and conversion ratios remain fixed during the life of the option, and since implied volatilities
are measured on the trading day before the observed trade, the sample investors could have
replicated this classification. Commission rebates or spread refunds offered by certain issuers
(as mentioned in Section IV) are only reflected in the returns of the options actually chosen,
not in the returns of similar options. This conservative assumption downwardly biases the
performance gap and rules out temporary issuer rebates as an explanation for an apparent gap
based on Euwax quotes.
Across all observations, the average performance gap between options chosen and elasticitymatched options is 0.4%. This gap appears to be economically significant given the average
holding period of 6 days; it translates into an average loss of roughly EUR 10 per transaction
relative to investing in an equally-weighted portfolio of similarly price-elastic options. It is also
statistically significant assuming that all observations are independent. Panels B through D
show that the performance gap obtains regardless of the holding period and that the gap is
largest for incomplete roundtrips.
As described in the previous section, trading on issuer platforms is possible after the Euwax
close and investors may be willing to tolerate a performance gap between options that can be
23
traded on such platforms and those that cannot. Column (2) of Table IV reports performance
gap statistics for platform-eligible options only – hence the slight decrease in the number of
observations. Conditioning on the possibility of platform trading has little effect – options
bought underperform similar options by the same margin of 0.4% as in Column (1).
The difference in roundtrip returns between any two options can be decomposed into three
components: differences in absolute spreads, differences in conversion ratios, and changes in
relative implied volatilities measured at the midpoint of the spread. Of course, one cannot
condition on the change in relative implied volatilities since this would require perfect investor
foresight. One can, however, condition on the level of implied volatility that is known at the
time of the trade (such as the volatility implied by previous closing prices). A comparison
of Columns (3)-(5) of Table IV suggests that all three attributes – differences in absolute
spreads, conversion ratios, and lagged implied volatility – contribute to the performance gap.
The performance gap ranges from an average of 0.5% (relative to similar options with weakly
lower spreads) to an average of 1.2% per trade (relative to similar options with weakly lower
spreads, weakly higher conversion ratios, and weakly lower implied volatilities). The mean gap
of 1.2% translates into an average loss of EUR 50 per transaction relative to investing in an
equally-weighted portfolio of similar options that can be classified ex-ante as weakly better in
terms of spread, conversion ratio, and lagged implied volatility.
Panel E of Table IV reports performance gap statistics where the average is first taken
across trades for a given trader and then across traders – put differently, observations are
assumed to be independent across traders but not over time. A trader loses an average 1.9%
relative to similar options (with weakly better spread, conversion ratio, and implied volatility
characteristics) he could have bought. This translates into an average loss of EUR 350 per
trader relative to investing in an equally-weighted portfolio of similar options that can be
classified ex-ante as better. The difference between the trade-based gap and the trader-based
gap suggests that more frequent option traders perform relatively better.
24
B
Performance Gap – Robustness Checks
It is possible that the attractiveness of the option chosen varies as a function of the time at
which the order is executed. To examine this possibility, one can compare the implied volatility
of options bought or sold with the implied volatility of similar options at different points in
time. Figure 2 offers such a comparison at 9:15am, 9:30am, 10am, 11am, noon, 1pm, 2pm,
3pm, 4pm, 5pm, 5:15pm, and 5:30pm (close) for the sample trades underlying Table IV. Options need to have a valid quote posted at most 15 minutes before each point in time to be
considered in the pool of similar options. The figure plots two ratios: the solid line represents
the average ratio of the implied volatility of the option bought to the average implied volatility
of similar options (options whose price elasticity is within 10% of the actual price elasticity);
the dotted line represents the average ratio of the implied volatility of the option sold to the
average implied volatility of similar options (options whose price elasticity was within 10% of
the actual price elasticity at the time of purchase).
Three patterns emerge. First, the two lines run roughly in parallel with the solid line always above the dotted line. This means that the options bought by the investors have become
cheaper relative to similar options by the time they are sold. Almost half of the sample trades
are intraday trades. For the purpose of Figure 2, the difference in implied volatilities for intraday trades is perfectly captured by the relative spread (determined by the absolute spread and
the conversion ratio) since the implied volatilities are calculated at exactly the same time. It
also appears that the options traded by the sample investors tend to become cheaper relative
to their non-traded peers during the course of the trading day. Price pressure is one possible
explanation for this pattern if the investors tend to buy early on and tend to sell later on
during the trading day (which is likely if only because of intraday trading). The price pressure
explanation also requires correlated trading in some options but not in others. Section V.C
examines this explanation in more detail. Third, both lines are at or below one, suggesting that
the sample investors buy and sell slightly cheaper-than-average options in implied volatility
terms.
25
The attractiveness of the option chosen does not vary much as a function of the time at
which the order is executed. This is not surprising. Two important attributes for performance,
absolute spread and conversion ratio, are fixed and implied volatility, a third important attribute, is persistent as well. The paper lacks data on issuer platform quotes outside regular
exchange hours, that is, after 5:30pm. Given the importance of fixed and persistent option
attributes for performance, there is little reason to believe that the relative attractiveness of
options should change, much less reverse, after-hours.
C
Determinants of the Performance Gap
The magnitude of the average performance gap is inconsistent with rational search. It is unclear
why rational investors would pick options that systematically underperform. The preference
for options with low nominal prices and the poor performance of such options, documented
previously, suggest that a behavioral heuristic may lead investors astray. Another possibility
is that investors are more likely to pick the options more aggressively marketed to them, as
reported in Section IV, and that such options are more expensive to trade.
Section V.A also documents substantial variation in the performance gap. Explaining this
variation can shed additional light on the competing hypotheses. According to the rational
null, variation in the performance gap should be related to variation in the risk and liquidity
characteristics of the securities. In contrast, the costly search hypothesis predicts that variation
in the performance gap should be related systematically to attributes that proxy for search
costs or search incentives.
Search costs and incentives The paper considers the following proxies for search costs
and search incentives: trade size, the number of issuers an investor has traded with during the
six months before the sample period, whether or not an investor has traded a particular option
before, and the number of available DAX calls at the time of purchase.
26
Other things equal, search incentives increase in trade size. Trade size is also a useful regressor to evaluate a story that makes the opposite prediction. Euwax requires market makers
to honor posted quotes only up to a volume of EUR 3,000 or 10,000 units. For investors who
submit larger orders, the posted quotes thus may not be a good indication for the prices at
which they trade. One might even conjecture that observed inferior selection is concentrated
in large trades because they exert more price pressure.
The number of different issuers an investor has traded with during a given past period – the
six-month period leading up to the sample period – can be a proxy for search intensity. Given
the existence of promotions and the rapidly changing menu of options, investors who have
shopped around in the past may be more likely to find an attractive option.4 The six-month
period is chosen because all sample investors had an active account during that period. To examine the effect of the status quo, one can include a dummy variable that is one if the investor
has bought the option in question before and zero otherwise. If an option is chosen repeatedly
because it is attractive relative to similar options, one would expect smaller performance gaps
in status quo trades. The behavioral interpretation of status quo decisions – a lack of search
for better options – makes the opposite prediction.
Although the sample period is short, the total number of available DAX calls varies substantially. In the quartile of observations with the smallest number of options to choose from,
investors face a choice between an average of 254 DAX calls at the time of purchase; in the
largest quartile, investors have to choose between an average of 389 DAX calls. One can
conjecture that search costs (or the propensity to employ a behavioral search heuristic) increase in the number of alternatives, and would thus expect a positive correlation between the
performance gap and the number of choices. If increases in the number of choices were associated with more intense price competition among issuers, one might expect the opposite result.
4
I thank an anonymous referee for suggesting this explanatory variable. The number of different issuers
subsumes the effect of the past number of option trades, a measure of investor experience used in a previous
draft of the paper.
27
In the presence of search frictions, advertising may effect both choices and prices. Section
IV documents that investors are more likely to buy options from issuers that advertise more
aggressively prior to the sample period. A priori, the association between advertising intensity
and the performance gap is unclear. Models of rational search and informative advertising,
such as developed in Nelson (1974) and Robert and Stahl (1993), predict an inverse relation.
If, in contrast, advertising is used to persuade rather than to inform, one might expect higher
performance gaps for more aggressively marketed options.
Column (1) of Table V reports the results of estimating the association between the performance gap and proxies for search costs and incentives. The results are consistent with the
search hypothesis. A one-standard deviation increase in trade size is associated with a 0.2%
decrease in the performance gap – half of the unconditional average gap of 0.4%; a one-standard
deviation increase in the number of issuers an investor has traded with has a similar effect.
Status quo decisions are associated with more than twice the unconditional performance gap.
Consistent with the persuasive marketing conjecture, purchases of options that are more aggressively marketed relative to similar options do poorly; a one-standard deviation increase in
the relative advertising of options bought is associated with a doubling of the unconditional
performance gap.
The regression’s R2 of 2% appears fairly low, despite the inclusion of the expected performance gap due to matching error (the difference between the price elasticity of the chosen
option and the price elasticity of the portfolio similar options). The noise in the performance
gap comes from three sources. First, matching options by their price elasticity works best for
relatively small returns; matching quality declines in absolute returns. Second, because prices
are only quoted up to two decimal places, options with high nominal prices typically reflect
small changes in the underlying whereas options with low nominal prices do not. Third, issuers update their quotes at different frequencies, as noted in Section IV. If the paper were to
28
condition trading strategies on real-time price information, the documented performance gaps
would increase. Since it is unclear to what extent investors had access to such information,
the paper relies on information from the previous close.
Liquidity and risk Investors may tolerate performance gaps for options that are more liquid in the sense that they can be traded on issuer platforms or are quoted more actively.
Moreover, the observed trades could cause or proxy for price pressure. This explanation has
the virtue of being consistent with the implied volatility decrease of options that investors
choose to trade relative to those they shun (as suggested by the negative slopes in Figure
2). Since individual trades are unlikely to cause price pressure and trades outside the sample
may offset the observed trades, however, this explanation requires that the observed trades
are either correlated or indicative of the actions of a broader population of investors. If trades
were correlated, then one might expect price pressure to be most severe in the options in
which most of the trading takes place. Two measures of aggregate trading activity in a given
option on a given day are available. First, Deutsche Börse publishes the trading volume in
each option across all German stock exchanges (including Euwax, but not including trading
on the issuer’s platform). Second, one can aggregate trading volume across all sample investors.
Since bank-issued derivatives are senior unsecured obligations of the issuer, differences in
counterparty risk may explain some price differences across options by different issuers. It
appears unlikely that such differences are of first-order importance given the magnitude of
the performance gap, the small differences in terms of credit risk (all banks are either A- and
AA-rated), and the short holding periods.
Column (2) of Table V shows that focusing on options that are available via issuer platforms
yields results similar to those reported in Column (1); put differently, variation in platform
availability does not drive performance gaps.
Column (3) of Table V reports the effects of controlling for differential quoting and trading
29
activity as well as credit risk. Differences in quoting frequency and credit risk are not significantly correlated with the performance gap, and the proxies for search costs and incentives
remain statistically significant.
Differential trading activity matters, at least at the market level. A one-standard deviation
increase in the market trading volume of options bought relative to similar options is associated with a 0.3% increase in the performance gap. One interpretation is that price pressure
contributes to the performance gap. It is also possible, however, that aggregate volume proxies
for the documented preference for options with low prices but large relative spreads. To discriminate between these interpretations, one can run a similar regression that also conditions
on the difference in conversion ratios and absolute spreads (that is, the determinants of relative spreads). Column (4) of Table V shows that differential trading activity loses much of its
explanatory power in that case, suggesting that price pressure plays a minor role in explaining
the performance gap. It is interesting to note that differential advertising activity also loses
explanatory power; more aggressive advertisers tend to issue options with low nominal prices.
Column (5) of Table V re-estimates the specification in Column (3) with issuer fixed effects. Issuer fixed effects can be identified separately from the gap variables that are based on
time-invariant issuer attributes (such as pre-sample advertising) because the reference group of
similar options changes over time and as a function of the option bought. The results resemble
those reported in Column (3), suggesting that the inferences about the performance gap are
not driven by a single issuer.
The explanatory power of trade and trader characteristics that proxy for search costs and
incentives thus appears robust to risk and liquidity considerations.
30
VI
Conclusion
Rapidly expanding menus of choices and price dispersion characterize the landscape of retail
financial products and services. The standard explanation for the observed plethora of choices
is that banks compete to respond to the product preferences of rational investors. Put differently, investors benefit from more competition and choices. An alternative explanation is
that low issuing costs and at most boundedly rational investors sustain equilibria with product
proliferation and prices that are dispersed and above marginal cost.
This paper examines the German market for OTC derivatives, a retail market in which
choices should be straightforward: up-to-date product information is available, products can
be compared in electronic databases free of charge, and product pricing is well understood,
at least in the case of the plain-vanilla instruments studied. Despite these features, prices are
dispersed even for simple, homogenous, products. Moreover, investors buy products that systematically underperform other similar products that they could have bought. The observed
mechanisms driving the underperformance – investors’ preferences for products with low nominal prices, more heavily advertised products, and the status quo – suggest that investors rely
on suboptimal choice heuristics even when placing large bets in a transparent environment.
Carlin (2009) conjectures that professional advice can help uninformed investors better
navigate the menu of choices, unless issuers raise industry complexity or offer advisors incentives to share in industry profits. And indeed, the complexity in OTC derivatives markets
has substantially increased as banks have rapidly expanded their product offerings during the
last decade. Moreover, much of the financial advice is dispensed by employees affiliated with
the issuers. Finally, it is unclear how much an impartial advice channel can improve choices,
given that the sample investors already have free access to price comparison tools. Appendix C
reports that, if anything, the gap between attractive and unattractive instruments has widened
after the sample period. Together with the dramatic increase in the number of different instruments, this suggests that the investor’s search problem has become even more challenging.
31
The paper’s results do not rule out that some investors benefit from the choice available in
OTC derivatives relative to markets that regulate product differentiation. For many investors,
however, product differentiation can be harmful because it complicates their search problem.
If retail investors have trouble identifying attractive products in this transparent market, they
will presumably do even worse in the more opaque environments that characterize many other
retail financial markets. Moreover, financial intermediaries may have incentives to engage in
spurious product differentiation to exploit investors’ reliance on simple choice heuristics.
32
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35
Figure 1: Distribution of Implied Volatilities of DAX Calls as of May 31, 2000. The histogram
summarizes the Black and Scholes (1973) volatilities implied by the first traded price for 90
Eurex-listed calls and by simulated transaction prices randomly drawn from the opening bidask quote for 350 Euwax-listed calls. Each option price is matched with the nearest intraday
value of the DAX 30 Performance Index which is recorded every 15 seconds. The German
treasury yield curve, available from Datastream at discrete points in time, is used to find the
appropriate risk-free rate given each option’s expiration date.
0.2
0.2
0.18
0.18
All Euwax
Frequency
0.16
All Eurex
0.16
0.14
0.14
0.12
0.12
0.1
0.1
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0.02
0
0
0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39
Implied Volatility Bin
36
Figure 2: Implied Volatilities (IV) of Traded Options Relative to Similar Options. This figure
compares the implied volatility of options traded with the implied volatility of similar options
at different points in time. Options need to have a valid quote posted at most 15 minutes before
each point in time to be considered in the pool of similar options. The solid line represents the
average ratio of the implied volatility of the option bought to the average implied volatility
of similar options (options whose price elasticity is within 10% of the actual price elasticity);
the dotted line represents the average ratio of the implied volatility of the option sold to the
average implied volatility of similar options.
1.005
1
0.995
0.99
Ratio of IV bought to average IV of similar options
0.985
Ratio of IV sold to average IV of similar options
0.98
9:15
9:30 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 17:15 17:30
37
38
Holding period [# days]
Trade size [EUR]
ractual
rEU W AX
rEU W AX,net
Number of observations
Mean
6
9,200
n/a
4.6%
3.2%
Median
1
2,900
n/a
1.0%
0.0%
All
7,205
Mean
0
15,600
1.9%
0.9%
0.0%
Median
0
4,700
1.6%
0.0%
-0.6%
Completed, Intraday
3,108
Mean
6
4,500
12.3%
13.6%
11.8%
Median
3
2,300
6.4%
5.4%
3.8%
Completed, Not Intraday
3,677
Mean
42
3,600
n/a
-46.1%
-48.9%
Median
43
1,600
n/a
-53.2%
-54.7%
Not Completed
420
The sample consists of 7,205 purchases of DAX calls made by 976 clients at a large German discount broker between November 22, 1999, and May 31, 2000. Holding
period is the number of days between a given purchase and the first subsequent sale within the sample period. If a position is not sold within the sample period, the
holding period is calculated assuming that the position is sold on May 31, 2000. Trade size is the size of the initial purchase. Performance is computed three ways.
ractual is the roundtrip return based on actual transaction prices and fees from the transaction records; it is only calculated for complete roundtrips, that is, for purchases
that are followed by a sale during the sample period. rEU W AX is the hypothetical return assuming that the investor buys at the Euwax ask in effect at 9:20am on the
actual day of the purchase and sells at the Euwax bid in effect at 5:30pm on the actual day of the sale, or at the Euwax bid in effect at 5:30pm on May 31, 2000, if the
position is not closed by the end of the sample period. rEU W AX,net is the return minus estimated trading commissions paid by the investor.
Table I: Trade Statistics
Table II: Attributes of Options Bought and Options Not Bought
Every time an option is purchased during the sample period, it is classified as an “Option Bought”. Similar options that
could have been bought instead are classified as “Options Not Bought.” Options are classified as similar if their price
elasticity with respect to the underlying is within 10% of that of the option actually chosen. Attributes of “Options
Bought” and “Options Not Bought” are averaged for each of the 950 investors whose purchases exceed EUR 200 and
for whom there are “Options Bought” and “Options Not Bought” (10 investors only make very small purchases and
16 investors buy options for which there are no similar options). These investor-means form the unit of observation
underlying the statistics reported below. “Absolute spread” is the fixed EUR spread. For each unit of the option held at
expiry, the issuer pays the amount equal to the product of the “Conversion Ratio” and the positive difference between the
DAX level and the strike price. “Implied volatility” is the Black-Scholes volatility implied by the midpoint of the Euwax
quote on the previous trading day. The “Reduced fee” dummy is one if the option’s issuer offered a rebate on the day of
purchase. “Number of quotes” is the number of times the issuer updated the option’s quotes on the previous trading day.
“Market trading activity” is the aggregate trading volume in the given DAX call divided by the aggregate trading volume
in all DAX calls across all German exchanges on the previous trading day. “Brokerage trading activity” is the aggregate
trading volume in a call divided by the aggregate trading volume in all DAX calls observed at the sample broker on the
previous trading day. “Credit rating” is a score that ranges from 1 (corresponding to a single-A rating, the lowest in the
sample) to 9 (a AA+ rating with stable outlook, the highest in the sample). The “Has traded issue” dummy is one if the
investor has bought the option before. The “Has traded with issuer” dummy is one if the investor has traded an option
from the same issuer before. The “Has traded issuer stock or funds” dummy is one if the investor has traded shares in
either the common stock or mutual funds of the issuer. “Distance(investor, issuer)” is the geographic distance between
the investor’s home and the issuer’s German headquarters. “Issuer Market Share” is the issuer’s share of trading volume
in DAX options at the sample broker between November 1998 and October 1999. “Issuer Number Share” is the number of
DAX options offered by the issuer divided by the total number of options available at the time of purchase. “Advertising
pre-sample” is the EUR advertising expenditure for the option issuer reported by Nielsen for the period January 1999
and October 1999. “Advertising past week” is the EUR advertising expenditure for the issuer reported by Nielsen during
the week before the observed trade. The “Issuer Platform” dummy is one if the option can be traded directly with the
issuer. ***/**/* indicate that investor means are significantly different across “bought” and “not bought” observations
at the 1%/5%/10% level.
Absolute spread
Conversion ratio
Implied volatility
Reduced fee
Number of quotes
Market trading activity
Brokerage trading activity
Credit rating
Has traded issue
Has traded with issuer
Has traded issuer stock or funds
Distance(investor, issuer)
Issuer market share
Issuer number share
Advertising pre-sample
Advertising past week
Issuer platform
Options Bought
Mean
Std
Median
0.019
0.003
0.020
0.008
0.002
0.008
30%
2%
30%
5.9%
17.3%
0.0%
1028
514
950
1.6%
1.8%
1.0%
3.1%
4.7%
1.4%
5.8
0.9
6.0
32%
33%
27%
93%
23%
100%
1%
11%
0%
297
144
288
56%
22%
68%
19%
4%
20%
6.4
3.8
7.1
0.2
0.1
0.2
98%
13%
100%
39
Options Not Bought
Mean
Std
Median
0.017***
0.006
0.017
0.009***
0.001
0.009
30%
2%
30%
5.4%
14.1%
0.0%
637***
170
645
0.3%***
0.4%
0.2%
0.7%***
1.2%
0.3%
5.3***
0.5
5.3
1%***
2%
0%
52%***
27%
50%
6%***
11%
0%
264***
113
228
18%***
8%
17%
14%***
2%
14%
6.6
2.6
6.2
0.1***
0.1
0.1
67%***
13%
66%
Table III: Panel Logit Model of Option Choice
Every time an option is purchased during the sample period, the associated dependent variable is set to one. Based on
the attributes of the option bought, one can identify similar options; the dependent variable for these options is set to
zero. The dependent variable is regressed on the attributes associated with the corresponding option as defined in Table
II. In Column (1), options are deemed similar to the option bought if they were available for purchase on the day the
investor actually bought his option and available for sale on the day the investor actually sold his option (or May 31,
2000, if the option was not sold within the sample period). In Column (3), options are deemed similar if, in addition, their
price elasticity with respect to changes in the underlying is within 10% of the elasticity of the option bought. Column (5)
reports coefficients for a similar regression as Column (3), focusing only on options that can be traded via issuer platforms.
Columns (2), (4), and (6) report the effect on the purchase probability of a one-standard deviation increase of significant
continuous variables and a 0-1 change of significant dummy variables, evaluated at the means of the other regressors.
The inverse of the number of similar options on a given day is an additional control variable (not reported). All reported
standard errors are robust to heteroskedasticity and allow for clustering of errors across same-investor observations (see
White (1980) and Williams (2000)). ***/**/* indicate that the coefficient estimates are significantly different from zero
at the 1%/5%/10% level.
(1)
Dependent variable
Similar options matched by
Constant
Absolute spread
Conversion ratio
Implied volatility
Reduced fee
ln(Number of quotes)
Market trading activity
Brokerage trading activity
Credit rating
Has traded issue
Has traded with issuer
Has traded issuer stock or funds
ln(Distance(investor, issuer))
Issuer market share
Issuer number share
ln(1+Advertising pre-sample)
ln(1+Advertising past week)
Issuer platform
Price elasticity
Ancillary Statistics
Number of Observations
Number of Clusters (investors)
Unconditional probability
Pseudo-R2
(2)
Availability
-18.694***
(3.773)
-60.150**
(28.374)
-0.024
(0.153)
-1.938***
(0.266)
-0.022
(0.062)
-0.224***
(0.051)
8.141***
(0.918)
5.275***
(0.341)
-0.040
(0.082)
3.794***
(0.127)
1.791***
(0.167)
-0.306*
(0.163)
0.036
(0.800)
0.890
(1.427)
-0.009
(0.057)
0.602***
(0.221)
0.040***
(0.014)
3.991***
(0.795)
0.058***
(0.004)
-0.2%
-0.1%
0.0%
0.0%
0.0%
4.2%
0.3%
-0.1%
0.3%
0.0%
0.4%
(3)
(4)
(5)
(6)
Option Bought Indicator
Availability, Elasticity
Availability, Elasticity, Platform
-13.791***
(3.229)
-22.474
(27.721)
0.626***
(0.112)
-1.064**
(0.466)
0.041
(0.073)
0.078
(0.056)
11.230***
(1.461)
3.482***
(0.329)
-0.008
(0.054)
3.723***
(0.163)
1.633***
(0.158)
-0.366
(0.226)
0.761
(0.923)
0.435
(1.689)
-0.041
(0.045)
0.368**
(0.172)
0.009
(0.022)
2.621***
(0.617)
1.6%
-0.2%
0.4%
0.4%
26.8%
3.1%
1.4%
-15.520***
(4.061)
-72.829**
(29.205)
0.586***
(0.116)
-0.889*
(0.485)
0.117
(0.074)
0.127**
(0.056)
11.329***
(1.528)
3.411***
(0.330)
0.055
(0.067)
3.718***
(0.162)
1.601***
(0.168)
-0.343
(0.248)
0.073
(1.132)
1.470
(1.825)
-0.047
(0.045)
0.665**
(0.272)
0.017
(0.022)
-2.8%
2.2%
-0.2%
0.3%
0.6%
0.6%
37.6%
4.4%
2.8%
4.1%
0.1%
2,346,422
963
0.3%
41.1%
40
133,141
963
5.4%
56.1%
89,962
950
7.9%
52.3%
41
3,632
0.4%***
8.3%
405
3.1%***
12.2%
Panel C: Roundtrips Completed in ≥ 1 Day
Number of observations
3,632
3,603
Mean gap
0.2%
0.3%**
Std of gap
8.4%
7.7%
398
2.8%***
10.7%
950
0.4%*
6.9%
Panel D: Incomplete Roundtrips
Number of observations
405
Mean gap
3.1%***
Std of gap
11.1%
Panel E: Performance gap by trader
Number of observations
963
Mean gap
0.3%
Std of gap
7.4%
963
0.5%**
7.6%
3,100
0.3%***
2.7%
3,097
0.1%**
3.0%
7,137
0.5%***
6.9%
All
Same or lower
All
All
(3)
Panel B: Intraday Roundtrips
Number of observations
3,100
Mean gap
0.2%***
Std of gap
3.1%
Platform only
All
All
All
(2)
7,098
0.4%***
6.4%
All
All
All
All
(1)
Panel A: All Observations
Number of observations
7,137
Mean gap
0.4%***
Std of gap
6.8%
Subset filters
Trading venue
Absolute spread
Conversion ratio
Implied volatility
963
0.9%***
8.2%
405
3.4%***
12.6%
3,632
0.7%***
8.0%
3,100
0.4%***
2.6%
7,137
0.7%***
6.7%
All
Same or lower
Same or higher
All
(4)
963
1.9%***
7.5%
405
4.6%***
17.0%
3,632
1.5%***
8.3%
3,100
0.3%***
2.2%
7,137
1.2%***
7.4%
All
Same or lower
Same or higher
Same or lower
(5)
For each sample purchase, the performance gap is the return of the option actually bought subtracted from the return of an equally weighted portfolio of similar options
that could have been bought as well (including the option bought). Hence, worse investor choices result in larger performance gaps. Options are considered similar if
they are available for trading on the actual trade dates and if their price elasticity is within 10% of the option bought. Returns are calculated assuming that investors
buy at the Euwax ask in effect at 9:20am on the actual day of purchase and sell at the Euwax closing bid (at 5:30pm) on the actual day of the first sale following the
purchase. Column (1), Panel A, summarizes the gap across all observations. Column (2) reports gap statistics only for options that can be traded on issuer platform.
Columns (3)-(5) report results for different sets of similar options – options that are similarly price-elastic as the option bought, but have weakly lower absolute spreads,
weakly higher conversion ratios, or weakly lower implied volatilities (calculated at the midpoint of the previous closing quote). Panels B-D report gap statistics by
holding period. The gap statistics reported in Panel E are first averaged across all transactions for a given trader, and then across traders. ***/**/* indicate that the
performance gap is significantly different from zero at the 1%/5%/10% level assuming that observations are independent either at the transaction level (Panels A-D) or
at the investor level (Panel E).
Table IV: Performance Gap – Baseline Results
Table V: Performance Gap Panel Regressions
The dependent variable is the performance gap between the chosen option and an equally-weighted portfolio of elasticitymatched options (options whose elasticity is within 10% of the chosen option); worse choices are associated with larger
performance gaps. The hypothetical trading strategy consists of investors buying at 9:20am on the actual day of purchase
and selling at 5:30pm on the actual day of sale. “Size” is the EUR volume of the trade. The “Number of issuers traded
with” is computed from the trading records during the 6 months before the sample period. The “Status quo” dummy is
one if the investor has bought a given option before. The number of “Available options” refers to the total number of
DAX calls that could have been bought on a given date. The “gap” variables refer to differences in attributes between
similar options and the option bought. For example, the “Advertising gap” is the log difference between the average
pre-sample advertising expenditures associated with similar options and the corresponding expenditures associated with
the option bought. All the variables underlying the gap calculations are defined as in Table III. All standard errors are
robust to heteroskedasticity (see White (1980)) and correlation across same-investor observations (see Williams (2000)).
***/**/* indicate that the coefficient estimates are significantly different from zero at the 1%/5%/10% level.
Dependent variable
Options matched by
Constant
ln(size)
ln(1+# issuers traded with)
Status quo
Advertising gap
ln(# available options)
(1)
(2)
(3)
(4)
(5)
Performance gap = Average return of similar options - Return of option chosen
Elasticity
Elasticity
Elasticity
Elasticity
Elasticity
Issuer Platform
-0.046
(0.034)
-0.002**
(0.001)
-0.003*
(0.002)
0.006***
(0.002)
-0.004***
(0.001)
0.011*
(0.006)
-0.020
(0.032)
-0.002***
(0.001)
-0.003**
(0.001)
0.005**
(0.002)
-0.003***
(0.001)
0.007
(0.005)
0.962**
(0.433)
-0.050
(0.035)
-0.002**
(0.001)
-0.003**
(0.002)
0.005***
(0.002)
-0.004**
(0.001)
0.012**
(0.006)
0.000
(0.001)
0.003
(0.002)
-0.144**
(0.058)
-0.006
(0.005)
1.001**
(0.386)
-0.047
(0.034)
-0.001*
(0.001)
-0.004**
(0.002)
0.005**
(0.002)
-0.001
(0.002)
0.010*
(0.005)
-0.001
(0.001)
0.000
(0.003)
-0.087
(0.053)
-0.004
(0.005)
0.976**
(0.388)
-0.486
(0.391)
2.181***
(0.441)
-0.036
(0.036)
-0.002**
(0.001)
-0.003**
(0.002)
0.005***
(0.002)
-0.005*
(0.003)
0.008
(0.006)
-0.001
(0.001)
0.000
(0.003)
-0.168***
(0.061)
-0.002
(0.006)
1.009***
(0.386)
0.993**
(0.384)
7,137
No
963
1.9%
7,098
No
950
1.8%
7,137
No
963
2.1%
7,137
No
963
2.5%
7,137
Yes
963
2.4%
Credit rating gap
Quotes gap
Market trading volume gap
Brokerage trading volume gap
Elasticity gap
Absolute spread gap
Conversion ratio gap
Ancillary Statistics
Number of Observations
Issuer Fixed Effects
Number of Clusters (Investors)
R2
42
A
The Market for OTC derivatives in Germany
OTC derivatives are non-standardized derivatives written by large banks such as Citigroup,
Commerzbank, and Deutsche Bank. The payoffs of these derivatives depend on the price movements in the underlying asset – individual stocks, stock indices, currencies, commodities, and
bonds. Issuers state in the prospectus that they continuously hedge their exposure by taking
positions in the underlying assets. This does not mean, however, that OTC derivatives are
free from issuer default risk as reported by Bartram and Fehle (2007). The prospectus also
states that such instruments are senior unsecured obligations of the issuer and thus subject to
issuer default risk. The attribute “non-standardized” refers to the fact that the issuing banks
have full discretion regarding the characteristics of the derivatives – in the case of options, for
example, underlying, strike price, issue date, maturity date, and earliest exercise date. The
distinction between primary and secondary market in these instruments is fluid. Interested
investors cannot subscribe to a particular issue ahead of time and there is no binding issue
price. Issuers typically reserve the right to continuously adjust issue size over time without
informing investors; in particular, not all warrants have to be issued at the outset.
Investors can trade these derivatives over the counter either on regular exchanges, where
the issuer typically serves as the exclusive market maker, or directly through the issuer as many
issuers provide an electronic link between retail brokers and their own trading platforms. Retail investors are effectively short-sale constrained – during the sample period, none of the
major retail brokers allows his retail clients to write options even if the clients maintain a long
position in the underlying.
The most important German exchange for OTC derivatives, and one of the largest of its
kind in the world (see Glaser and Schmitz (2007)), is the European Warrant Exchange (Euwax)
based in Stuttgart. Its market share of OTC derivatives trading in Germany averaged 60%
in 1999 and increased to 80% by the end of 2000 (see Wertpapierbörse (2001)). In 2007, the
Euwax listed roughly 250,000 different OTC derivatives and reported a trading volume of EUR
43
128 billion (trading volume here refers to the price paid for the instrument, not the notional;
see Wertpapierbörse (2008a)). It is difficult to assess the magnitude of the volume executed
on the issuers’ proprietary trading platforms because this volume is not publicly reported and
not included in the Euwax trading volume reported above. In the sample considered in this
paper, more than 80% of the trading volume is handled by the issuer directly which suggests
that Euwax trading volume is a conservative estimate of the total trading volume in covered
warrants. To put these numbers in perspective: During the same period, the EuRex (one of
the world’s largest derivatives exchanges based in Frankfurt) reported a premium volume of
EUR 455 billion in roughly 15,000 different options (author’s estimates from the Eurex website http : //www.eurex.de). Hence, if the sample ratio of proprietary platform to exchange
volume were representative of the aggregate ratio, the trading activity in covered warrants
would be similar to that in traditional exchange-traded options. During the sample period,
retail investors at major retail brokers could not participate in the trading of standardized
options contracts that takes place on the Eurex. Bartram and Fehle (2007) provide a detailed
comparison of the Euwax and the Eurex. Glaser and Schmitz (2007) provide a description of
the German market for OTC derivatives and retail investors who participate in this market.
The focus of this paper is on the simplest type of OTC derivatives: plain-vanilla index
options. The issuing process of these options is quick and cheap which partly explains the
plethora of instruments listed. A selling prospectus, which can be used to issue entire series of
options, can be approved within 10 business days by the German securities regulator BAFIN at
a cost of EUR 1,000 (Justizministerium (2005)). The issuer further bears the cost of publishing
the prospectus as well as exchange listing fees. Euwax listing fees are EUR 500 per option
(Wertpapierbörse (2008b)), although Euwax caps listing fees by issuer such that issuers with
more than 80 new listings in a calendar year have zero marginal listing fees; large banks such as
Deutsche Bank issued hundreds of covered warrants during 1999. As part of the Euwax listing,
the issuer commits to making a liquid market in his issues (or to hiring another firm to do so).
Market maker quotes on Euwax are subject to fixed minimum depth requirements (EUR 3,000
44
or 10,000 units). The issuer’s commitment to quote spreads below a stated maximum is also
published by Euwax, but varies across issuers. In most cases, the maximum absolute spread
corresponds to roughly one Euro per unit. This maximum is hypothetical during the sample
period given that almost all options have absolute spreads of less than 4 cents.
The market appears to be highly concentrated. Citigroup, the top issuer in the sample,
accounts for more than 70% of sample trades and two thirds of the sample trading volume;
the top four issuers (Citigroup, HSBC, UBS, and Société Générale) together have a brokerage
market share of 99%. Glaser and Schmitz (2007) report similar issuer concentrations for a
sample of option trades at a German discount broker between 1997 and 2001 for a broader
range of underlyings. They also report that the top four issuers accounted for three quarters
of the market-wide trading volume in OTC derivatives during 2005.
B
Price Dispersion on Euwax versus Eurex
It is possible, indeed likely, that part of the observed price dispersion is due to well-documented
option price anomalies (relative to the Black and Scholes (1973) model). One would expect
similar price dispersions in the market for OTC derivatives (Euwax) and in the market for
exchange-traded derivatives (Eurex), however. Figure 1 in the paper illustrates the price
dispersion in terms of Black-Scholes implied volatilities across the 350 available DAX calls
on May 31, 2000 (available refers to being quoted on Euwax). The interquartile range of
implied volatilities is 24.3% to 30.6%. In contrast, the interquartile range of implied volatilities
computed from the prices of 90 active DAX calls traded on Eurex on the same date is 21.4% to
24.3%.5 The two distributions are not directly comparable partly because the range of Eurex
options features differs from that of Euwax. For example, the range of Eurex strike prices
(6,000-10,000) is smaller than that of Euwax strikes (5,800 to 11,000). Moreover, according
to Bartram and Fehle (2007), Eurex spreads tend to be higher than Euwax spreads and the
implied volatilities reflect both sides of the spread; Eurex implied volatilities are based on
5
The underlying data were obtained from Deutsche Börse’s data webshop.
45
actual transaction prices and Euwax volatilities are based on simulated transaction prices (by
randomly using bid and ask quotes) . Since there are many more Euwax calls than Eurex calls,
one can match a given Eurex instrument with a Euwax instrument that has an identical or very
similar strike price and maturity. Figure 3 below contrasts the implied volatility distributions of
Eurex calls and their best Euwax matches. Despite the matching and the fact that the Eurex
distribution captures larger spreads, the standard deviation of Euwax implied volatilities is
substantially larger than the standard deviation of Eurex implied volatilities (3.5% versus
2.8%). Because Eurex options are quoted and traded in minimum quantities, their prices are
much higher than those of similar Euwax options which can be traded individually. It is possible
that the prices of “penny” Euwax options drive the wider distribution of implied volatilities.
To examine this conjecture, one can hypothetically lift the minimum quantity requirements
for Eurex options, randomly impose Euwax-type conversion ratios, and thus repeatedly obtain
artificial sets of Eurex options that are subject to similar price rounding issues as their Euwax
counterparts. The standard deviations of these artificially generated implied volatilities average
2.9% (versus the actual 2.8%) – rounding issues thus appear to account for only a small part
of the difference in the dispersion of implied volatilities. It thus appears that prices of Euwax
options are higher, on average, and more dispersed than prices of comparable Eurex options.
Bartram and Fehle (2007) attribute the higher average Euwax implied volatilities to the fact
that individual investors are unable to write options on the Euwax; they conjecture that large
Eurex spreads prevent institutional arbitrage between Eurex and Euwax instruments.
C
Looking Ahead
One might be concerned about the robustness of the results, given that the underlying trades
were made ten years ago during a short and turbulent period. Over time, OTC options may
have become cheaper to trade and option investors may have learned to identify higher value
investments. It is difficult to examine the learning conjecture without detailed investor-level
data. The conjecture that option trading has become cheaper over time (presumably as more
issuers have discovered this market segment and stimulated competition) can be evaluated
46
more easily.
For recent years, Datastream provides a searchable database of OTC DAX options that
includes the options’ security identifier (ISIN) for most issues. This, in turn, means that most
of the Datastream option data can be merged with Euwax quote data, when available. To examine the conjecture that option spreads have declined over time, Table VI reports summary
statistics of Euwax spreads on three trading days: 15 December 1999, 12 December 2007, and
10 December 2008. The two first dates were chosen such that the prior one-month performance
of the index was roughly equal for both dates.6 (Given that spreads tend to be constant in
absolute terms, poor performance will be associated with higher relative spreads. The opposite is true for positive performance.) Average relative spreads are not significantly different
in 1999 and 2007 (1.3% in 1999 versus 1.5% in 2007); spread dispersion is slightly higher in
2007. Absolute spreads are significantly higher in 2007 than in 1999: 2 cents versus 1.7 cents.
Importantly, the dispersion of absolute spreads has gone up by an order of magnitude. At the
same time, the number of available investment alternatives increases more than tenfold. The
statistics for December 2008 presumably reflect the higher market volatility and poor returns
leading up to the snapshot date which makes for a difficult comparison. Although the number
of plain vanilla DAX options declined substantially between 2007 and 2008, the total number
of derivatives with the DAX as their underlying was relatively steady at about 6,500.
The dramatic increase in the number of different DAX calls and the wider dispersion of
characteristics such as absolute spreads suggest that, if anything, the search problem for the
best option has become even more difficult since the sample period. Moreover, the results are
not consistent with the conjecture that trading costs have trended lower over time.
6
Downloading the quote data is a time-consuming process, hence only two additional dates were considered.
47
Figure 3: Distribution of Implied Volatilities of DAX Calls as of May 31, 2000. The histogram
summarizes implied volatilities of all Eurex-listed DAX calls and their matching Euwax counterparts. For a given Eurex options, all Euwax options with the same strike price are identified
(or the closest strike price in 10% of the cases in which an exact match cannot be found).
From this subset of options, the match is chosen as the Euwax option with the expiration date
closest to that of the Eurex option in question.
0.2
0.2
Only Euwax That Match Eurex
0.18
0.18
Frequency
All Eurex
0.16
0.16
0.14
0.14
0.12
0.12
0.1
0.1
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0.02
0
0
0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39
Implied Volatility Bin
48
Table VI: Spreads During and After the Sample Period
The statistics below summarize DAX call option spreads quoted on Euwax on 15 December 1999, 12 December 2007, and
10 December 2008. The absolute spread is the difference between the opening Euwax ask and bid quotes. The relative
spread is the absolute spread divided by the quote midpoint.
Date
# DAX call options
December 15, 1999
238
December 12, 2007
2,974
December 10, 2008
1,674
49
Spread
Type
Relative
Absolute
Relative
Absolute
Relative
Absolute
Mean
1.32%
0.017
1.49%
0.020
47.76%
0.033
Spread
Std
7.51%
0.005
8.54%
0.090
69.46%
0.125
Median
0.27%
0.020
0.28%
0.020
7.66%
0.020