Download The Performance of Individual Investors in Structured Financial

The Performance of Individual Investors in Structured
Financial Products
Oliver Entrop1, Michael McKenzie2, Marco Wilkens3 and Christoph Winkler4
Abstract. The literature often casts structured financial products in a negative light.
Reasons are overpricing by issuing banks, high transaction costs and individual
investors’ own poor selection abilities. This paper is the first to establish the impact of
each of these factors on individual investors’ wealth using a large database of trades
and portfolio holdings for 133,353 retail investors in discount and bonus certificates
and common stocks. Our main findings are: (i) individual investors’ risk-adjusted
performance in certificate and in stock investments is negative, both before and after
deduction of costs; (ii) their underperformance can mainly be explained by the
overpricing of structured financial products and the investors’ poor underlying/stock
selection ability; we find evidence (iii) that certificate investors suffer from product
complexity and (iv) that certificate and stock investors are prone to the disposition
effect.
Keywords: Retail derivatives, certificates, investor behavior
JEL Classification: G 11, G 12, D 83
* Part of this research was undertaken while Marco Wilkens was visiting the University of Sydney. We
would like to thank Rainer Baule for providing us valuable data on certificate characteristics. Some of
the data used in this paper was supplied by Securities Industry Research Centre of Asia-Pacific
(SIRCA) on behalf of Thomson Reuters.
1
Oliver Entrop, University of Passau, Chair of Finance and Banking, Innstr. 27, D-94032 Passau,
Germany, phone: +49 851 509 2460, email: [email protected]
2
Michael McKenzie, University of Sydney, Chair of Discipline of Finance, H69 - Economics and
Business Building, NSW 2006 Australia, phone: +61 2 9114 0578, email:
[email protected] 3
Marco Wilkens, University of Augsburg, Chair of Finance and Banking, Universitätsstr. 16, D-86159
Augsburg, Germany, phone: +49 821 598 4124, email: [email protected] 4
Christoph Winkler, University of Augsburg, Chair of Finance and Banking, Universitätsstr. 16, D86159 Augsburg, Germany, phone: +49 821 598 4121, email: [email protected] The Performance of Individual Investors in Structured
Financial Products
Abstract. The literature often casts structured financial products in a negative light.
Reasons are overpricing by issuing banks, high transaction costs and individual
investors’ own poor selection abilities. This paper is the first to establish the impact of
each of these factors on individual investors’ wealth using a large database of trades
and portfolio holdings for 133,353 retail investors in discount and bonus certificates
and common stocks. Our main findings are: (i) individual investors’ risk-adjusted
performance in certificate and in stock investments is negative, both before and after
deduction of costs; (ii) their underperformance can mainly be explained by the
overpricing of structured financial products and the investors’ poor underlying/stock
selection ability; we find evidence (iii) that certificate investors suffer from product
complexity and (iv) that certificate and stock investors are prone to the disposition
effect.
Keywords: Retail derivatives, certificates, investor behavior
JEL Classification: G 11, G 12, D 83
1. Introduction
Structured financial products became a very popular investment alternative for retail
investors during the last decade. In contrast to the more traditional asset classes (such
as stocks, bonds or investment funds), structured financial products offer a far greater
diversity of payoff profiles which often cannot be realized by retail investors on their
own due to market restrictions or transaction costs. Structured financial products also
help to satisfy individual investors’ frequent desire to diversify their portfolios by
investing in various assets like single stocks, indices, baskets, commodities,
currencies or interest rates. This flexibility heavily contributed to the success of this
asset class, in particular in Europe which accounts for US$1.3tn of the estimated
US$2tn global market (Demos (2012)).1
Despite their ability to close the gap of market imperfection for individual
investors, structured financial products have a bad reputation in the academic
literature since their potential negative effects on investors’ wealth are manifold. The
most frequently discussed issue relates to price premia on top of fair theoretical values
found in the quotes of structured financial products. This premium has been
documented for products sold in the primary market, where prices are typically well
above their theoretical fair value. It has also been documented in the secondary
market, where issuers act as market makers both on their own trading platforms and
on retail derivative exchanges such as the European Warrant Exchange (Euwax) and
Scoach. By acting in the role of the market maker, banks are able to sell certificates
above their fair theoretical values and redeem them at lower prices. Empirical
evidence of price premiums over the course of the certificates’ life are found in
Wilkens et al. (2003) and Stoimenov and Wilkens (2005) for almost all subgroups of
retail structured products in the German market. Baule (2011) finds evidence to
suggest that issuers anticipate the order flows of certificates and price them higher in
periods of positive expected net sales. Henderson and Pearson (2011) conclude that
the overpricing of U.S. structured financial products is sufficiently high so as to
1
Lord (2011) reports that the value of structured retail products under management globally is
comparable in size to the hedge fund industry.
1 generate an expected return that is below the risk free rate, and most likely negative.
Bergstresser (2008) considers a much larger sample of over 1,000,000 note issues and
provides further evidence in support of the conclusions of Henderson and Pearson
(2011).
A further and more obvious source of losses for retail structured product investors
are transaction costs. This includes indirect transaction costs in the form of the bid/ask
spread which is earned by issuers acting in the role of market maker in the secondary
market. It also includes direct costs in the form of commissions which the literature
has shown to be very detrimental to investors’ wealth (see, e.g., Barber and Odean
(2000) for equity traders and Bauer et al. (2009) for option traders). Entrop et al.
(2012) attempt to quantify the relative impact of overpricing, bid/ask spreads and
commissions on the realized returns of short term leveraged retail products. They find
that direct and indirect transaction costs decrease roundtrip returns of warrants and
leverage certificates by an economically large 3.5% and 4.0%, respectively. Finding
no evidence for poor market or volatility timing, they conclude the negative gross
performance of investors is primarily driven by issuers’ margins.
From issuer’s perspective, it is often argued that structured financial products
help retail investors optimizing their portfolios. However, in the absence of financial
advisers, individual investors are exposed to the problem of choosing from among the
myriad of available products – which are more or less overpriced. Research has
shown that individual investors typically struggle with the task of stock selection and
often make suboptimal decisions that result in underperforming equity portfolios,
even before costs are taken into consideration (see, e.g., Odean (1999), Barber and
Odean (2000, 2001), Barber et al. (2009)). Investing in structured financial products is
arguably far more complex compared to simple stock selection, since investors have
the choice between various payoff profiles, underlying assets, maturities, issuers and
other product specific characteristics. For example, Dorn (2012) documents
substantial price variation among similar structured securities and finds that even
experienced warrant traders are unable to identify attractively priced options. This
complexity means that retail investors incur substantial search costs; hence, losses
from poor choices will be compounded in the context of structured products. This
2 issue is further complicated by the fact that most structured products have a fixed life.
Therefore, unlike a buy and hold strategy, asset selection is not a one-time
proposition, as structured products that mature will need to be replaced.
We extend this work by analyzing the realized performance of retail investors
who trade investment certificates. In particular, we are the first to identify the
influence of issuers’ pricing policy, transaction costs and effects of investors’
selection abilities on the realized portfolio returns. Our study is based on a unique
combination of multiple datasets – portfolio holdings and trade data for 133,353 retail
customers of a large German direct bank, price data for all certificates offered to the
customers from the SIRCA Thomson Reuters Tick History (TRTH) database 2 and
Datastream and a classification dataset including detailed certificate level
characteristics. We focus on discount and bonus certificates with DAX stocks as
underlyings, as these are the most popular types of investment certificates, sampled
over the period 2004 to 2008. To account for the certificates’ nonlinear risk
exposures, we apply a three-factor alpha model including a stock index, a call and a
put option factor. We also compare investors’ certificate portfolio performance to the
performance of their direct investments in DAX stocks. Moreover, we are the first to
examine retail investors’ certificate choices in detail, distinguishing between the
selection of the certificates’ underlying, their cap or bonus/barrier level and their
issuer.
The results of this paper can be summarized as follows. Overall, we find
economically large negative risk-adjusted performance for investors in discount and
bonus certificates, both before and after transaction costs are taken into account.
Transaction costs, the banks’ pricing policy and investors’ selection abilities all play
an important role in explaining these negative returns. In particular, we find that the
losses caused by overpricing are larger for bonus certificates. Further, the issue of
product complexity and choice is especially interesting. The results of this study
suggest that, while investors make positive choices when it comes to the cap levels for
their discount certificates, they tend to lose a lot of money by selecting inferior barrier
2
See the website of the SIRCA Thomson Reuters Tick History (TRTH) database, www.sirca.org.au/products/.
3 and bonus levels for their bonus certificate investments. This evidence provides
support for Dorn’s (2012) observations on warrant traders being overstrained by
identifying most promising product characteristics. Thus, retail investors suffer from
structured product complexity both through larger product overpricing and their own
limited selection abilities. Examining investors’ physical holdings, we find that their
poor selection abilities in structured products are mirrored in their stock choices,
leading to significant underperformance for their DAX stock portfolios, both in gross
and net terms. This latter result provides further support for the evidence provided by
previous studies such as Odean (1999), Barber and Odean (2000, 2001) and Barber et
al. (2009). Finally, we find that certificate and stock investors are prone to the
disposition effect, i.e., they sell winning certificates and stocks soon. In brief, we find
that individual investors do not profit from the large variety of structured financial
products. However, we also find that investors do not make good choices when it
comes to their direct stock investments.
The remainder of the paper is organized as follows. Section 2 briefly describes
the market for investment certificates and the characteristics of discount and bonus
certificates. Section 3 introduces the data sample used in our empirical study. Section
4 evaluates investor performance in certificate and stock investments. Section 5
examines individual investors’ certificate selection abilities. In Section 6 we check the
robustness of our results. Section 7 concludes.
2. Investment Certificates
2.1 Market of Investment Certificates
This paper analyzes German retail investors’ performance in investment certificates.
In contrast to leverage certificates, investment certificates have a longer time to
maturity (usually between one and two years from issuance) and are held for around
20 months on average (in our sample). In 2008, the total amount invested in German
investment certificates was around EUR 67 billion which is almost 99% of all
certificates. For the same period, investment certificates made up about 50% (around
4 EUR 36 billion) of the total retail order volume of certificates on the Euwax. In our
study, we focus on discount and bonus certificates. These are the most popular types
of investment certificates, with market shares of around 30% and 25% of total order
volume. 3
Investment certificates can be traded on exchanges as well as on trading
platforms provided by the issuers. In Germany, the Euwax and Scoach are the
dominant exchanges with market shares of 63% vs. 37% as at December 2008. 4
Issuers are obliged to provide liquidity on the exchanges, so they act as a market
maker and continuously quote binding prices for their certificates. In taking this role,
the issuers are able to make profits by quoting bid and ask prices that deviate from the
certificate’s theoretical fair value.
2.2 Discount and Bonus Certificates
In our analysis, we focus on a subset of homogenous certificates called classic
discount certificates and classic (non-capped) bonus certificates, neither of which
have exotic features. While discount and bonus certificates are issued on a wide range
of stocks, most trading activity takes place in certificates that are written against
stocks in the DAX index. As such, the analysis in this paper concentrates solely on
transactions and holdings data for classic discount and classic bonus certificates on
the 30 stocks listed in the DAX index in the corresponding months. For reasons of
consistency, we also limit our analysis of investors’ direct stock investments to the
same set of DAX stocks.
Buying a discount certificate, the investor participates in the underlying’s price
movements. Its upside potential however is limited by a cap. To compensate this cap,
discount certificates will trade at a lower price compared to the underlying. The
payoffs to a discount certificate can thereby be replicated by a combination of the
underlying and a short call (strike = cap) which is equivalent to a covered call position
(see Figure 1 for payoff profiles).
3
4
See the website of the German Derivatives Association, available at www.deutscher-derivate-verband.de.
See the website of the German Derivatives Association, available at www.deutscher-derivate-verband.de.
5 A bonus certificate promises a fixed payment above the underlying’s value at
maturity (bonus level) if the underlying does not touch or fall below a lower barrier
during the lifetime of the product and if the underlying quotes below the bonus level
at maturity. In all other cases the investor receives the underlying or its cash value at
maturity. The payoff profile for a bonus certificate equals a combination of a call
(strike = 0) and a down-and-out put (strike = bonus level; barrier of the option =
barrier of the certificate). A bonus certificate will trade close to the price of the
underlying if the barrier has been breached or if the underlying price is well above the
bonus level. A bonus certificate will trade above the underlying’s price if there is
potential for the investor to receive the bonus of a larger value than the current
underlying price.
It should be noted that, in contrast to direct stock investments, investors do not
receive dividend payments through their discount and bonus certificate positions.
However, they should also profit from the underlying’s dividend payments as these
should be incorporated in the issuers’ pricing formula in a fair price setting.
3. Data
This paper uses a unique account level dataset for 133,353 retail customers of a large
German direct bank. Individual transaction and monthly portfolio holdings
information is provided for all stocks included in the DAX index as well as for
discount and bonus certificates having those same stocks as underlying assets. This
data spans the period from February 2004 through December 2008. We further have
information on each certificate’s name, ISIN, issue date, maturity date, underlying,
issuer, cap level (for discount certificates), bonus and barrier level (for bonus
certificates). This level of detail allows us to uniquely classify each certificate by its
payoff profile.
Table I presents a range of summary statistics for the dataset and reveals that, of
the 133,353 retail investors in the dataset, 3,895 (2.9%) trade discount certificates at
least once, 8,165 (6.1%) trade bonus certificates at least once and almost every
investor trades stocks (132,515 or 99.4%). The average number of trades (No. trades)
6 per investor for discount certificates (8.06) is almost twice as much as it is for bonus
certificates (4.32). Similarly, the average transaction size per trade (Trade size) is also
higher for discount certificates (EUR 5,947) compared to bonus certificates (EUR
4,865) and both are higher when compared to the average trade size for common
stocks (EUR 3,803).
The number of different securities traded (Securities) in the database is very large
for discount certificates (8,918) relative to bonus certificates (3,306). All of these
certificates have one of the 35 stocks, which were listed in the DAX index during our
sample period, as underlying. The total number of trades for discount certificates
(31,391) is similar to bonus certificates (35,258); as while discount certificates have a
lower number of investors, they tend to trade almost twice as often. The average
relative commission (Commission) for certificate transactions is low compared to
stock transactions which may be the result of smaller stock trade sizes.
[Insert Table I about here.]
In addition to this individual account data, daily bid and ask closing prices for all
discount and bonus certificates were sourced from the SIRCA Thomson Reuters Tick
History (TRTH) database. The equivalent data for all stocks in the DAX index is
sourced from Datastream. Using this data, we computed bid/ask spreads for every
security on each trading day
. where
and
during our sample period:
,
(1)
are closing bid and closing ask prices, respectively. Spreads for
certificates are known to be relatively constant during the day. Moreover, since
issuers act as market makers, they are obliged to execute orders at the respective bid
or ask price which means that the use of closing prices is unlikely to have any
significant impact on the estimates. As regards stocks, Keim and Madhavan (1998)
point out that quoted bid/ask spreads may be imprecise estimates of the true spread,
because trades are often executed inside the quoted spread. This argument is of less
relevance in our case since we only consider highly liquid DAX stocks with small
bid/ask spreads. The final column of Table I shows that the average bid/ask spread of
7 DAX stocks is relatively low (0.23%) in comparison to discount certificates (0.38%)
and bonus certificates (0.77%).5 These results imply that investors have to pay for
complexity in structured products through larger spreads. Summing up the costs of
commissions and spreads, an investor loses 0.68% (1.09%) of his invested money
through direct and indirect transaction costs for each roundtrip trade in discount
(bonus) certificates. Trading with DAX stocks is cheaper with average roundtrip costs
of 0.67%.
4. Investor Performance
4.1 Methodology
4.1.1 Return Calculation
To analyze individual investor performance across the different types of
securities considered in this paper, we estimate monthly returns to discount
certificates, bonus certificates and stocks. Following Bauer et al. (2009), we assume
that all securities are purchased at the beginning of the month and are sold or
redeemed on the last day of the month. We acknowledge that this approach will bias
both the positive and the negative returns towards zero and the results should be
interpreted accordingly.
To isolate the impact of commissions and bid/ask spreads on investor
performance, three different measures of return are calculated. The first measure is a
gross return (
) which ignores any transaction fees apart from bid/ask spreads, and
is calculated for the position in security j held by investor i as:
,
(2)
5
Our spread estimates for discount certificates are comparable to Baule et al. (2008) who report bid/ask
spreads of 0.35% for discount certificates on DAX stocks in 2004. Baule and Tallau (2011) report
bid/ask spreads of between 0.07% and 0.22%, depending on the issuer, for bonus certificates on the
DAX index. This suggests that bid/ask spreads are larger for certificates on single stocks than on equity
indices.
8 where
is the position value of security j at the end of month t,
denotes the
net of purchases and sales/redemptions, based on actual execution prices, during
month t.
are dividends received during month t (always zero for certificates).
stands for the amount of invested capital in month t which is the sum of
and the value of purchases made by investor i in security j during month t.
A second measure of gross returns (
) is calculated which assumes that
purchases and sales are executed at the mid price:
,
(3)
i.e., half the bid/ask spread estimated in equation (1) is added to (subtracted from) the
execution price of a sale (purchase).
The third measure is a monthly net return (
negative effects of both commissions (
) which takes into account the ) and bid/ask spreads:
.
Across these three return measures, it logically follows that
(4)
≥
≥
.
Following Barber and Odean (2000), the returns to a single security are
aggregated to form value-weighted monthly portfolio returns at the investor level for
each security group,
∑
where
,
(5)
is the proportion of security j in the security group portfolio held by
investor i during month t, measured on the basis of the invested capital (
and
),
is the number of different securities of the same security group held by
investor i in month t.
Finally, we obtain monthly returns for the average investor for their security
group sub-portfolio as
∑
,
(6)
9 where
is the number of investors who are invested in the same security group in
month t.
The end result of this process is three different estimates of monthly returns
(
,
,
) for each class of asset, i.e., discount certificates, bonus certificates
and stocks, respectively.
4.1.2 Risk-adjusted Performance
In addition to the three measures of returns to investors’ certificate and common
stock portfolios introduced in the previous section, performance may also be assessed
using a measure of risk-adjusted performance. To this end, we specify the following
multifactor model which can be individually estimated for discount certificate, bonus
certificate and stock portfolios:
(7)
where
,
and
are coefficients to be estimated and
is the error
term. The intercept ( ) in this equation provides an estimate of the risk-adjusted
performance of the average investor’s security group sub-portfolio.
is the month t risk-free rate which is proxied by the one-month money market
rate reported by Deutsche Bundesbank (series SU0104).
is the monthly DAX
performance index excess return which is the proxy for the market factor. The use of
the DAX index is a logical outcome of our choice to only consider stocks included in
the index or certificates written against those stocks.
and
denote the monthly excess returns to a call and put trading
strategy, respectively. To understand the role of these two factors, recall that the
payoffs to a discount certificate can be replicated using the underlying and a short call
position, while the payoffs to a bonus certificates are represented as the sum of a zerostrike call and a down-and-out put. This means that a portfolio containing discount or
bonus certificates is subject to some form of nonlinear risk. The market factor is
unable to fully account for this nonlinearity and so, additional variables must be
employed to perform in this role. Following Glosten and Jagannathan (1994),
Agarwal and Naik (2004) and Bauer et al. (2009), we include the variables
10 and
which measure the excess returns of at-the-money (ATM) calls and puts
on the DAX performance index, respectively. These call and put factors are
constructed as follows: at the end of each month, ATM call and put options on the
DAX expiring on the third Friday of the month following the next month are
purchased. At the end of the next month these options are sold and again ATM calls
and puts with a maturity of then almost two months are purchased. Thus, we obtain a
time series of monthly excess returns for the call factor and for the put factor. As
these options are ATM, we are careful to only select those options whose strike price
is closest to the current index value. Further, to avoid multicollinearity, we
orthogonalize the call and the put factor by the market factor. All option prices were
sourced from Datastream.
Note that Fama and French’s (1993) SMB and HML factors and Carhart’s (1997)
WML factor are not included in this multifactor regression model specification.
Recall that the focus of our model is on explaining the returns of only 30 blue chip
stocks and their derivatives. Fama and French’s size and value factors and Carhart’s
momentum factor are typically employed to explain a much larger investment
universe and the construction of SMB, HML and WML factors for a sample of only
30 stocks is neither sensible nor feasible.
4.2 Results
Each of the different measures of raw (
,
,
) and risk adjusted
returns ( ) are individually estimated for discount certificates, bonus certificates and
stocks. The results for the full sample are presented in Panel A of Table II. Before the
deduction of direct and indirect transaction costs (
), investors win on average
0.01% per month with their discount certificate investments, lose 0.18% on their
bonus certificate investments and earn 0.08% per month on their DAX stock
investments. After the deduction of direct and indirect transaction costs (
),
however, investors lose on their investments in discount and bonus certificates
(-0.07% and -0.23%, respectively). Their investments in stocks in the DAX index,
however, earn a net positive return of 0.03% per month. It is interesting to note that
11 these raw returns to DAX stock holdings are consistently less than the average
monthly DAX performance index returns (0.40%).
[Insert Table II about here.]
Comparing across the two different measures of gross returns (
and
),
bid/ask spreads reduce certificate returns by about 0.02% for discount certificates and
0.03% for bonus certificates per month. The effects of bid/ask spreads on DAX stock
returns are close to zero (0.01%). The differences between the net and gross return
after spreads (i.e.,
and
) show that investors lose an average of 0.06% per
month for discount certificates, 0.02% for bonus certificates and 0.04% for stocks
through trade commissions. These numbers are low when compared to Barber and
Odean’s (2000) results who find that stock investors lose 0.13% on average per month
in return terms through direct and indirect trading costs. Bauer et al. (2009) calculate
an even larger negative monthly return impact of almost 1%, caused by direct
transaction costs for stock portfolios. The lower costs in this study may be a reflection
of the longer holding periods and lower transaction costs in our sample. This is not to
suggest, however, that our cost estimates are insignificant – in annual terms, the direct
and indirect trading costs add up to economically significant 0.93% (0.67%) for
discount (bonus) certificate portfolios and 0.56% for stock portfolios, respectively.
Panel A of Table II also presents the estimated
coefficient from equation (5).
This is a measure of risk adjusted return which accounts for linear and non-linear
market risk exposures. Even when trading costs are ignored (
), monthly alphas
are negative for discount certificates at -0.17% which is equivalent to -2.02% per
year. The risk-adjusted performance of bonus certificate investments is even worse,
with a significant and negative alpha equal to -0.80%. This is equivalent to -9.19% per
year. The sample of investors performs poorly with their direct investments as well –
the estimate of alpha for stocks is a significant -0.27% (or -3.19% per year). Recall
that for the purposes of these calculations, dividend payments are incorporated into
the stock return calculations. Thus, this latter result implies that the investors
systematically overweight poor performing DAX stocks compared to the DAX
performance index composition. This finding is consistent with Barber and Odean
12 (2000) who also document poor risk adjusted stock performance before the deduction
of costs for U.S. equity traders. Gross alphas estimated by Bauer et al. (2009) for
Dutch equity traders, however, are close to zero. Taking trading costs into account
(
), alphas worsen even more, resulting in highly negative net alphas of -0.25% for
discount certificates, -0.85% for bonus certificates and -0.31% for direct stock
investments per month.
To test the robustness of these results to the choice of sample period, we reestimated the raw and risk-adjusted measures of return in two sample periods. The
first subperiod runs from February 2004 to July 2006 and includes the bull market
period (the average monthly return of the DAX performance index is 1.18%). The
second subperiod runs from August 2006 to December 2008 and so captures the end
of the bull market run and the subsequent collapse due to the subprime crisis (the
average monthly DAX return is -0.40%). The investment performance for both
subperiods is presented in panels B and C of Table II, respectively.
The magnitude of the different cost components in the subperiods is similar to
that previously discussed for the full sample. The main difference to the full sample
results is that returns are typically positive across all asset classes in the first
subperiod, while returns are negative across the board in the second subperiod. This is
to be expected given the first subperiod captures the bull market, while the second
subperiod includes the crisis where markets dropped dramatically. In terms of risk
adjusted performance, the subperiod alphas are again negative, although less so for
the second subperiod. The p-values are typically larger on average compared to those
for the full sample period, although this may be the result of the smaller sample size
in each subperiod.
Details of the individual coefficient estimates for the multifactor regression
equation, where returns are measured exclusive of the spread and commissions (i.e.,
), are presented in Panel D of Table II.6 The market betas for discount certificates
are considerably lower than 1 and their call factor loadings are negative and
6
The estimation results are qualitatively similar, where
or
are specified as the dependent
variable. These results are not presented to conserve space and are available on request.
13 significant. This is to be expected given that discount certificates can be duplicated by
a combination of a long underlying position and a short call position. For rising
markets in particular, when the option is more likely to be in the money, this capped
payoff structure results in reduced sensitivity to price movements of the underlying.
By way of comparison, classic bonus certificates are more prone to underlying price
changes since they are not capped. Therefore, their market beta is closer to 1 and we
find that their option factor loadings change over time. As expected, individual
investors’ portfolios of DAX stocks have a market beta of almost 1 and no evidence
can be found of significant nonlinear risk factors. The R² value for all estimated
equations is large which suggests that the factor model specified explains discount
certificate, bonus certificate and stock returns very well and is robust over time.
The finding that the risk-adjusted performance of discount and bonus certificates
is consistently negative is an important result and warrants further investigation. To
this end, the discussion that follows is aimed toward examining the various causes of
this poor performance. To begin, we note that transaction costs, like bid/ask spreads
and commissions, only contribute to a small proportion of the net losses (0.08% for
discount, 0.05% for bonus certificates in monthly alpha terms).
One potential explanation for these negative alphas is the overpricing of
certificates by the issuing banks. For example, Wilkens et al. (2003), Stoimenov and
Wilkens (2005) and Baule (2011) find that discount certificates on the DAX index are
issued at an average premium to fair value of 4.2%, 2.06% and 0.42%, respectively.
Further, the overpricing of discount certificates on stocks is larger than for
(performance) index certificates (default-free margins for discount certificates on
DAX stocks are estimated by Stoimenov and Wilkens (2005) of 3.63% and by Baule
et al. (2008) of between 0.39% and 1.97%).7 Stoimenov and Wilkens (2005) find that,
in comparison to classic instruments like discount certificates, complex products with
embedded exotic options like bonus certificates are priced with a higher margin.
Baule and Tallau (2011) provide further support for this finding and estimate an
7
It is probable that issuers often do not embed dividend payments in their pricing formula. Hence,
stock certificate investors lose alpha compared to a benchmark including positive dividend effects (e.g.,
the DAX performance index used in our factor model).
14 average margin for bonus certificates on the DAX index of between 2.09% and
4.85%. For both discount and bonus certificates, issuers tend to reduce their margins
as the time to maturity falls (for evidence on this lifecycle hypothesis see Wilkens et
al. (2003), Stoimenov and Wilkens (2005), Baule (2011) and Baule and Tallau
(2011)). This known price setting behavior is expected to have a negative effect on
both raw returns and alphas in the case of a buy-and-hold strategy.
If discount and bonus certificates are overpriced and these margins decrease
during their lifetime, the multifactor model value for alpha should be negative. To test
this proposition, we estimate the alphas of portfolios consisting of all available
certificates in the corresponding months. To this end, price data for all discount and
bonus certificates on DAX stocks that were traded at Euwax during our sample period
are gathered over the sample period.8 For each certificate, monthly excess buy-andhold returns from issuance to maturity on the basis of mid prices are calculated. 9
These monthly returns are averaged across all certificates to get the final series which
is specified as the dependent variable in the three-factor model specified in equation
(5). To test the possibility that alphas are driven by over- and under-weighting certain
underlying stocks, we also average certificate excess returns of the same underlying
stock and then average across all underlying stocks.
The results of this analysis for the full sample period are presented in Panel A of
Table III. Negative monthly alphas of -0.22% are estimated for discount certificates
and -0.39% for bonus certificates. Results for equally-weighted returns on the
underlying are similar and they are robust to testing within subperiods. Thus,
consistent with the prior literature, these results suggest that discount and bonus
certificates are priced above their fair value at the beginning of their lifetime and that
the issuers’ margins reduce as maturity approaches. Furthermore, overpricing for
complex products, such as bonus certificates, is larger than for discount certificates.
This latter result is also in line with the observations of the past literature.
[Insert Table III about here.]
8
This data is sourced from the SIRCA TRTH database.
Intramonth returns in the months of issuance and maturity are treated as if they refer to the full month.
This ensures comparability to the above calculated realized returns.
9
15 Comparing the alpha estimates of Table III to the equivalent values in Table II,
which are based on investors’ actual portfolio holdings of certificates, two
observations are immediately apparent. The realized alphas of bonus certificates are
much more negative (-0.80% for the full period results for the mid-price returns,
) compared to the alpha of a benchmark portfolio including all available bonus
certificates (-0.39%). This suggests that overpricing explains only part of investors’
underperformance in bonus certificates. Realized alphas of discount certificate
portfolios, however, are less negative (-0.17%) than benchmark portfolio alphas of all
discount certificates (-0.22%), i.e., the investor partially compensate losses from
overpricing by their trading behavior/decisions.
Overall, the results of this section show that investors’ risk adjusted performance
is negative for certificates and stocks, both before and after transaction costs. Further,
while the overpricing of certificates can explain some of this underperformance, other
factors are clearly at play. One factor we can rule out is the influence of investors’
abilities to time the market.10 As we only consider the average realized returns of the
investors’ actual monthly portfolio positions, and we do not take their overall
portfolios (including their cash holdings) into account, the effects of unrealized
returns from before the purchase or after the sale date are neglected.
Hence, the differences between investors’ realized alphas and the benchmark
portfolio alphas may rather be explained by their ability to choose certificates from a
large range of (overpriced) products. Therefore we analyze individual investors’
selection abilities concerning various certificate characteristics in the following
section. The above results indicate that, while investors’ overall bonus certificate
selection skills are poor, their discount certificate selection abilities are good.
10
However, as our data is monthly, we cannot rule out intra-month timing as a factor.
16 5. Certificate Selection
5.1 Methodology
The literature suggests that individual investors (see inter alia Barber and Odean
(2011)), and even institutions (see inter alia Malkiel (1995) and Gruber (1996)), have
poor stock selection abilities. Certificate selection, however, is far more complex than
simple stock selection as investors are exposed to a large variety of payoff profiles
from which they have to choose the most appropriate certificate type for their
investment strategy. Further, they have the choice between various maturity dates,
numerous underlying assets and several issuers.
Dorn (2012) addresses the issue of derivative selection complexity by analyzing
how well individual investors choose warrants among similar alternatives. He finds
that warrant traders fail to identify preferable options and lose 1.2% per one-week
roundtrip trade compared to a benchmark portfolio of ex ante superior available
warrants. He also finds that traders would have been better off by an average of 0.4%
per one-week roundtrip trade if they had chosen warrants randomly. Nicolaus (2010)
analyses a data set consisting of daily quotes and trading data from Euwax to
investigate whether investors choose well in discount, bonus, capped bonus
certificates and warrants on the DAX and the EuroStoxx50 index compared to similar
available products. His results are mixed however, as investors were found to choose
poorly for some assets (bonus certificates on the DAX, capped bonus certificates and
warrants), while for others, they chose well (discount and bonus certificates on the
EuroStoxx50).
To analyze individual investors’ certificate selection abilities, we obtain detailed
information on the characteristics of all discount and bonus certificates on DAX
stocks which were tradable at Euwax during our sample period. This detailed
information allows us to identify certificate selection abilities with regard to issuer,
moneyness (discount certificates) and distance to barrier/bonus level (bonus
certificates), respectively. Moreover, since the certificates used in our study have
stocks as the underlying asset, rather than an index, we are also able to examine
investors’ selection abilities with regard to the underlying asset.
17 To assess investors’ certificate selection ability, we use the Return Difference
(RD) between investors’ realized returns and benchmark sub-portfolio returns, i.e.:
,
where
,
,
∑
∈
,
,
is the roundtrip return of certificate purchased on trading day
sold/redeemed on trading day
and
(8)
and
is the number of certificates in the benchmark
sub-portfolio.
A roundtrip trade is considered complete if a previously established position is
entirely closed out – either through selling or through redemption at maturity.
Moreover, the certificate’s underlying has to be included in the DAX at the purchase
and sale/redemption date and the position has to be closed by December 31, 2008 at
the latest. Returns are calculated under the assumption that certificates are purchased
at the Euwax closing ask price of the purchase day and sold at the closing bid price on
the sale/redemption day. As such, the analysis does not account for intraday return
effects. We also calculate
,
for incomplete roundtrips assuming that all open
positions at the end of the sample period are sold at the Euwax closing bid on
December 31, 2008.
For each roundtrip trade, RD is calculated relative to one of four different subportfolios. Sub-portfolio one (SP1) reflects a very broad benchmark containing all
certificates with similar remaining time to maturity (±5 trading days) as the purchased
certificate which could have been purchased at the Euwax on that day. Sub-portfolio
two (SP2) is a restricted version of SP1, in which only those certificates with the same
underlying as the purchased certificate are included. Sub-portfolio three (SP3) has a
further restriction that only certificates with a similar level of moneyness (±5%) for
discount certificates, or a similar distance to barrier and distance to bonus level (±5%)
for bonus certificates, compared to the purchased certificate are included.11 Finally,
sub-portfolio four (SP4) excludes certificates from SP3 that are not issued by the
11
Moneyness is calculated as the ratio of the underlying’s closing price at the purchase date to the
certificate’s cap level. Distance to barrier is the ratio of the underlying’s closing price at the purchase
date to the certificate’s barrier. Distance to bonus level is the ratio of the certificate’s bonus level to the
underlying’s closing price at the purchase date.
18 same financial institution as the purchased certificate. Thus, SP1 to SP4 are
benchmark portfolios consisting of certificates that are matched by increasing strict
criteria – the number of certificates included in the sub-portfolios therefore reduces
from SP1 until SP4. RDs are only calculated if the particular benchmark sub-portfolio
consists of at least three certificates.
This process results in a maximum of four RDs for each roundtrip trade. Since
SP1, SP2 and SP3 contain every benchmark certificate, which is also included in the
SP of the next lower similarity level, the comparison of RDs between the SPs
indicates, how good investors are at selecting underlyings, cap levels, barrier/bonus
levels and issuers when they buy certificates.
5.2 Do Investors Choose the Wrong Certificates?
Each RD is calculated for the actual holding period of the purchased certificate
and summarized by averaging these estimates across the whole sample. One possible
concern is that this process involves averaging RDs measured across (possibly very)
different roundtrip lengths. To address this issue, we also estimate summary statistics
for the average RD distinguishing between roundtrip lengths of less than 100 days
(not annualized) and roundtrip lengths of at least 100 days (annualized and not
annualized).
The estimation results are presented in Table IV, distinguishing between the
different sub-portfolios (SP1 to SP4), discount and bonus certificates and across
different time periods. We begin our analysis by considering the set of results
benchmarked against the most restrictive portfolio for the whole sample period and
the results reveal that the RDs of SP4 are on average close to zero for discount
certificates. This means that investors do not appear to make significant mistakes
when selecting a certificate from among a group of certificates with a similar time to
maturity, similar moneyness, the same underlying and the same issuer. We do note
however, that compared to the other SPs, the number of observations in SP4 is
relatively low.
[Insert Table IV about here.]
19 The next set of results we consider is for investors in discount certificates when
faced with the choice between certificates with a similar time to maturity, the same
underlying and similar moneyness, but from different issuers, i.e., the benchmark
portfolio SP3. The RDs of SP3 are higher than the previously discussed RDs of SP4
which suggests that individual investors are able to choose favorable issuers (i.e.,
those with a relatively low level of overpricing) from among those who offer discount
certificates with similar characteristics.
In contrast to SP3, SP2 contains discount certificates with different levels of
moneyness. Return differences between these portfolios indicate gains or losses
caused by selecting discount certificates with beneficial or detrimental caps. The
results presented in panels A to E show that the RDs of SP2 are significantly positive
and much larger than the RDs of SP3. Hence, investors profit from their ability to
choose discount certificates with superior caps, compared to other discount
certificates with the same underlying and similar time to maturity.
The final comparison for discount certificates is with respect to the RDs of SP1
relative to SP2. Across all roundtrips, the results show a slight increase in the RD
(0.62% vs. 0.60% previously), indicating a slightly positive underlying selection. This
observation, however, appears to be driven by short term and incompleted roundtrips,
as can be seen by comparing panels B and E of Table IV (SP1’s RDs of 0.68% and
4.12%12 versus SP2’s RDs of 0.40% and 2.40%). For roundtrips of longer durations,
the outcomes are reversed (SP1’s RD of 0.35% vs. SP2’s RD of 0.98% in annualized
terms). Hence, investors’ ability to choose appropriate underlyings for their discount
certificates seems to be fairly well for shorter and incompleted roundtrips, but very
poor for long term roundtrips. Taken together, the results for SP1 across panels A to E
of Table IV suggest that discount certificates chosen by investors do significantly
outperform those discount certificates of similar time to maturity which were also
available at the purchase date.
To test the veracity of these results for the full sample period, Table IV also
presents the equivalent set of results across the two subperiods. The results for SP4
12
Large RD numbers for incompleted roundtrips might result from market distortions during the
financial crisis by end of 2008.
20 and SP3 in both subperiods serve to confirm our findings regarding the investors’
ability to find preferable issuers for their demanded certificate characteristics for both
subperiods. The selection of certificates by moneyness is positive for all roundtrips of
the second subperiod and for short roundtrips of the first subperiod. The individual
investors’ ability to select favorable discount certificates with respect to their
underlying can be rated positive for all roundtrips of the first subperiod and for short
term and incompleted roundtrips of the second subperiod. Regarding roundtrips with
longer durations, however, underlying selection has a tremendous negative impact on
RDs in the second subperiod and more than offsets the positive effects of the selection
by the moneyness criteria.
Return differences for bonus certificates are presented in panels F to J of Table
IV. In contrast to discount certificates, RDs of bonus certificates benchmarked against
SP4 are significantly negative at -0.33% across all roundtrips in the full sample period
(although we note the relatively low number of observations). The fact that the
purchased bonus certificate has a similar time to maturity, a similar distance to
barrier/bonus level, the same underlying and the same issuer as those included in SP4,
implies that investors choose the most detrimental maturities and barrier/bonus levels
from a small sample of very similar alternatives. These losses are compensated by
advantageous issuer selection, as can be seen from the estimated SP3 RDs which are
close to zero.
Comparing across SP2 and SP3 in panels F to J of Table IV, it is obvious that
investors are very weak in choosing the appropriate barrier and bonus level when they
purchase a bonus certificate. The poor choices made by investors produces a negative
return impact of -1.28% per roundtrip trade on average. Recall that investors did well
in selecting beneficial cap levels for their discount certificates. By way of contrast, the
evidence for bonus certificates suggests the opposite is true and investors seem to
have great difficulty in selecting from among the various complex payoff structures of
bonus certificates.
The situation gets even worse when we take into account individual investors
poor underlying selection choices as the RD for SP1 is -4.78% which is nearly four
times as large as the average loss of -1.25% benchmarked against SP2. Panels G to J
21 of Table IV show that these losses are associated with longer roundtrips with an
extremely negative RD of -8.04% against SP1 compared to a RD of -2.51% against
SP2, expressed in annualized terms. By way of contrast, we find that the average RDs
improve from SP2 to SP1 for shorter and incomplete roundtrips.
To summarize the results for bonus certificates, we find that investors suffer large
losses of -4.78% per roundtrip trade (with an average duration of 234 calendar days)
compared to all available bonus certificates of similar maturity. Thus, investors would
be better off selecting bonus certificates randomly instead of actively choosing certain
barrier and bonus levels and underlyings. The RDs estimated for the subperiods serve
to reinforce these whole sample period results as can be seen in columns 5 to 12 of
panels F to J of Table IV.
5.3 Certificate Investors and the Disposition Effect
One may be tempted to interpret the results of the previous section as suggesting that
investors choose favorable certificates with respect to the underlying asset when
trading short term, however, they fail to identify promising opportunities for long
term buy and hold strategies. While possible, this interpretation may be misleading
since individual investors often do not determine their investment horizon ex ante.
Instead, they may be prone to the disposition effect, i.e., they tend to sell winning
investments soon and hold losing investments longer. This effect was first
documented by Shefrin and Statman (1985) and later confirmed for warrants by
Schmitz and Weber (2007). If the disposition effect is present in our sample of
investors, better (i.e., more positive or less negative) RDs of SP1 compared to SP2 for
short term roundtrips, could be explained by investors’ selling behavior rather than by
their short term underlying selection ability.
To test for the presence of the disposition effect, we calculate RDs based on the
hypothetical assumption that the purchased certificates are sold either 30, 90, 180, 270
or 360 days after their purchase date. We use the same roundtrip durations for the
certificates in the respective benchmark sub-portfolios. The results are presented in
panels A-E of Table V for discount certificates and panels F-J for bonus certificates.
[Insert Table V about here.]
22 The results reveal that SP1 displays slightly more positive RDs compared to SP2
only in the very short term (30 days) and only for discount certificates. In all other
cases (i.e., across both discount and bonus certificates), the RDs for SP1 are worse
than the RDs for SP2. These results imply that the choice as to the underlying asset
does not lead to superior short term certificate returns compared to a benchmark
including certificates with other underlying assets. Instead, the results suggest that the
superior RDs of SP1 compared to SP2 for short term roundtrips (panels B and G of
Table IV) are in fact the result of the investors’ tendency to sell winner discount and
bonus certificates sooner. Further to this point, the positive short term and negative
long term SP1 RDs of discount certificates for the various hypothetical roundtrip
lengths (see panels A to E in Table V) show that investors’ performance gets worse
(relative to the broad benchmark of available certificates) the longer they hold their
purchased certificates. The same can be observed for bonus certificates, resulting in a
remarkably negative SP1 RD of -8.50% for a hypothetical holding period of one year
(see panels F to J in Table V). This may be taken as evidence of investors holding on
to losing trades longer which is again supportive of the presence of the disposition
effect.
5.4 Poor Underlying Selection – Poor Stock Selection?
The results of the previous sections clearly highlight the problems individual
investors have in choosing the underlying stock for their discount and bonus
certificate investments. This raises the question as to whether they are any better when
choosing actual stocks for their portfolios. The negative alphas estimated in Section 4
for
suggest not, at least compared to the DAX index composition. In this
section, we test how well investors’ actual DAX stock purchases perform compared to
an equally-weighted portfolio of all DAX stocks. We therefore measure the difference
between the return of the purchased DAX stock and the average return of all DAX
stocks (including the purchased stock) for each roundtrip trade during our sample
period (we refer to these stock purchase return differences as RD).
Table VI reports average RDs, divided up into roundtrips completed in less than
100 days, roundtrips completed in at least 100 days (annualized and not annualized),
and incomplete roundtrips which are again assumed to be closed on December 31,
23 2008. We find that the RDs are negative across all observations, as well as for long
term roundtrips and incompleted roundtrips. Returns of roundtrips completed in less
than 100 days, however, beat the benchmark.
[Insert Table VI about here.]
As discussed above, positive short term RDs might result from the disposition
effect. Hence, we calculate RDs for hypothetical roundtrip durations of 30, 90, 180,
270 and 360 days. The results are presented in Table VII and the results provide
evidence of highly significant negative RDs for all roundtrip durations. This result
suggests that investors are very poor in selecting stocks from a rather small
investment universe of only 30 alternatives. Further, it seems that individual investors
tend to sell their winning stocks soon and are therefore prone to the disposition effect.
[Insert Table VII about here.]
6. Robustness Checks
In Section 4, monthly raw returns and monthly alphas were obtained by weighting
every single investor portfolio return equally (see equation (6)). For robustness, we
weight each investor portfolio by its invested capital in the corresponding month t,
. The unreported results (available from the authors upon request) confirm our
findings of individual investors’ underperformance in discount certificate, bonus
certificate, and stock investments.
With regard to the conclusions drawn from Section 5, one may criticise the
manner in which we compare return differences across benchmark sub-portfolios of
different sample sizes, i.e., the number of observations is gradually increasing from
SP4 to SP1. This may bias our results. To address this issue, we modify our method
by equalizing our sample size based on the number of trades in SP3. Hence, SP1 and
SP2 include only those roundtrip trades which are contained in SP3. 13 Return
differences resulting from this adjustment are presented in Table VIII. The results
reveal that, compared to results presented in Table IV, while marginal changes in the
13
The sample size of SP4 is too small, especially for bonus certificates.
24 reported statistics for SP1 and SP2 are observed across both discount and bonus
certificates, the basic tenor of our conclusions remains intact.
[Insert Table VIII about here.]
7. Conclusion
While structured financial products have proven to be an increasingly popular
investment tool for retail investors, the academic literature suggests that the
overpricing by the issuing banks, transaction costs and the choices made by investors
often lead to poor investment performance. Our paper is the first to identify the
various potential sources of losses for individual investors and it is the first to quantify
the relative contribution of each of those potential drawbacks to investors’
underperformance. To this end, this paper measures the realized risk-adjusted returns
to investors’ actual discount and bonus certificate portfolios, where each investors’
stock portfolio returns are used as a benchmark. The highly detailed nature of our
unique dataset allows us to investigate individual investors’ certificate selection
ability in a very differentiated and precise manner.
The results of this paper suggest that, in net risk-adjusted terms, individual
investors lose 0.25% in discount certificates and 0.85% in bonus certificates per
month which is almost 3% and 10% per year, respectively. Their equity portfolio net
performance is negative as well with a monthly alpha of -0.31% (-3.66% per year).
Transaction costs are found to contribute to these losses, but only to a small extent.
Rather, it is the overpricing of certificates by issuers and poor certificate selection
skills of investors that are found to be the main drivers of the certificate investments’
underperformance. A more detailed analysis of certificate selection provides evidence
that individual investors suffer from large losses by systematically selecting inferior
underlying assets for their discount and bonus certificates. This observation is
supported by additional evidence of poor selection skills of investors when buying
stocks for their physical equity portfolios.
25 Furthermore, we find that discount and bonus certificate investors as well as
stock investors are prone to the disposition effect, i.e., they sell winner certificates and
stocks soon while they appear to hold on to losing positions for relatively longer.
Finally, we find that investors have great difficulty in selecting appropriate
barrier and bonus levels for their bonus certificates, whereas they are well equipped to
find appropriate cap levels for their discount certificates. This latter result is
particularly interesting and suggests that individual investors struggle to choose bonus
certificates successfully which is not surprising given their complex payoff structures.
In addition, the overpricing of certificates by issuers is found to affect bonus
certificate performance to a larger negative extent compared to discount certificate
investments. These findings give evidence that product complexity is detrimental to
investors’ wealth.
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28 Figure 1: Payoff profiles of discount and bonus certificates
This figure shows payoff profiles of discount and bonus certificates dependent on the price of their
underlying at the maturity date. The value of the certificate is indicated by the solid line, the value of
the underlying is indicated by the dotted line. The dashed line in the right figure indicates the value of
the bonus certificate at maturity if the underlying has touched or fallen below the barrier level during
its lifetime.
29 Table I. Summary statistics
This table reports descriptive statistics for a sample of 133,353 retail investors and their portfolios of
discount and bonus certificates with DAX stocks as underlyings and of DAX stocks from a large
German direct bank. The sample period is from February 2004 to December 2008. We include investors
who made at least one transaction in at least one of the three security classes. No. investors stands for
the number of investors making at least one transaction in the particular security class. No. trades is the
average number of transactions per investor during our sample period. Avg. trade size is the mean value
per trade. No. securities is the number of different securities traded in our sample. No. trades is the total
number of purchase and sale transactions and maturity repayments. Avg. commission denotes the
average commission paid for each trade in relation to the trade value. Avg. spread is the average bid/ask
spread per roundtrip trade, estimated by
, where
. and
are closing bid and
closing ask prices of security on trading day , respectively. Avg. roundtrip costs stands for the
average loss per roundtrip trade, caused by commissions and spreads, in relation to the purchase value.
Certificates
Stocks
Discount
Bonus
No. investors (#)
3,895
8,165
132,515
No. trades (#)
8.06
4.32
27.79
Avg. trade size (EUR)
5,947
4,865
3,803
No. securities (#)
8,918
3,306
35
No. trades (#)
31,391
35,258
3,682,606
Avg. commission (%)
0.15%
0.16%
0.22%
Avg. spread (%)
0.38%
0.77%
0.23%
Avg. roundtrip costs (%)
0.68%
1.09%
0.67%
30 Table II. Performance of individual investors‘ certificate and stock portfolios
This table reports average raw returns and three-factor alphas of discount, bonus and equity portfolios in
,
and
terms. Panel A presents the performance for the
full sample period, February 2004 to December 2008, Panel B for the first subperiod from February 2004 to July 2006, and Panel C for the second subperiod from August
excess
2006 to December 2008. Panel D presents estimated coefficients for the full period and the two subperiods and for all three security group sub-portfolios, using
returns as dependent variables. p-values based on Newey-West heteroskedasticity and autocorrelation robust standard errors are in parenthesis. ***, ** and * denote
significance at the 1, 5, and 10 percent levels, respectively.
Discount
Bonus
Panel A: Performance full period: 2004/02-2008/12
Raw return
-0.07%
-0.23%
Alpha
-0.25%
-0.85%**
(0.277)
(0.039)
Panel B: Performance subperiod 1: 2004/02-2006/07
Raw return
0.50%
0.11%
Alpha
-0.27%
-1.09%
(0.263)
(0.102)
Panel C: Performance subperiod 2: 2006/08-2008/12
Raw return
-0.65%
-0.59%
Alpha
-0.22%
-0.55%
(0.515)
(0.356)
Stocks
Discount
Bonus
Stocks
Discount
Bonus
Stocks
0.03%
-0.31%**
(0.011)
-0.01%
-0.20%
(0.391)
-0.21%
-0.83%**
(0.046)
0.07%
-0.28%**
(0.024)
0.01%
-0.17%
(0.450)
-0.18%
-0.80%*
(0.053)
0.08%
-0.27%**
(0.027)
0.62%
-0.56%***
(0.001)
0.56%
-0.21%
(0.377)
0.14%
-1.06%
(0.114)
0.66%
-0.52%***
(0.002)
0.58%
-0.19%
(0.423)
0.19%
-1.00%
(0.114)
0.66%
-0.52%***
(0.002)
-0.58%
-0.11%
(0.515)
-0.61%
-0.18%
(0.601)
-0.58%
-0.53%
(0.372)
-0.54%
-0.06%
(0.693)
-0.58%
-0.15%
(0.654)
-0.56%
-0.51%
(0.372)
-0.53%
-0.06%
(0.693)
Full Period: 2004/02-2008/12
Subperiod 1: 2004/02-2006/07
Subperiod 2: 2006/08-2008/12
Discount
Bonus
Stocks
Discount
Bonus
Stocks
Discount
Bonus
Stocks
0.6653***
(0.000)
-0.0260***
(0.000)
0.0116*
(0.099)
78.43
0.9765***
(0.000)
0.0217**
(0.043)
-0.0149
(0.163)
65.27
0.9882***
(0.000)
-0.0021
(0.536)
0.0037
(0.329)
94.19
0.6123***
(0.000)
-0.0130**
(0.040)
0.0041
(0.550)
80.62
1.2448***
(0.001)
-0.0163
(0.680)
0.0179
(0.593)
61.70
0.9756***
(0.000)
0.0035
(0.485)
-0.0021
(0.676)
92.39
0.6009***
(0.000)
-0.0389***
(0.000)
0.0137
(0.128)
77.70
1.0624***
(0.000)
0.0399**
(0.019)
-0.0197**
(0.017)
67.49
0.9738***
(0.000)
-0.0070
(0.209)
0.0048
(0.259)
94.61
Panel D: Factor loadings ATMC
ATMP
Adj. R² (%)
31 Table III. Performance of certificate benchmark portfolios
This table reports monthly average raw returns and three-factor alphas of portfolios consisting of all discount
and bonus certificates on DAX stocks which were tradable in the corresponding months. For each certificate,
monthly buy-and-hold returns from issuance to maturity are calculated on the basis of mid prices. Intramonth
returns in the months of issuance and maturity are treated as if they refer to the full month. These results can
terms. Monthly returns are aggregated in two ways: (i) equally-weighted
therefore be compared to realized
across all certificates and (ii) equally-weighted across all certificates of the same underlying and then across all
underlyings. Panel A presents the performance for the full sample period, February 2004 to December 2008,
Panel B for the first subperiod from February 2004 to July 2006, and Panel C for the second subperiod from
August 2006 to December 2008. Panel D presents estimated coefficients for the full period. p-values based on
Newey-West heteroskedasticity and autocorrelation robust standard errors are in parenthesis. ***, ** and *
denote significance at the 1, 5, and 10 percent levels, respectively. Equally-weighted at
the certificate level
Discount
Bonus
Panel A: Performance full period: 2004/02-2008/12
Raw return
0.00%
0.14%
Alpha
-0.22%
-0.39%*
(0.275)
(0.072)
Panel B: Performance subperiod 1: 2004/02-2006/07
Raw return
0.71%
1.07%
Alpha
-0.31%
-0.70%***
(0.182)
(0.004)
Panel C: Performance subperiod 2: 2006/08-2008/12
Raw return
-0.68%
-0.74%
Alpha
-0.19%
-0.17%
(0.501)
(0.499)
Equally-weighted at
the certificate level
Discount
Panel D: Factor loadings (full period)
0.7017***
(0.000)
ATMC
-0.0270***
(0.001)
ATMP
0.0129*
(0.075)
Adj. R² (%)
80.16
Discount
Bonus
0.01%
-0.22%
(0.280)
0.06%
-0.44%*
(0.071)
0.76%
-0.21%
(0.314)
1.10%
-0.68%***
(0.006)
-0.71%
-0.93%
-0.25%
-0.36%
(0.350)
(0.199)
Equally-weighted at
the underlying level
Bonus
Discount
Bonus
1.1192***
(0.000)
-0.0079
(0.292)
-0.0011
(0.873)
88.94
0.6769***
(0.000)
-0.0261***
(0.000)
0.0118*
(0.090)
81.11
1.0832***
(0.000)
-0.0102*
(0.072)
0.0007
(0.923)
89.43
32 Equally-weighted at
the underlying level
Table IV. Return differences of certificate roundtrips
This table reports average roundtrip return differences (RD) between purchased certificates and four benchmark portfolios including available certificates of a certain grade of similarity compared to the actually
purchased certificate (including the actually purchased certificate). SP1 includes all available certificates with similar time to maturity (±5 trading days) as the purchased certificate. SP2 includes all certificates of SP1
with the same underlying as the purchased certificate, respectively. SP3 contains all certificates of SP2 with similar moneyness (±5%) or similar distance to barrier and bonus level (±5%), SP4 includes all certificates
of SP3 issued by the same financial institution as the purchased certificate. Panels A-E report results for discount certificates, panels F-J for bonus certificates. Panels A and F summarize return differences across all
observations, panels B and G for roundtrips completed in less than 100 days, panels C and H for roundtrips completed in at least 100 days (not annualized), panels D and I for roundtrips completed in at least 100 days
(annualized). Panels E and J report return differences for incompleted roundtrips (not annualized), assuming that they are closed on December 31, 2008. ***, ** and * denote that the return difference is significantly
different from zero at the 1, 5, and 10 percent levels, respectively, under the assumption that observations are independent. All results have been winsorized at the 1 percent level.
Subset filters (Benchmark certificates must
have matched criteria to the purchased
certificate.)
Time to maturity (±5 trading days)
Underlying
Moneyness (±5%)
Issuer
SP1
SP2
SP3
SP4
SP1
SP2
SP3
SP4
SP1
SP2
SP3
SP4
Yes
No
No
No
Yes
Yes
No
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
No
No
No
Yes
Yes
No
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
No
No
No
Yes
Yes
No
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Full Period: 2004/02-2008/12
Panel A: Discount certificates – all roundtrips (not annualized)
Mean difference
0.62%*** 0.60%*** 0.16%***
0.02%**
p-value
(0.000)
(0.000)
(0.000)
(0.032)
Std. dev. of difference
10.14%
5.78%
0.86%
0.25%
# of observations
14,256
14,318
9,778
1,194
Panel B: Discount certificates – roundtrips completed in < 100 days (not annualized)
Mean difference
0.68%*** 0.40%*** 0.11%***
0.01%
p-value
(0.000)
(0.000)
(0.000)
(0.338)
Std. dev. of difference
4.88%
3.25%
0.66%
0.19%
# of observations
4,542
4,606
3,165
419
Panel C: Discount certificates – roundtrips completed in ≥ 100 days (not annualized)
Mean difference
0.00% 0.41%*** 0.16%***
0.01%
p-value
(0.977)
(0.000)
(0.000)
(0.430)
Std. dev. of difference
10.83%
6.22%
0.96%
0.34%
# of observations
8,361
8,370
5,728
586
Panel D: Discount certificates – roundtrips completed in ≥ 100 days (annualized)
Mean difference
0.35%** 0.98%*** 0.21%***
0.00%
p-value
(0.016)
(0.000)
(0.000)
(0.817)
Std. dev. of difference
13.19%
7.57%
1.15%
0.46%
# of observations
8,361
8,370
5,728
586
Panel E: Discount certificates – incompleted roundtrips (not annualized)
Mean difference
4.12%*** 2.40%*** 0.25%***
0.05%**
p-value
(0.000)
(0.000)
(0.000)
(0.010)
Std. dev. of difference
16.46%
8.75%
0.90%
0.25%
# of observations
1,353
1,342
885
189
Subperiod 1: 2004/02-2006/07
0.65%***
(0.000)
6.19%
6,526
0.00%
(0.946)
4.77%
6,456
0.20%***
(0.000)
0.56%
4,208
0.01%
(0.388)
0.22%
238
0.51%***
(0.000)
12.78%
7,730
1.09%***
(0.000)
6.52%
7,862
0.12%***
(0.000)
1.09%
5,570
0.02%**
(0.049)
0.26%
956
0.53%***
(0.000)
3.02%
1,665
0.18%***
(0.000)
1.80%
1,663
0.13%***
(0.000)
0.40%
1,115
0.05%*
(0.055)
0.19%
55
0.76%***
(0.000)
5.88%
2,877
0.53%***
(0.000)
4.02%
2,943
0.10%***
(0.000)
0.80%
2,050
0.00%
(0.683)
0.20%
364
0.65%***
(0.000)
6.99%
4,832
-0.06%
(0.489)
5.51%
4,773
0.23%***
(0.000)
0.61%
3,092
0.00%
(0.986)
0.24%
183
-1.00%***
(0.000)
14.85%
3,529
1.04%***
(0.000)
7.10%
3,597
0.09%***
(0.000)
1.34%
2,636
0.02%
(0.390)
0.39%
403
0.97%***
(0.000)
7.82%
4,832
0.15%*
(0.065)
5.64%
4,773
0.28%***
(0.000)
0.73%
3,092
-0.01%
(0.608)
0.25%
183
-0.43%
(0.188)
19.25%
3,529
2.18%***
(0.000)
9.92%
3,597
0.14%***
(0.000)
1.60%
2,636
0.00%
(0.926)
0.53%
403
8.13%**
(0.013)
16.59%
29
0.84%
(0.194)
2.81%
20
4.03%***
(0.000)
16.45%
1,324
2.42%***
(0.000)
8.81%
1,322
0.25%***
(0.000)
0.90%
884
0.05%**
(0.010)
0.25%
189
33 Subperiod 2: 2006/08-2008/12
Table IV. Continued.
Subset filters (Benchmark certificates must
have matched criteria to the purchased
certificate.)
Time to maturity (±5 trading days)
Underlying
Distance to barrier (±5%) and
bonus level (±5%)
Issuer
SP1
SP2
SP3
SP4
SP1
SP2
SP3
SP4
SP1
SP2
SP3
SP4
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
No
No
Yes
Yes
No
No
Yes
Yes
No
No
Yes
Yes
No
No
Yes
No
No
No
Yes
No
No
No
Yes
No
Full Period: 2004/02-2008/12
Panel F: Bonus certificates – all roundtrips (not annualized)
Mean difference
-4.78%*** -1.25%***
0.03% -0.33%***
p-value
(0.000)
(0.000)
(0.564)
(0.000)
Std. dev. of difference
17.97%
5.64%
2.05%
1.46%
# of observations
10,886
8,069
1,750
326
Panel G: Bonus certificates – roundtrips completed in < 100 days (not annualized)
Mean difference
-0.37%*** -0.48%***
0.04% -0.36%***
p-value
(0.008)
(0.000)
(0.527)
(0.008)
Std. dev. of difference
8.92%
4.03%
1.82%
1.65%
# of observations
4,146
3,244
751
155
Panel H: Bonus certificates – roundtrips completed in ≥ 100 days (not annualized)
Mean difference
-8.10%*** -1.69%***
0.00% -0.33%***
p-value
(0.000)
(0.000)
(0.974)
(0.004)
Std. dev. of difference
21.53%
6.66%
2.33%
1.39%
# of observations
6,135
4,303
839
155
Panel I: Bonus certificates – roundtrips completed in ≥ 100 days (annualized)
Mean difference
-8.04%*** -2.51%***
-0.01%
-0.44%*
p-value
(0.000)
(0.000)
(0.922)
(0.053)
Std. dev. of difference
26.59%
9.03%
3.64%
2.80%
# of observations
6,135
4,303
839
155
Panel J: Bonus certificates – incompleted roundtrips (not annualized)
Mean difference
-1.33% -2.10%***
0.07%
-0.08%
p-value
(0.108)
(0.000)
(0.528)
(0.701)
Std. dev. of difference
20.42%
5.22%
1.49%
0.83%
# of observations
605
522
160
16
Subperiod 1: 2004/02-2006/07
-6.32%***
(0.000)
20.19%
5,279
-0.73%***
(0.000)
4.82%
2,813
0.23%*
(0.063)
1.95%
248
-0.47%**
(0.013)
1.29%
51
-3.30%***
(0.000)
15.81%
5,607
-1.52%***
(0.000)
5.99%
5,256
-0.01%
(0.894)
2.07%
1,502
-0.31%***
(0.001)
1.58%
275
-0.20%
(0.324)
7.96%
1,552
-0.38%***
(0.000)
2.47%
809
0.03%
(0.876)
1.88%
82
-0.84%***
(0.006)
1.41%
26
-0.48%**
(0.010)
9.52%
2,594
-0.53%***
(0.000)
4.47%
2,435
0.04%
(0.537)
1.86%
669
-0.26%*
(0.084)
1.69%
129
-9.08%***
(0.000)
23.10%
3,665
-0.88%***
(0.000)
5.57%
1,962
0.34%**
(0.040)
2.12%
163
-0.08%
(0.705)
1.05%
25
-6.68%***
(0.000)
19.22%
2,470
-2.38%***
(0.000)
7.41%
2,341
-0.08%
(0.408)
2.43%
676
-0.38%***
(0.003)
1.45%
130
-7.77%***
(0.000)
24.97%
3,665
-1.01%***
(0.000)
5.96%
1,962
0.32%*
(0.070)
2.25%
163
-0.32%
(0.579)
2.86%
25
-8.38%***
(0.000)
29.04%
2,470
-3.77%***
(0.000)
11.09%
2,341
-0.09%
(0.538)
3.98%
676
-0.46%*
(0.063)
2.80%
130
1.44%
(0.664)
25.94%
62
-0.66%
(0.500)
6.30%
42
0.68%
(0.449)
1.26%
3
-1.68%**
(0.047)
19.72%
543
-2.23%***
(0.000)
5.12%
480
0.06%
(0.599)
1.49%
157
-0.08%
(0.701)
0.83%
16
34 Subperiod 2: 2006/08-2008/12
Table V. Return differences of certificate roundtrips for fixed roundtrip lengths
This table reports average return differences (RD) between purchased certificates and four benchmark portfolios
including available certificates of a certain grade of similarity compared to the actually purchased certificate
(including the actually purchased certificate). Roundtrip returns are based on the hypothetical assumption that
the actually purchased certificates are sold either 30, 90, 180, 270 or 360 days after their purchase date. We use
the same roundtrip durations for the certificates in the respective benchmark sub-portfolios. SP1 includes all
available certificates with similar time to maturity (±5 trading days) as the purchased certificate. SP2 includes
all certificates of SP1 with the same underlying as the purchased certificate, respectively. SP3 contains all
certificates of SP2 with similar moneyness (±5%) or similar distance to barrier and bonus level (±5%), SP4
includes all certificates of SP3 issued by the same financial institution as the purchased certificate. Panels A-E
report results for discount certificates, panels F-J for bonus certificates. ***, ** and * denote that the return
difference is significantly different from zero at the 1, 5, and 10 percent levels, respectively, under the
assumption that observations are independent. All results have been winsorized at the 1 percent level. Subset filters (Benchmark certificates must have
matched criteria to the purchased certificate.)
Time to maturity (±5 trading days)
Underlying
Moneyness (±5%)
Issuer
SP1
SP2
SP3
SP4
Yes
No
No
No
Yes
Yes
No
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Full Period: 2004/02-2008/12
Panel A: Discount certificates – roundtrip duration = 30 days
Mean difference
0.24%***
p-value
(0.000)
Std. dev. of difference
3.38%
# of observations
13,317
0.21%***
(0.000)
2.13%
13,151
0.08%***
(0.000)
0.36%
9,237
0.00%
(0.708)
0.14%
997
Panel B: Discount certificates – roundtrip duration = 90 days
Mean difference
0.26%***
p-value
(0.000)
Std. dev. of difference
5.19%
# of observations
12,017
0.30%***
(0.000)
2.90%
11,854
0.12%***
(0.000)
0.40%
8,351
0.01%*
(0.065)
0.21%
865
Panel C: Discount certificates – roundtrip duration = 180 days
Mean difference
0.39%***
p-value
(0.000)
Std. dev. of difference
6.86%
# of observations
10,845
0.50%***
(0.000)
3.96%
10,687
0.15%***
(0.000)
0.45%
7,503
0.02%**
(0.010)
0.21%
734
Panel D: Discount certificates – roundtrip duration = 270 days
Mean difference
-0.25%***
p-value
(0.007)
Std. dev. of difference
9.22%
# of observations
9,891
0.47%***
(0.000)
5.04%
9,748
0.17%***
(0.000)
0.53%
6,774
0.03%**
(0.012)
0.27%
553
Panel E: Discount certificates – roundtrip duration = 360 days
Mean difference
-0.25%**
p-value
(0.021)
Std. dev. of difference
10.20%
# of observations
8,600
0.16%**
(0.011)
5.83%
8,460
0.18%***
(0.000)
0.59%
5,791
0.06%***
(0.004)
0.38%
409
35 Table V. Continued.
Subset filters (Benchmark certificates must have
matched criteria to the purchased certificate.)
Time to maturity (±5 trading days)
Underlying
Distance to barrier (± 5%) and
bonus level (±5%)
Issuer
SP1
SP2
SP3
SP4
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
No
No
Yes
Yes
No
No
Yes
No
Full Period: 2004/02-2008/12
Panel F: Bonus certificates – roundtrip duration = 30 days
Mean difference
-0.46%***
p-value
(0.000)
Std. dev. of difference
6.43%
# of observations
10,840
-0.12%***
(0.000)
2.68%
7,717
0.00%
(0.972)
1.41%
2,797
-0.12%***
(0.006)
1.29%
916
Panel G: Bonus certificates – roundtrip duration = 90 days
Mean difference
-1.70%***
p-value
(0.000)
Std. dev. of difference
10.84%
# of observations
10,281
-0.29%***
(0.000)
3.94%
7,350
-0.14%***
(0.001)
2.23%
2,617
-0.40%***
(0.000)
2.16%
855
Panel H: Bonus certificates – roundtrip duration = 180 days
Mean difference
-3.77%***
p-value
(0.000)
Std. dev. of difference
14.22%
# of observations
9,615
-0.60%***
(0.000)
4.87%
6,830
0.05%
(0.456)
3.23%
2,369
-0.65%***
(0.000)
2.15%
747
Panel I: Bonus certificates – roundtrip duration = 270 days
Mean difference
-6.37%***
p-value
(0.000)
Std. dev. of difference
17.80%
# of observations
8,969
-1.25%***
(0.000)
5.20%
6,326
-0.28%***
(0.000)
2.73%
2,069
-0.60%***
(0.000)
2.07%
613
Panel J: Bonus certificates – roundtrip duration = 360 days
Mean difference
-8.50%***
p-value
(0.000)
Std. dev. of difference
21.15%
# of observations
8,308
-1.27%***
(0.000)
5.63%
5,770
-0.39%***
(0.000)
2.70%
1,742
-0.82%***
(0.000)
2.17%
521
36 Table VI. Return differences of stock roundtrips
This table reports average return differences (RD) between purchased DAX stocks and a benchmark portfolio
containing all DAX stocks (including the purchased stock). Panel A summarizes return differences across all
observations, panel B for roundtrips completed in less than 100 days, panel C for roundtrips completed in at
least 100 days (not annualized), panel D for roundtrips completed in at least 100 days (annualized). Panel E
report return differences for incompleted roundtrips (not annualized), assuming that they are closed on
December 31, 2008. ***, ** and * denote that the return difference is significantly different from zero at the 1,
5, and 10 percent levels, respectively, under the assumption that observations are independent. All results have
been winsorized at the 1 percent level.
Full Period:
2004/02-2008/12
Subperiod 1:
2004/02-2006/07
Subperiod 2:
2006/08-2008/12
Panel A: Stocks – all roundtrips (not annualized)
Mean difference
-0.57%***
p-value
(0.000)
Std. dev. of difference
14.74%
# of observations
284,245
-2.01%***
(0.000)
17.12%
118,649
0.49%***
(0.000)
13.26%
165,596
Panel B: Stocks – roundtrips completed in < 100 days (not annualized)
Mean difference
0.81%***
p-value
(0.000)
Std. dev. of difference
6.96%
# of observations
148,350
0.31%***
(0.000)
4.90%
57,819
1.10%***
(0.000)
8.21%
90,531
Panel C: Stocks – roundtrips completed in ≥ 100 days (not annualized)
Mean difference
-3.05%***
p-value
(0.000)
Std. dev. of difference
21.82%
# of observations
81,486
-4.18%***
(0.000)
23.20%
55,136
-0.78%***
(0.000)
18.67%
26,350
Panel D: Stocks – roundtrips completed in ≥ 100 days (annualized)
Mean difference
-1.82%***
p-value
(0.000)
Std. dev. of difference
25.72%
# of observations
81,486
-3.21%***
(0.000)
22.21%
55,136
1.23%***
(0.000)
32.91%
26,350
Panel E: Stocks – incompleted roundtrips (not annualized)
Mean difference
-0.35%***
p-value
(0.000)
Std. dev. of difference
19.13%
# of observations
54,409
-4.41%***
(0.000)
34.08%
5,694
0.15%*
(0.067)
17.54%
48,715
37 Table VII. Return differences of stock roundtrips for fixed roundtrip lengths
This table reports average return differences (RD) between purchased DAX stocks and a benchmark portfolio
containing all DAX stocks (including the purchased stock). Roundtrip returns are based on the hypothetical
assumption that the actually purchased stocks are sold either 30, 90, 180, 270 or 360 days after their purchase
date. We use the same roundtrip durations for the stocks in the respective benchmark sub-portfolios. ***, ** and
* denote that the return difference is significantly different from zero at the 1, 5, and 10 percent levels,
respectively, under the assumption that observations are independent. All results have been winsorized at the 1
percent level. Full Period: 2004/02-2008/12
Panel A: Stocks – roundtrip duration = 30 days
Mean difference
-0.31%***
p-value
(0.000)
Std. dev. of difference
7.79%
# of observations
135,223
Panel B: Stocks – roundtrip duration = 90 days
Mean difference
-1.13%***
p-value
(0.000)
Std. dev. of difference
9.86%
# of observations
158,163
Panel C: Stocks – roundtrip duration = 180 days
Mean difference
-1.78%***
p-value
(0.000)
Std. dev. of difference
13.70%
# of observations
114,415
Panel D: Stocks – roundtrip duration = 270 days
Mean difference
-2.93%***
p-value
(0.000)
Std. dev. of difference
17.63%
# of observations
114,487
Panel E: Stocks – roundtrip duration = 360 days
Mean difference
-2.95%***
p-value
(0.000)
Std. dev. of difference
21.98%
# of observations
102,746
38 Table VIII. Return differences with equalized samples
This table reports average roundtrip return differences (RD) between purchased certificates and four benchmark
portfolios including available certificates of a certain grade of similarity compared to the actually bought
certificate (including the actually purchased certificate). SP1 includes all available certificates with similar time
to maturity (±5 trading days) as the purchased certificate. SP2 includes all certificates of SP1 with the same
underlying as the purchased certificate, respectively. SP3 contains all certificates of SP2 with similar moneyness
(±5%) or similar distance to barrier and bonus level (±5%), SP4 includes all certificates of SP3 issued by the
same financial institution as the purchased certificate. In this table, the sample size is equalized on the level of
SP3. Hence SP1 and SP2 include only those roundtrip trades which are contained in SP3. Panels A-E report
results for discount certificates, panels F-J for bonus certificates. Panels A and F summarize return differences
across all observations, panels B and G for roundtrips completed in less than 100 days, panels C and H for
roundtrips completed in at least 100 days (not annualized), panels D and I for roundtrips completed in at least
100 days (annualized). Panels E and J report return differences for incompleted roundtrips (not annualized),
assuming that they are closed on December 31, 2008. ***, ** and * denote that the return difference is
significantly different from zero at the 1, 5, and 10 percent levels, respectively, under the assumption that
observations are independent. All results have been winsorized at the 1 percent level.
Subset filters (Benchmark certificates must have
matched criteria to the purchased certificate.)
Time to maturity (±5 trading days)
Underlying
Moneyness (±5%)
Issuer
SP1
SP2
SP3
SP4
Yes
No
No
No
Yes
Yes
No
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Full Period: 2004/02-2008/12
Panel A: Discount certificates – all roundtrips (not annualized)
Mean difference
0.51%***
p-value
(0.000)
Std. dev. of difference
9.66%
# of observations
9,517
0.62%***
(0.000)
5.00%
9,746
0.16%***
(0.000)
0.86%
9,778
0.02%**
(0.023)
0.25%
1,187
Panel B: Discount certificates – roundtrips completed in < 100 days (not annualized)
Mean difference
0.66%***
0.33%***
p-value
(0.000)
(0.000)
Std. dev. of difference
4.66%
2.47%
# of observations
3,066
3,155
0.11%***
(0.000)
0.66%
3,165
0.01%
(0.339)
0.19%
418
Panel C: Discount certificates – roundtrips completed in ≥ 100 days (not annualized)
Mean difference
-0.20%
0.43%***
p-value
(0.154)
(0.000)
Std. dev. of difference
10.38%
5.45%
# of observations
5,566
5,706
0.16%***
(0.000)
0.96%
5,728
0.01%
(0.353)
0.34%
580
Panel D: Discount certificates – roundtrips completed in ≥ 100 days (annualized)
Mean difference
0.10%
0.98%***
p-value
(0.566)
(0.000)
Std. dev. of difference
12.94%
6.97%
# of observations
5,566
5,706
0.21%***
(0.000)
1.15%
5,728
0.00%
(0.886)
0.46%
580
Panel E: Discount certificates – incompleted roundtrips (not annualized)
Mean difference
4.05%***
2.81%***
p-value
(0.000)
(0.000)
Std. dev. of difference
15.97%
7.66%
# of observations
885
885
0.25%***
(0.000)
0.90%
885
0.05%**
(0.010)
0.25%
189
39 Table VIII. Continued.
Subset filters (Benchmark certificates must have
matched criteria to the purchased certificate.)
Time to maturity (±5 trading days)
Underlying
Distance to barrier (±5%) and
bonus level (±5%)
Issuer
SP1
SP2
SP3
SP4
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
No
No
Yes
Yes
No
No
Yes
No
Full Period: 2004/02-2008/12
Panel F: Bonus certificates – all roundtrips (not annualized)
Mean difference
-3.84%***
p-value
(0.000)
Std. dev. of difference
15.70%
# of observations
1,732
-1.42%***
(0.000)
5.69%
1,749
0.03%
(0.564)
2.05%
1,750
-0.33%***
(0.000)
1.46%
326
Panel G: Bonus certificates – roundtrips completed in < 100 days (not annualized)
Mean difference
-1.19%***
-0.58%***
p-value
(0.001)
(0.000)
Std. dev. of difference
9.49%
4.08%
# of observations
739
751
0.04%
(0.527)
1.82%
751
-0.36%***
(0.008)
1.65%
155
Panel H: Bonus certificates – roundtrips completed in ≥ 100 days (not annualized)
Mean difference
-6.64%***
-1.98%***
p-value
(0.000)
(0.000)
Std. dev. of difference
18.63%
7.15%
# of observations
833
838
0.00%
(0.974)
2.33%
839
-0.33%***
(0.004)
1.39%
155
Panel I: Bonus certificates – roundtrips completed in ≥ 100 days (annualized)
Mean difference
-6.93%***
-3.04%***
p-value
(0.000)
(0.000)
Std. dev. of difference
27.83%
9.93%
# of observations
833
838
-0.01%
(0.922)
3.64%
839
-0.44%*
(0.053)
2.80%
155
Panel J: Bonus certificates – incompleted roundtrips (not annualized)
Mean difference
-2.20%
-2.04%***
p-value
(0.178)
(0.000)
Std. dev. of difference
20.60%
3.82%
# of observations
160
160
0.07%
(0.528)
1.49%
160
-0.08%
(0.701)
0.83%
16
40