ISSN (Print) 0473-453X

Discussion Paper No. 1143

ISSN (Online) 2435-0982

RISK MISPERCEPTIONS OFSTRUCTURED FINANCIAL PRODUCTS
WITH WORST-OF PAYOUT
CHARACTERISTICS REVISITED
Nobuyuki Hanaki

Revised November 2021
September 2021

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, JapanRisk misperceptions of structured financial
products with worst-of payout characteristics
revisited*
Nobuyuki Hanaki†
forthcoming in
Journal of Behavioral and Experimental FinanceNovember 5, 2021

Abstract
In this paper, we reexamine a bias revealed by Kunz et al. (2017) regarding
structured financial products known as barrier reverse convertibles (BRCs) withworst-of payout characteristics. Namely, using a nonincentivized survey of investor risk perceptions, Kunz et al. (2017) found that when safe assets are included
with risky assets to provide the underlying assets of a BRC, investors erroneously
perceive a lower risk for the BRC when in fact it becomes higher. We confirm thesame bias among student participants using the results of an incentivized experiment. However, we do not observe any similar bias among finance professionals.

Keywords: Experiment, Barrier Reverse Convertibles
JEL Code: G11, G41, C99* This work was supported by the Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Nos. 18K19954, and 20H05631, and the Joint Usage/Research Center, Institute of Socialand Economic Research, Osaka University. The experiments reported in the paper were approved by theInstitutional Review Board of the Institute of Social and Economic Research, Osaka University. We thank
Claude Messner for sharing the Qualtrics questionnaire used in Kunz et al. (2017), Yuta Shimodaira foran excellent research assistance, and Takeshi Murooka, Claude Messner, Martin Wallmeier, Katsuhiko
Okada, Kentaro Iwatsubo, and anonymous reviewers for comments on earlier draft.
†
Institute of Social and Economic Research, Osaka University. E-mail: nobuyuki.hanaki@iser.osakau.ac.jp1

1

Introduction

Since the introduction in 1990’s, the market of retail structured financial products hasgrown tremendously. According to SRP, there are currently more than 31 million products with total sales of more than 12 trillion USD.1 While European market, which is
the oldest, has been the largest market for a long time, now the Asia-Pacific market has
surpassed European market.2
While being popular, these products are so complex that one, including regulators,
may ask whether investors correctly understand and assess the risk associated with theseproducts (Hunt et al., 2015). In fact, it is possible that complexity of these products
are used to take advantage of behavioral biases of investors such as their focusing onheadline returns. Indeed, based on their analyses of 55,000 products issued in Europe
between 2002 to 2010, Célérier and Vallée (2017) suggests that the more complex andrisker products with higher headline rates appear more profitable to the financial institutions distributing them. Similarly, Vokata (2021) shows that based on the analysesof her sample of more than 28,000 yield enhancement products issued between 2006
to 2015, these products in fact generate negative returns both ex ante and ex post due
to their embedded fees despite of the attractive yields they offer. Henderson and Pearson (2011) who analyze 64 products, and Bernard et al. (2011) who focus on locallycapped investment products, both reach a similar conclusion. Understanding the impact
of various behavioral/psychological bias that influence investors when assessing the risk
associated with these complex financial products is, therefore, important in designing
regulator framework to protect investors from being exploited.
1

https://www.structuredretailproducts.com/data, last accessed on Sep. 27, 2021.
See,“A short history of structured products” by SRP (https://www.
structuredretailproducts.com/srp-academy/structured-products-history,
last accessed on Sep. 27, 2021.)2

2

In this paper, we experimentally reexamine a bias revealed by Kunz et al. (2017) regarding investor risk perceptions regarding a type of structured financial products known
as barrier reverse convertibles (BRCs) with worst-of payout characteristics. Namely,
Kunz et al. (2017) found using an online survey that when relatively safe assets areadded to risky assets that provide the underlying assets of a BRC, investors erroneously
perceive the risk of the BRC as lower when in fact it becomes higher.
BRCs are a popular type of structured financial product (Rieger, 2012; Hens andRieger, 2014; Kunz et al., 2017) that offers a fixed interest payment and some protectionof capital against downside risk in exchange for foregoing any possible capital gain.
Typically, the BRC has a set of underlying assets (such as stocks) and its repaymentof the invested amount at maturity depends on the price movements of these underlying
assets during the contracted period. In a typical example, investors will receive backcash equal to their nominal invested amount if one of the following two conditions are
met: (1) none of the prices of the underlying assets have fallen below their respective
preset barrier prices during the contracted period, and (2) the prices of all the underlying
assets are above their respective initial prices at maturity. Note that barrier prices are
set well below their initial prices to offer some capital protection against potential pricefalls. However, if neither of these two conditions is satisfied, investors will receive only
the fixed number of shares of the worst performing asset (i.e., the asset with the lowest
price relative to its initial price) from among the underlying assets. The number ofshares that investors receive is then equal to their nominal invested amount divided by
the asset’s initial price.
From this description, investors then forego any capital gain (from any price increasein the underlying assets) by investing in a BRC. For this reason, Hens and Rieger (2014)
argues that after taking fees into account, investment in BRCs cannot be explained by3

standard expected utility maximizing models, rather only behavioral models such asprospect theory (Kahneman and Tversky, 1979) can.3
Note, however, that repaying investors with the worst performing asset implies thathaving more underlying assets only increases the downside risk they must bear. Thus, it
is puzzling why such products are popular among investors even from the point of viewof prospect theory. To account for this apparent anomaly, Rieger (2012) argues that investors’ behavioral biases, such as their use of availability heuristics (e.g., assessing risk
based on their familiarity with the underlying asset), increases the perceived attractiveness of these products. Elsewhere, Kunz et al. (2017) offers an interesting explanation
by referring to a misconception known as “dieter’s paradox” (Chernev, 2011) “whereby
people erroneously believe that eating healthy foods in addition of unhealthy ones candecrease a meal’s calorie count” (Chernev, 2011, p.178), Kunz et al. (2017) hypothesizethat when relatively safe assets are added to risky assets to serve as the underlying assets
of a BRC, investors erroneously perceive the risk of the BRC becomes lower when it is,
in fact, higher.
Kunz et al. (2017) confirm this hypothesis using an online survey of active capital
market investors, revealing that investors consider the likelihood of receiving their invested cash back at maturity being significantly higher with a BRC comprising two safeand one unsafe stocks4 than with a BRC covering just one unsafe stock. On average, thedifferences in the average estimated probability of repayment are 6.12% and 13.64%(both significant at the 1% level) for investors with and without experience of investing3

Indeed, investors focusing on likelihood of making / avoiding loss seems to be a natural way forhumans to perceive risks. Holzmeister et al. (2020) conducted a large-scale survey experiment on riskperception in nine countries (Brazil, China, Germany, India, Japan, Russia, UK, USA, and South Africa)
with more than 2000 financial professionals and 4500 lay people. They find that the skewness of the return
distribution, not the variance, is the only moment that systematically affects respondents perceptions offinancial risk, although the latter is the main measure of the financial risk used in analyses.
4
Where safe and unsafe stocks refer to stocks with low and high price volatility, respectively.

4

in BRCs within 5 years of the survey, respectively (Kunz et al., 2017, p.72, Table 4).
This dieter’s paradox is thought to arise because of the tendency of people to categorize food items into opposing categories (good vs bad), and to evaluate the total impactof the combination of these items by averaging rather than adding their individual impacts (Chernev and Gal, 2010). Consistent with this view, Kunz et al. (2017, p.72, Table4) finds that this misperception is not simply because the number of underlying assets
is larger. The average estimated probability of a cash repayment for a BRC with threesafe underlying asset is 2.76% lower than that of one safe underlying asset (significant
at the 1% level), while that of BRCs with three unsafe underlying assets is 6.48% lower
than that of one unsafe underlying asset (again significant at the 1% level).
In this paper, we reexamine the finding in Kunz et al. (2017) by employing an incentivized experiment. Because the survey participants used by Kunz et al. (2017) did
not face any monetary consequences concerning the accuracy of their stated estimates,
we consider the results there may suffer from hypothetical bias.5 Further, we are not
only interested in participant risk misperceptions, but also whether such misperceptions
impact upon investment behavior. Thus, in our experiments, participants are repeatedly
asked to decide how much of their endowment to invest across various BRCs. These
participants, if chosen for performance-based payment, are then paid according to theoutcomes of their investment decisions.
Moreover, because BRCs are complex financial products, even in the highly simplified version we constructed for our experiment, by conducting an experiment using
university students without much experience in investing, even those from a highly selective university, may not provide us with useful insights about the behaviors of active
5

Döbeli and Vanini (2010) conclude that a large gap exists between the stated willingness to purchase astructured financial product in a hypothetical survey and the revealed purchase decision using investment
data.

5

investors. Therefore, we repeat the same experiment using a sample of certified financial
analysts (CFAs).
We obtain support for the findings in Kunz et al. (2017) only among student participants. For these participants, the average amount invested in BRCs with three underlying assets, comprising one asset with low price volatility and two assets with high pricevolatility, is significantly higher than the minimum amount invested among three BRCs
where only one constitutes three underlying assets. For the CFAs, however, the averageamount invested in the former is not significantly different from the latter. This suggeststhat the effect of probability misperception a la the “dieter’s paradox” is significant only
among naive investors, not more sophisticated investors.
The rest of the paper is organized as follows. Section 2 describes the experiment,
followed by the results in Section 3. Section 5 concludes.

2

Experiment

In our experiment, participants repeatedly make an investment decision. There are 14 investment tasks in total. In each task (t), each participant (i) is given 1,000 experimental
currency units (ECUs) from which they choose to invest Invti ∈ {0, 100, · · · , 900, 1000}
ECUs in the financial product described in the task. The amount not invested will be
kept as cash and will be included in the final payment (but cannot be used to invest
in financial products presented in other investment tasks). The invested amount will
generate a return according to the description of the financial product.6
These financial products are either investment in the stock of one of four hypothetical companies whose daily prices for 250 business days prior to the investment day (day6

An English translation of our experiment can be found at https://bgt.au1.qualtrics.
com/jfe/form/SV_2n8rx9QEDzRJ1Ai.

6

Figure 1: Four hypothetical stocks
Stocks with low price volatility
Stock 1

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Note: The initial price (100) as well as a barrier price (70) are shown in addition to the stock
price.

0) are shown in Figure 1, or a BRC based on either one or three of these four hypothetical companies. These products are all hypothetical in that the four stock prices are
generated by simulating a model, and all the stock prices are normalized so that theirinitial prices (i.e., the prices at the investment day (day 0) are all equal to 100. The
investment horizon is 1 year (250 business days) for all 14 financial products.
As shown in Figure 1, two of these four companies are characterized by high stock
price volatilities (Stocks 3 and 4), and the remaining two are characterized by low stock
price volatilities (Stocks 1 and 2).77

In the model, the price dynamics follow√ a geometric Brownian motion with an expected daily returnof 0% and a standard deviation of (sd/ 250)% where sd = 10 and sd = 30 for low and high volatility
stocks, respectively. Participants are informed that the stocks and their prices (and hence returns) are

7

Four of the 14 financial products are simply the stock of one of these four companies.
Each unit of stock can be bought at 100 ECUs on the investment day and generates adividend income of 5 ECUs. The payoff for participants investing Invti ECUs in thestock is simply
1000 − Invti + 5 ×

Invti
Invti
+ Ps
.
100
100

where Ps is the realized price of the stock s at maturity, i.e., after 250 simulated business
days.
The remaining ten financial products are BRCs. Six of these have a single stock as
their underlying asset and four have three stocks (one low price volatility stock and twohigh price volatility stocks) as their underlying assets.
All these BRCs have the following features:• 5% interest on the invested amount (Inv) is paid in cash at maturity.
• If the price(s) of the underlying stock(s) always stay(s) above the barrier price(either 70 or 50) until maturity, the invested amount is returned in cash at maturity(case 1).
• Alternatively, if the price (of at least one of the underlying stocks) falls below
the barrier before maturity at least once, then what investors receive at maturity
depends on the (lowest) price of the underlying stock(s) at the maturity. If the(lowest) price of the underlying stock(s) is– greater or equal to 100 (i.e., the initial price), the invested amount is returnedin cash (case 2).
hypothetical, but are not informed how the prices are generated.

8

– less than 100, then Inv/100 units of the stock (with the lowest price at thematurity) is returned to the investors (Case 3).
The BRCs using three stocks as their underlying asset have “worst-of” payout characteristics because their payout then depends on the worst-performing stock.
In our experiment, when Case 3 arises, the payoff of participants for this investment
task is computed based on the realized price of the received stock at maturity. Thus, thepayoff for participants from investing Invti ECUs in the BRC is:5
× Invti
100
5Invti
1000 − Invti +× Invti + Ps
100
100

1000 +

in case 1 or 2
in case 3

where Ps is the realized (lowest) price of the underlying stock(s) at the maturity date.
Table 1 summarizes the features of the 14 financial products considered in our experiment.
To isolate the effects of the protection offered by BRCs and the associated costs forforegoing the possibility of capital gain on investment decisions, we intentionally set theremaining aspects, that is, the rate of interest/dividend earning as well as (the absenceof) the possibility of liquidation before maturity, the same for the investment in stocks
and the BRCs.
Each participant receives a participation fee of either 500 JPY (for students) or 1,000
JPY (for CFAs). In addition, participants completing the experiment have a 10% chanceof being selected for an additional financial reward. If a participant is selected for the
additional reward at the end of the experiment, one of the 14 investment tasks is chosenrandomly, and the participant paid according to the ECUs earned in the selected task

9

Table 1: Fourteen financial products
Product
StockLV 1
StockLV 2
StockHV 1
StockHV 2
BRCLV,70−1
BRCLV,70−2
BRCHV,70−1
BRCHV,70−2
BRCHV,50−1
BRCHV,50−2
W-BRC70−1
W-BRC70−2
W-BRC50−1
W-BRC50−2

Underlying stock Interest / dividend
Stock 1Dividend 5 ECUs / unit
Stock 2
Dividend 5 ECUs / unit
Stock 3
Dividend 5 ECUs / unit
Stock 4
Dividend 5 ECUs / unit
Stock 1
5% interest on invested amount
Stock 2
5% interest on invested amount
Stock 3
5% interest on invested amount
Stock 45% interest on invested amount
Stock 3
5% interest on invested amount
Stock 45% interest on invested amount
Stocks 1, 3, and 4 5% interest on invested amount
Stocks 2, 3, and 4 5% interest on invested amount
Stocks 1, 3, and 4 5% interest on invested amount
Stocks 2, 3, and 4 5% interest on invested amount

Barrier price
n.a.
n.a.
n.a.
n.a.
70
70
70
70
50
50
70
70
50
50

Note: For all the products, the unit price at the date of investment is 100.

with an exchange rate of 1 ECU equals either 5 JPY (for students) or 10 JPY (for theCFAs). Participants are paid using an Amazon gift card (e-mail version).
In addition to these investment tasks, the participants are asked to estimate the frequency (out of 1,000) in which a BRC does not return the principal in cash, but in unitsof the underlying stock instead, under three barrier prices (70, 60, and 50). For this task,
participants are informed that the underlying stock prices are generated by simulating amodel that is well known to capture real stock price movements and are also shown fiverealizations of such simulations (Figure 2).
If a participant is chosen for the additional financial reward, one of the three estimates is chosen randomly for an additional reward. If the chosen estimate falls within
10% of the realized frequency, the participant is given 100 ECUs in addition to the reward earned in the randomly selected investment task. Participants are not informed

10Figure 2: Graph shown for the estimation task
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Note: initial price (100) as well as two barrier prices (70 and 50) are also
shown.

about this task until they complete all 14 investment tasks.
The results of the selected investment and estimation tasks were shown to those participants selected to receive these additional rewards at the very end of the experiment(after the postexperiment questionnaire). After the estimation task, a questionnaire including questions on demographics and the participant’s knowledge and experience ininvesting in a structured financial product is administered. For students, we also implemented a financial literacy quiz taken from Fernandes et al. (2014). See Appendix C for
the questionnaire.

3

Results

The online experiment was conducted in August to September 2021.8 An invitation email was sent on Monday, August 30, 2021, to 195 students at Osaka University and 110
CFAs that had previously participated in an earlier finance-related online experiment
8

The experiment was implemented using the Qualtrics survey platform (www.qualtrics.com).

11

and who had agreed to participate in a future experiment. The deadline to participate andcomplete the experiment was set at 23:59 on September 3, 2021.9 Among those invited,
87 students and 84 CFAs completed the experiment. On average, the participants took
1,500 seconds to complete the experiment. The average score of the financial literacy
quiz of these 87 students is 8.5 (with the standard deviation of 2.19, and the minimum
and the maximum scores are 2 and 12, respectively.)
Of the 87 students and 84 CFAs, 3 students and 38 CFAs declared that they hadsome knowledge of BRCs. Most of the participants, comprising 87 students and 81
CFAs, reported that they had not purchased any BRCs in the past 5 years.10
To obtain reliable results, we report here the results of the analyses based on thesample excluding those participants that had spent an extremely short time (shortest
10%, less than 586 seconds) or an extremely long time (longest 10%, more than 6,527
seconds) to complete the experiment. We also excluded from the analyses those participants whose submitted estimates in the estimation task were not monotonically decreasing as the barrier price became lower.11 Thus, we have 63 students and 64 CFAs in ourdata used in the results presented below. We report the results without excluding theseparticipants from the analyses in Appendix A. The results based on the full sample arelike those we report in the main text.
9

Participants were asked to complete the experiment without taking a long break in the middle; however, the software was configured so that participants could return to the experiment anytime within 24
hours from the start of the experiment. The participants were also asked to participate in the experiment
only once and the software was configured so that each participant could access the experiment only oncefrom the same browser. If they wished, however, the participants could access the experiment multiple
times by using different browsers or different devices. To check where participants responded on multiple
occasions, we kept a record of participant IDs and dropped one participant who completed the experiment
twice from the sample.
10
Two CFAs declared having bought structured financial product, not necessary BRCs, once and 1 CFA
declared having bought more than eight times in the past 5 years.
11
Recall that participants submit their estimates of the probability of receiving stocks instead of cash
at the maturity. We allow for the estimated probabilities to remain constant.

12

Figure 3: Amount invested in stocks vs BRCs with a single underlying asset.
Low volatility
n.s.

n.s.

1000
800
600
400
200
0

Stock

BRC70

Stock

Students

BRC70

CFAs

High volatility
**
*

***
n.s

***

***

1000
800
600
400
200
0

Stock

BRC70 BRC50

Stock

Students

BRC70 BRC50
CFAs***, **, and * denote statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed Wilcoxon signedrank (WSR) test, respectively.

3.1

Investment in stocks and BRCs with a single underlying asset

We commence our analyses by comparing participant investment in stocks and the
BRCs. Figure 3 depicts, with a box plot, the distribution of investment in stocks and
BRCs with one underlying asset. The top (bottom) panel show those based on stocks
with low (high) price volatility. For both panels, we first take the average investment in
the same category for each participant and use it as an independent observation. For example, for stocks with low price volatility, we take the average investment in StockLV 1

13and StockLV 2 . Similarly, for BRCs based on a low price volatility stock, we take the average investment in BRCLV,70−1 and BRCLV,70−2 . In each panel, the results for students
and the CFAs are shown separately. The box in the middle shows the 25% to 75% range
with the median in the middle line, and the upper and the lower bounds correspond tothe highest and the lowest amounts.12
As expected, the investment in stocks with high price volatility is significantly lower
than the investment in stocks with low price volatility for both students and the CFAs.
The median investment for high and low volatility stocks for students are 450 and 550(p<0.001, two-tailed Wilcoxon signed-rank (WSR) test), respectively, and those for the
CFAs are 200 and 425 (p=0.002, two-tailed WSR). Similarly, students invest significantly more in stocks than the CFAs (p=0.036 for low volatility stocks and p=0.005 forhigh volatility stocks, using a two-tailed Mann–Whitney test (MW)).
The top panel of Figure 3 indicates that there is no statistically significant difference
between the investment for the low-price volatility stocks and the BRCs (with barrier
price 70) created using the same stocks.13 This suggests that the participants, bothstudents and the CFAs, did not consider these BRCs to offer significant benefits or to
introduce significant costs compared to the underlying stocks.
The bottom panel of Figure 3 shows that for stocks with high price volatility, students invest significantly more in the stocks than the BRC70 s (with barrier price 70),and significantly less than the BRC50 s (with the barrier price 50) created using the samehigh price volatility stocks.14 This suggests that students consider that BRC70 s intro12

See Appendix B.1 for the results for each product.
The median investments in BRC70 based on the low volatility stocks are 550 for students and 400 for
CFAs and are not significantly different from those in stock (p=0.800 for students and p=0.478 for CFAs,
two-tailed WSR test).
14
The median investments by students are 450, 350, and 500 for high volatility stocks, BRC70 s, and
BRC50 s, respectively. p=0.066 (stock vs BRC70 ), p=0.025 (stock vs BRC50 ), and p<0.001 (BRC70 vs
BRC50 ), two-tailed WSR
13

14

Figure 4: Probability estimates

Estimates

1000

***

***

***

***

60

50

70

***

*

60

50

800
600
400
200
0

70

Students

CFAs

Horizontal bars represent the realized number of events based on 1,000
simulations.
***, **, and * denote the estimate is statistically significantly different
from the realization of the model simulation at the 1%, 5%, and 10%
significance level using the two-tailed WSR test, respectively.

duces more cost than benefit compared to the underlying stocks, while the opposite is
the case for BRC50 s. For the CFAs, while there are no significant differences between
the investments in the stocks and BRC70 s, the investment in BRC50 s is significantly
higher than for the underlying stocks.15 Thus, the CFAs also consider that BRC50 s offer
more benefit than cost compared to the underlying stock with high price volatility.
Figure 4 illustrates the distribution, by the box plot, of the estimated frequency (outof 1,000) an investment in BRC results in a loss (i.e., the BRC returns the stock insteadof cash) for three barrier prices (70, 60, 50). As shown, the estimated frequencies are
significantly higher than the outcomes of the stochastic model for both students andthe CFAs and for all three barrier prices.16 Thus, both students and the CFAs are more
15

The median investments by students are 200, 200, and 400 for high volatility stocks, BRC70 s, and
BRC50 s, respectively. p=0.778 (stock vs BRC70 ), p<0.001 (stock vs BRC50 ), and p<0.001 (BRC70 vs
BRC50 ), two-tailed WSR
16
The outcomes of the model are 245, 92, and 22 for barrier prices 70, 60, 50, respectively. The
corresponding median estimated frequencies for students are 400, 200, and 50, and those for CFAs are
387.5, 200, and 17.5.

15

“pessimistic” when compared to the stochastic model. We do not, however, observe any
significant relationship between the estimated probability of loss and the preference forinvesting in BRCs over stocks (measured as the difference between the invested amountin BRCHV s and StockHV s). See Appendix B.2.

4

Investment in Worst-of BRCs

Figure 5 compares the distributions, by box plot, of the amount invested in W-BRC70
and the minimum investment among three BRC70 s (min(BRC70 )) based on one of thethree underlying stocks of the W-BRC70 . Note that the expected return of W-BRC70 is
the same as the worst among these three BRC70 s. The left-hand side of Figure 5 showsthat for students, the investment in W-BRC70 is significantly higher than the minimum
among the three BRC70 suggesting evidence of behavioral bias similar to the dieter’s
paradox.17 For the CFAs, there is no significant difference between the two.18
Does the same behavioral bias continue to be observed even when the barrier priceis 50? Figure 6 compares the distributions, by box plot, of the amount invested in WBRC50 and the average minimum investments among the two BRC50 s (min(BRC50 ))based on one of the underlying stocks that constitute the W-BRC50 . Note that we do
not have participant investment for a BRC with a barrier price of 50, which has a low
price volatility stock as its unique underlying asset.19 Thus, min(BRC50 ) is based on theinvestment into BRCHV,50−1 and BRCHV,50−2 .
17The median amount is 300 for W-BRC70 and 200 for min(BRC70 ), p = 0.002 two-tailed WSR test.
We regressed the difference between WS-BRC70 and min(BRC70 ) on the score of the financial literacy
quiz and a constant for student participants. The estimated coefficient of the score is not statisticallysignificant (p-value= 0.927). See Appendix B.3.
18
The median amount is 100 for W-BRC70 and 100 for min(BRC70 ), p = 0.381 two-tailed WSR test.
19
This is because we implicitly assumed that investments for BRCs based on a high price volatility
stock are lower than those for BRCs based on low price volatility stock.

16

Figure 5: Investment in W-BRCs. Barrier price 70
***

n.s.

min(BRC70 ) W-BRC70

min(BRC70 ) W-BRC70

Students

CFAs

1000
800
600
400
200
0

min(BRC70 ) refers to the minimum investment among the three
BRC70 s each based on only one of the underlying stocks used in WSBRC70 .
***, **, and * denote statistically significant difference at 1%, 5%,
and 10% significance level using the two-tailed WSR test, respectively.

However, we find that a nonnegligible number of participants (24 of 63 students and
25 of the 65 CFAs) invested less in a BRC based on a single low price volatility stock(either BRCLV,70−1 or BRCLV,70−2 ) than in those based on a single high volatility stock(BRCHV,70−1 and BRCHV,70−2 ). For these participants, it is possible that comparing
min(BRC50 ), which does not consider BRCLV,50 , and W-BRC50 yields a biased result.
We therefore compare min(BRC50 ) and W-BRC50 for the restricted set of participants
whose investments in BRCLV,70−1 and BRCLV,70−2 are higher than in BRCHV,70−1 and
BRCHV,70−2 .
The top panel of Figure 6 which is based on the unrestricted sample suggests thatthe behavioral bias is no longer observed, even among students when the barrier priceis 50 instead of 70.20 However, in the restricted sample, we continue to observe the20

The median amounts for students are 500 for W-BRC50 and 400 for min(BRC50 ) (p=0.105, twotailed WSR test). For CFAs, they are 250 for both BRC50 and min(BRC50 ) (p=0.631, two-tailed WSRtest).

17

Figure 6: Investment in W-BRCs. Barrier price 50
Unrestricted sample
n.s.

n.s.

min(BRC50 ) W-BRC50

min(BRC50 ) W-BRC50

Students

CFAs

1000
800
600
400
200
0

Restricted sample
**

n.s.

min(BRC50 ) W-BRC50

min(BRC50 ) W-BRC50

Students

CFAs

1000
800
600
400
200
0

min(BRC50 ) refers to the minimum investment among the two
BRC50 s each based on only one of the underlying stocks used in WBRC50 .
***, **, and * denote statistically significant difference at 1%, 5%,
and 10% significance level using the two-tailed WSR test, respectively.

behavioral bias among students, even when the barrier price is 50.21
Let ∆iB =BRCiB -min(BRCiB ) be the observed degree of the behavioral bias a ladieter’s paradox for participant i when barrier price is B ∈ {70, 50}. Note that it is abias only when ∆iB > 0. Figure 7 shows the empirical cumulative distribution (ECD)
21

In the restricted sample, the median amounts for students are 550 for W-BRC50 and 400 formin(BRC50 ) (p=0.047, two-tailed WSR test). For CFAs, they are 350 for BRC50 and 400 for min(BRC50 )(p=0.627, two-tailed WSR test). Furthermore, for the restricted sample of students, the financial literacy test score is negatively correlated with the difference between W-BRC50 and min(BRC50 ) (pvalue= 0.072). See Appendix B.3.

18

Figure 7: Distributions of ∆iB
∆i70

-����

-���

∆i50

∆i50 , restricted

����

����

����

���

���

���

���

���

���

���

���

���

���

���

���

���

���
���

p = 0.047

����

Δ��

-����

���
���

-���

����

Δ��

-����

-���

p = 0.105

���

����

Δ��

p = 0.069

CFAs: dashed blue. Students: Red.
p-values are based on the two-tailed MW test.

of ∆i70 (left), ∆i50 (center), and ∆i50 for the restricted sample (right) for students (solidred) and CFAs (dashed blue). As can be observed for both CFAs and students, ∆iB ≤ 0
for a half of our sample for both B = 70 and B = 50. However, for remaining half, thedistribution of ∆iB for students lie on the right of that for CFAs demonstrating, as wehave seen above, the observed behavioral bias is larger of students than for CFAs. In
particular for ∆i70 and ∆i50 for the restricted samples, the differences between CFAs andstudents are statistically significant at 5% and 10% level, respectively.

5

Conclusion

In this paper, we experimentally reexamine the bias found by Kunz et al. (2017) ininvestor risk perception regarding the structured financial products known as barrier
reverse convertibles (BRCs) with worst-of payout characteristics.
Using an online survey of active capital market investors, Kunz et al. (2017) obtainsupport for the hypothesis that when relatively safe assets are added to risky assets toform the underlying assets of a BRC, investors erroneously perceive the risk of the BRC
19

to fall when in fact it becomes higher. However, because participants in the survey did
not face any monetary consequences from their stated estimates being accurate or not,this result may suffer from a hypothetical bias.
Employing an incentivized experiment with university students and CFAs, we foundsupport for the result in Kunz et al. (2017) among student participants, but not among
CFAs. These findings suggest that the effect of probability misperception a la the “dieter’s paradox” (Chernev, 2011) is likely to be observed among naive but not moresophisticated investors. Our results strengthen their evidence reported by Kunz et al.
(2017) that the magnitude of the bias is smaller among those investors who have experiences in investing in BRCs. Just as we expect professional nutritionists to be able toevaluate calories without suffering from the “dieter’s paradox,” experts in financial analyses are able to evaluate the risk associated with the worst-of BRCs without sufferingfrom a similar mis-perception.
Interestingly, Chernev (2011) shows that the “dieter’s paradox” is stronger among
those who are more concerned about managing their weight. Similarly, it is possible thatthe probability mis-perception reported in this paper is stronger among those investors
who are concerned about managing returns on their investments. This question deserves
a future investigation.
Future research could investigate how different ways of presenting the risk associated with complex financial products as BRCs can mitigate risk misperception by naive
investors. See, for example, Anic and Wallmeier (2019) for such an investigation, an
approach that would be of great importance in helping to protect investors.
There are other behavioral biases that have been proposed as an explanation for
puzzling investments in structured financial products. For example, Castellano and Cerqueti (2013, 2018), in a stochastic dominance framework, argue that a mis-perception in20

trends is an important reason for investments in less profitable products. Future researchthat experimentally investigate other possible explanations would also be very fruitful.

References
A NIC , V. AND M. WALLMEIER (2019): “Perceived attractiveness of structured financial products: The role of presentaion format and reference instruments,” Journal of
Behavioral Finance, 21, 78–102.
B ERNARD , C., P. B OYLE , AND W. G ORNALL (2011): “Lacally-capped investment
products and the retail investors,” Journal of Derivatives, 18, 72–88.
C ASTELLANO , R. AND R. C ERQUETI (2013): “Roots and effects of financial misperception in a stochastic dominance framework,” Quality & Quantity, 47, 3371–3389.
——— (2018): “A theory of misperception in a stochastic dominance framework andits application to structured financial products,” IMA Journal of Management Mathematics, 29, 23–37.
C ÉLÉRIER , C. AND B. VALLÉE (2017): “Catering to investors through security design:
Headline rate and complexity,” Quarterly Journal of Economics, 132, 1469–1508.
C HERNEV, A. (2011): “The Dieter’s Paradox,” Journal of Consumer Psychology, 21,
178–183.
C HERNEV, A. AND D. G AL (2010): “Categorization effects in value judgements: Averaging bias in evaluating combinations of vices and virtues,” Journal of Marketing
Research, 47, 738–747.

21

D ÖBELI , B. AND P. VANINI (2010): “Stated and revealed investment decisions concerning retail structured products,” Journal of Banking & Finance, 34, 1400–1411.
F ERNANDES , D., J. G. L. J R ., AND R. G. N ETEMEYER (2014): “Financial Literacy,
Financial Education, and Downstream Financial Behaviors,” Management Science,60, 1861–1883.
H ENDERSON , B. J. AND N. D. P EARSON (2011): “The dark side of financial innovation: A case study of the pricing of a retail financial product,” Journal of Financial
Economics, 100, 227–247.
H ENS , T. AND M. O. R IEGER (2014): “Can utility optimization explain the demand
for structured investment products?” Quantitative Finance, 14, 673–681.
H OLZMEISTER , F., J. H UBER , M. K IRCHLER , F. L INDNER , U. W EITZEL , AND
S. Z EISBERGER (2020): “What Drives Risk Perception? A Global Survey with Financial Professionals and Lay People,” Management Science, 66, 3799–4358.
H UNT, S., N. S TEWART, AND R. Z ALIAUSKAS (2015): “Two plus two makes five?
Survey evidence that investors overvalue structured deposits,” Occasional Paper 9,
Financial Conduct Authority.
K AHNEMAN , D. AND A. T VERSKY (1979): “Prospect Theory: An Analysis of Decision under Risk,” Econometrica, 47, 263–292.
K UNZ , A. H., C. M ESSNER , AND M. WALLMEIER (2017): “Investors’ risk perceptions of structured financial products with worst-of payout characteristics,” Journalof Behavioral and Experimental Finance, 15, 66–73.

22

R IEGER , M. O. (2012): “Why do investors buy bad financial products? Probability misestimation and preferences in financial investment decision,” Journal of Behavioral
Finance, 13, 108–118.
VOKATA , P. (2021): “Engineering Lemons,” Journal of Financial Economics, forthcoming.

23

A

Results based on full sample

This Appendix reports the results based on the full sample by reproducing the Figures 3
to 7 in the main text as Figures A.1 to A.5. The qualitative results are the same as thosereported in the main text, except that the dieter’s paradox is observed (at the 10% significance level) for CFAs when the barrier is 70, and the marginally significant differencein the magnitude of the dieter’s paradox for the restricted sample when barrier is 50
becomes insignificant. Note, however, the observed magnitude of the dieter’s paradox
continues to be significantly larger for students than CFAs at 5% level when the barrieris 70.

24

Figure A.1: Amount invested. Full sample
Low volatility
n.s.

n.s.

1000
800
600
400
200
0

Stock

BRC70

Stock

Students

BRC70

CFAs

High volatility
**
*

***
n.s

***

***

1000
800
600
400
200
0

Stock

BRC70 BRC50

Stock

Students

BRC70 BRC50
CFAs***, **, and * denote statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed WSR test, respectively.

25

Figure A.2: Probability estimates. Full sample

Estimates

1000

***

***

***

***

60

50

70

***

***

60

50

800
600
400
200
0

70

Students

CFAs

Horizontal bars represent the realized number of events based on 1,000
simulations.
***, **, and * denote the average estimate is statistically significantly
different from the realization of the model simulation at the 1%, 5%, and
10% significance level using the two-tailed WSR test, respectively.

Figure A.3: Investment in W-BRCs. Barrier price 70. Full sample****

min(BRC70 ) W-BRC70

min(BRC70 ) W-BRC70

Students

CFAs

1000
800
600
400
200
0

min(BRC70 ) refers to the minimum investment among the three
BRC70 s each based on only one of the underlying stocks used in WSBRC70 .
***, **, and * represent statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed WSR test, respectively.

26

Figure A.4: Investment in W-BRCs. Barrier price 50. Full sample
Unrestricted sample
n.s.

n.s.

min(BRC50 ) W-BRC50

min(BRC50 ) W-BRC50

Students

CFAs

1000
800
600
400
200
0

Restricted sample
**

n.s.

min(BRC50 ) W-BRC50

min(BRC50 ) W-BRC50

Students

CFAs

1000
800
600
400
200
0

min(BRC50 ) refers to the minimum investment among the two
BRC50 s each based on only one of the underlying stocks used in WBRC50 .
***, **, and * represent statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed WSR test, respectively.

27

Figure A.5: Distributions of ∆iB
∆i70

∆i50

����

����

����

���

���

���

���

���

���

���

���

���

���

���

���

���
-����

-���

∆i50 , restricted

���
���

p = 0.028

����

Δ��

-����

���
���

-���

p = 0.300

CFAs: dashed blue. Students: Red.
p-values are based on the two-tailed MW test.

28

����

Δ��

-����

-���

���

p = 0.144

����

Δ��

B

Additional results

B.1

Result for each productFigure B.1: Average amount invested.
Stock 1
n.s.

1000
800
600
400
200
0

Stock 2n.s.

Stock BRC70

Stock BRC70

Students

CFAs

1000
800
600
400
200
0

n.s.

n.s.

Stock BRC70

Stock BRC70

Students

CFAs

Stock 3
n.s.
1000
800
600
400
200
0

n.s.
**

Stock BRC70 BRC50
Students

Stock 4
n.s

***

***

***
1000
800
600
400
200
0

Stock BRC70 BRC50
CFAs

**

***

Stock BRC70 BRC50
Students

n.s

***

***

Stock BRC70 BRC50
CFAs***, **, and * represent statistically significant differences at the 1%, 5%, and 10% significance level
using the two-tailed WSR test, respectively.

29

Figure B.2: Investment in BRCs. Barrier price 70
W-BRC70−1
++
***

n.s.

min(BRC70 ) W-BRC70

min(BRC70 ) W-BRC70

Students

CFAs

1000
800
600
400
200
0

W-BRC70−2
n.s.
n.s.

n.s.

min(BRC70 ) W-BRC70

min(BRC70 ) W-BRC70

Students

CFAs

1000
800
600
400
200
0

min(BRC70 ) refers to the minimum investment among the three
BRC70 s each based on only one of the underlying stocks used in WBRC70 .
***, **, and * represent statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed WSR test, respectively.
+++, ++, and + represent statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed MW test, respectively.

30

Figure B.3: Investment in BRCs. Barrier price 50. Unrestricted sample
WS-BRC50−1
+
*

n.s.

min(BRC50 ) W-BRC50

min(BRC50 ) W-BRC50

Students

CFAs

1000
800
600
400
200
0

WS-BRC50−2
n.s.
*

n.s.

min(BRC50 ) W-BRC50

min(BRC50 ) W-BRC50

Students

CFAs

1000
800
600
400
200
0

Note: min(BRC50 ) refers to the minimum investment among the two
BRC50 s each based on only one of the underlying stocks used in WBRC50 .
***, **, and * represent statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed WSR test, respectively.
+++, ++, and + represent statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed MW test, respectively.

31

Figure B.4: Investment in BRCs. Barrier price 50. Restricted sample.
WS-BRC50−1
n.s.
*

n.s.

min(BRC50 ) W-BRC50

min(BRC50 ) W-BRC50

Students

CFAs

1000
800
600
400
200
0

WS-BRC50−2
++
***

n.s.

min(BRC50 ) W-BRC50

min(BRC50 ) W-BRC50

Students

CFAs

1000
800
600
400
200
0

Only those participants whose investment to BRCLV,70−i >min(BRCHV,70−1 , BRCHV,70−2 ).
min(BRC50 ) refers to the minimum investment among the two
BRC50 s each based on only one of the underlying stocks used in WBRC50 .
***, **, and * represent statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed WSR test, respectively.
+++, ++, and + represent statistically significant differences at the 1%,5%, and 10% significance level using the two-tailed MW test, respectively.

32

B.2

Probability estimate and investment in BRC

We regress the difference between the invested amount in the BRCHV,B and the highprice volatility stock (averaged across two underlying stocks for each participant) on theestimated probability of losing the invested cash (PrB ) for barrier price B ∈ {70, 50},
a CFA dummy, and the interaction between the CFA dummy and PrB . Further, in thethird column, we regress the difference in the amount invested in the BRCs between
B=70 and B=50, namely, ∆BRC = BRCHV,50 − BRCHV,70 on the difference in theestimated probability of losing the invested cash ∆P r = P r50 − P r70 , a CFA dummy
and the interaction between CFA and ∆P r.
We do not observe any significant relationship between the probability estimates oflosing the invested cash and any additional investment in BRCs over the stock. Notethat the sum of the estimated coefficients for P rB and CFA×PrB are not significantly
different from zero (p-values are 0.120 for B=70 and 0.215 for B=50).

33

Table B.1: Probability estimate and investment premium

CFA
PrB
CFA×PrB

B=70-45.38(69.58)-0.16(0.11)
0.34∗∗(0.16)∆P r
CFA×∆P r
constant
R2
N

7.28(48.73)
0.083
127

∗∗∗

B=50 ∆BRC
74.79
20.51
(57.14) (73.53)-0.11(0.26)
0.48(0.40)
0.003(0.14)-0.003(0.20)
80.00
127.02(42.86) (50.18)
0.054
0.002
127
127

, ∗∗ , ∗ denote statistically significant difference
from zero at the 1%, 5%, and 10% level, respectively.
Standard errors in parentheses.

34

B.3

Financial literacy and dieter’s paradox among student participants

We report the results of regressing our measure of the dieter’s paradox on student scoresfor the financial literacy quiz (FLQ) score. Our measure of the dieter’s paradox ofparticipant i, DPBi ≡ W-BRCiB −min(BRCBi ) is the difference between the investment
in W-BRCiB and the minimum investment among BRCiB (min(BRCBi ) ) where B ∈{70, 50} are the barrier prices.
Table B.2: Financial literacy and dieter’s paradox among student participants

FLQ score
constant
R2
N

B=70
1.22
(13.2)
59.39(116.56)0.000163

B=50
B=50 res+-15.30-41.57∗(15.14)(22.40)162.10436.15(133.60) (201.42)
0.01650.0851
63
39+: Restricted sample based on those with investment in BRCLV,70−1 and BRCLV,70−2 are higher than
BRCHV,70−1 and BRCLV,70−2∗∗∗ ∗∗ ∗, , denote statistically significant difference fromzero at the 1%, 5%, and 10% level, respectively.
Standard errors in parentheses.

35

C

Questionnaire

C.1

Financial literacy (students only)

These questions are from Fernandes et al. (2014).
1) Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year. After 1 year, would you be able to buy:
• More than today with the money in this account• Exactly the same as today with the money in this account• Less than today with the money in this account• Don’t know
• Refuse to answer
2) Do you think that the following statement is true or false? ‘Bonds are normallyriskier than stocks.’• True• False• Don’t know
• Refuse to answer
3) Considering a long time period (for example 10 or 20 years), which asset described below normally gives the highest return?
• Savings accounts• Stocks• Bonds• Don’t know
• Refuse to answer
4) Normally, which asset described below displays the highest fluctuations over
time?
36

• Savings accounts• Stocks• Bonds• Don’t know
• Refuse to answer
5) When an investor spreads his money among different assets, does the risk oflosing a lot of money:• Increase• Decrease• Stay the same
• Don’t know
• Refuse to answer
6) Do you think that the following statement is true or false? ‘If you were to invest$1000 in a stock mutual fund, it would be possible to have less than $1000 when you
withdraw your money.”• True• False• Don’t know
• Refuse to answer
7) Do you think that the following statement is true or false? ‘A stock mutual fundcombines the money of many investors to buy a variety of stocks.”• True• False• Don’t know
• Refuse to answer
8) Do you think that the following statement is true or false? ‘A 15-year mortgage
typically requires higher monthly payments than a 30-year mortgage, but the total interest paid over the life of the loan will be less.”37• True• False• Don’t know
• Refuse to answer
9) Suppose you had $100 in a savings account and the interest rate is 20% per year
and you never withdraw money or interest payments. After 5 years, how much would
you have on this account in total?
• More than $200
• Exactly $200
• Less than $200
• Don’t know
• Refuse to answer
10) Which of the following statements are correct?
• Once one invests in a mutual fund, one cannot withdraw the money in the firstyear• Mutual funds can invest in several assets, for example invest in both stocks andbonds• Mutual funds pay a guaranteed rate of return which depends on their past performance• None of the above• Don’t know
• Refuse to answer11) Which of the following statements is correct? If somebody buys a bond of firm
B:
• He owns a part of firm B• He has lent money to firm B• He is liable for firm B’s debts
38• None of the above• Don’t know
• Refuse to answer
12) Suppose you owe $3,000 on your credit card. You pay a minimum payment of$30 each month. At an Annual Percentage Rate of 12% (or 1% per month), how many
years would it take to eliminate your credit card debt if you made no additional new
charges?
• Less than 5 years• Between 5 and 10 years• Between 10 and 15 years• Never• Don’t know
• Refuse to answer

C.2

Other questions

1) How much did you know about structured financial products before participating tothis experiment?
• Almost none. Never heard of structured financial products.
• Not very much. Did not have much knowledge about structured financial products.
• More or less. Had a basic knowledge about structured financial products.
• Knew well. Could explain what are structured financial products in simple manner.
• Knew very well. Have researched on or worked with structured financial productsin the past.
2) How often have you purchased structured financial product in the past 5 years?
• Never• Once39• Twice• Three times• Four times• Five times• Six times• Seven times• More than eight times3) Please select all the assets you are currently investing in from the list below.
• Fixed term deposit• Stocks• Mutual fund
• Bonds• Rare metals• Real estate• REIT• Derivatives• Arts and antiques• Others (asked to specify in the next page)• No investment
4) Please select your sex.
• Female• Male• Neither• Prefer not to answer
5) Please provide your age.
40