When Do Structured Funds Become Too Good to Be True? An Experiment

In this experiment, structured funds are sequentially offered to investors as an alternative to bonds. Our results show that the order in which information is presented generates significant biases in decision‐making. These biases can have both positive and negative consequences on investors' financial behaviour. In fact, when the investment alternatives are made easier to compare, ‘too good to be true’ offers are more easily spotted. Simultaneously, when funds' expected performance shows an apparently positive trend, funds are more often chosen. The ‘too good to be true’ effect is alleviated by high transparency of the information on the funds return.


INTRODUCTION
Structured products make up a significant part of most developed countries' financial systems. According to the Structured Products Association, in 2005 over US$180bn was invested in the European fund market, US$70bn in the US market and almost US$50bn in the Asian market. Trends have not changed since 2005, despite the Great Recession. In 2012, according to Moore (2012), the sales of structured products continued to rise despite warnings by financial regulators about their risks and complexity.
Parallel to the growth of structured products, the growth of the mutual funds industry over recent decades highlights the ability of these funds to channel investors' money into the financial markets. Khorana and Servaes (2012) report that assets in the mutual fund industry increased by a factor of 200 in the period . Moreover, about 45% of the households in the U.S. invest in them, according to ICI (2010). Hence, investment in mutual funds is a widespread activity, in which non-specialized agents also participate. In fact, many citizens invest in guaranteed mutual funds as part of their retirement plans.
The significant role of mutual funds in most markets has aroused both social and academic interest. Within this context, the aim of the present paper is to analyse the individual demand for structured mutual funds according to varying levels of the difference in expected return when compared to a bond, and under different information conditions.
The demand for mutual funds has been extensively analysed in the literature concerned with evaluating fund efficiency. An example of research on structured product demand is Breuer and Perst (2007), who successfully explain demand for two structured products using a modified hedonic framing rule. Behavioural biases have been found in experimental studies focusing on mutual funds. Annaert et al. (2005) carried out an experiment on framing in capital guaranteed funds and observed that investors tend to choose in a different way when they are aware of some characteristics of the probability distribution of the potential gains/losses. Barreda-Tarrazona et al. (2011) experimentally analysed the importance of providing accurate information about the socially responsible character of a mutual fund in order to help investors express their ethical preferences. Kliger et al. (2003) also opted for an experimental approach to uncover inconsistency with the standard Expected Utility Theory in mutual fund investor behaviour: investors' tendency to delegate money to a fund increases with performance, even when performance is uninformative. Choi et al. (2010) designed an experiment to study the 'law of one price' in fund investment. They presented the subjects with a menu of four funds with the same fundamentals but charged higher fees for the funds presenting higher past performances (due to the different launching dates). The authors found that people relied heavily on the annualized past return of funds in making fund selection decisions, even ignoring the fees in many cases. Similar results were obtained by Anufriev et al. (2012) in an experiment in mutual fund choice, but in their case, centred on the role of past information and fee structure. They observed that fund choice is heavily driven by past returns, even when this information is irrelevant. A very similar bias to this one is obtained in our experiment for the role of information about alternative scenarios.
The abovementioned literature analyses investor behaviour and demand for mutual funds and, in most cases, unpredicted behaviour appears, to a great extent, to be related to the information available to the investors or to the framing of that information. These articles add to a growing body of evidence that individual investors make suboptimal asset allocation decisions. The present study proposes a simple experimental design that allows for an analysis of individual investor behaviour in structured mutual funds according to variables such as expected return and risk (we vary the former while we keep the latter constant), and, at the same time, attempts to eliminate possible behavioural biases such as past performance effect, disclosure of the probability distribution of the potential gains/losses effect, or other features that might complicate comparisons (e.g. fees and non-portfolio services). This approach also allows us to evaluate the effect that the structure of the available information has on investor behaviour and, consequently, on the demand for the funds.
The study was undertaken in the Laboratory for Experimental Economics at the Universitat Jaume I, where a sample of university students made investment decisions according to different expected return and information conditions. They had to invest a fixed amount either in a bond or in a structured product, which secured part of the invested capital and yielded additional benefits if the (simulated) stock market experienced a positive evolution. Our results show that information available to investors, and particularly the order in which it is presented, generates significant biases in their decision-making that can have both positive and negative effects on their behaviour.
The paper is organized as follows. The design of the experiment is outlined in Section 2. The hypotheses are presented in Section 3 and the results obtained in the experiment are analysed in Section 4. Section 5 concludes.

Participants
A total of 607 undergraduate students from different majors, mainly business administration, engineering and economics, participated in the between-subjects study: 287 in Treatment 1, 227 in Treatment 2 and 93 in Treatment 3. Subjects were recruited using the Orsee System (Greiner, 2004) and none of them participated in more than one session. Our experiment consisted of 60 scenarios with the agents having to choose between two investment options in each of them: a risk-free asset (a bond) and a structured mutual fund. Each of the 60 scenarios presented a particular combination of the interest rate of the bond on one hand, and the secured and expected additional benefits of the fund on the other hand.
The experiments were programmed in PHP and Java and carried out in the Laboratory for Experimental Economics at Universitat Jaume I in Castellón, Spain. To give a real value to each of the decisions made using experimental units (EU), the equivalence of 1 € = 8000 EU was introduced. Average earnings were 163 962 EU (20.5 €) per participant in approximately one and a half hours.

Experimental design and framework
The experiment consists of three parts. The first part is the most central to this research: subjects make investment decisions in each one of the 60 scenarios.
The second part of the experiment is a risk-aversion test using a lottery task. Finally, in the last part of the experiment, subjects fill out a personal questionnaire. 1 For the first part of the experiment, subjects were given specific instructions about their tasks, which were also read to them aloud by the experimentalist. The experiment was then run for each subject on an individual computer. A screen appeared for each scenario and the investor had to choose where to invest his or her total endowment of 100 000 EU between two investment alternatives, 'A' or 'B'. 2 The investment alternative 'A' was a fixed return risk-free bond. Equation 1 describes the final value of the investment after n periods (Vn,j) for the j scenario as the result of reinvesting the initial V0 up to n yearly periods, given a simple rj capitalization. In the experiment setting, for each scenario, n is equal to 3 years and V0 is 100 000 EU. In Treatment 1, for scenarios going from 1 to 30, this investment yields a 3% annual interest, which implies a 9% appreciation within 3 years. In order to simplify to the maximum the investor's calculations, the yields were calculated with a simple capitalization. Starting with the scenario number 31 up to the 60th, the bond yields 7% yearly, which implies a 21% rj in 3 years (see Table 1): On the other hand, the alternative 'B' was to invest in a structured mutual fund. At the end of a 3-year period this investment fund has a final value, shown in equation 2. The first component represents a guaranteed part of the investment (1 + gj), which varies from −3 to 12% depending on the scenario. Technically speaking, it is when this percentage is positive that we can actually consider the fund a guaranteed mutual fund. The second component yields an extra value depending on the positive evolution of an index representing the stock market. In each of the scenarios, subjects are offered a particular percentage (ρj) over the appreciation of the stock market (rm). As equation 2 shows, this component is asymmetric, given that it yields an additional benefit when the stock market appreciates, but does not entail losses when the stock indicator does not have a good performance. This asymmetry is typical of the options: 3 In Treatment 1, every 5 scenarios the value of the upside participation ρj is successively: 10, 30, 60, 100 and 110%. This structure is repeated 12 times 1 The experimental instructions and the questionnaire are available upon request to the authors. 2 Note that the investors could not divide their endowment: they had to invest it fully in one of the two options presented to them. 3 In fact, the mutual guaranteed funds are products normally structured by means of investment in bonds which at the due date provide the invested capital security, and the payment of an option premium which is bounded to a certain stock market evolution gives us the second component. Holmen et al. (2014) experimentally study how option-like incentives in asset markets can induce higher prices and more risk taking by agents.  throughout the whole session. Table 1 summarizes the values of gj and ρj parameters in each scenario for the fund investment 'B' as well as rj for the bond investment 'A'. Please note that the particular order of the scenarios presented in Table 1 was used in Treatments 1 and 3, while in Treatment 2 the exact same scenarios were presented in different random orders to each of the subjects. As in real financial markets, the value of the stock market evolution rm is not known. For this experiment we considered it a random variable with a normal distribution (for Treatments 1 and 2). Even though any simulated data could have been used, we have taken the annualized standard deviation of the Ibex 35 daily return over the 3-year period 2008-2010 and the annualized mean of the daily return over the past 10 years. As this mean is positive, the probability of a positive rm is higher than that of a negative value, which is expected from the equity risk premium hypothesis.
Subjects were informed about investment in stock markets being risky. They were also informed that in the simulated stock market there was a 60% probability of the revaluation being positive and a 40% probability of it being negative. The standard deviation and a table summarizing the distribution of rm were reported in the instructions for Treatments 1 and 2. These values were generated, as we explained above, using a normal distribution for the 3-year return with 12.021% mean and 46.8% standard deviation parameters. In Treatment 3, in order to determine the stock market revaluation, we replaced the computer generated value taken from the normal distribution of rm with a simple roll of a dice by a person. In particular, a volunteer subject rolled a 10-sided dice offering an equivalent 40% probability of negative revaluation and an equal 12% mean expected revaluation to that of the normal.
After the 60 scenarios were run and all subjects made their choices, the program randomly provided a value for rm (in Treatments 1 and 2) drawn from the aforementioned normal distribution, which was converted to 0 in cases where it was negative. In Treatment 3 a 10-sided dice rolled by a volunteer participant determined the stock market revaluation after all participants had made their decisions and it was also converted to 0 in cases where it was negative. Immediately afterwards, another participant volunteered to roll the dice in order to randomly obtain a value j′ from 1 to 60, which determined the scenario that would be paid out in cash in that session. 4 Finally, subjects who had decided to invest in option A in the selected scenario received the amount corresponding to equation 1; for those who had chosen investment B, their earnings were determined by equation 2 according to the realized value of rm and the parameters gj and ρj for the selected scenario j′.
We ran nine sessions of Treatment 1 in which the scenarios were sequentially presented as shown in Table 1 (with increasing expected returns for the fund). In Treatment 2, the exact same 60 scenarios (combinations of fixed and additional potential benefits of the two investment options) were presented in random order, independent for each subject, to a new pool of subjects. We ran five sessions of Treatment 2. Two other sessions were run under Treatment 3 conditions, with the rolling dice mechanism determining the stock market revaluation and the same 60 scenarios sequentially presented as in Treatment 1.
We had three main goals: (i) to observe any changes in the way the capital endowment was invested between the risky and the risk-free assets when the expected return varied; (ii) to see if the ordering in which the investment scenarios were presented to the participants made a difference in their investment decisions by comparing treatments 1 and 2; and, finally, (iii) to study whether more transparent information about the return generation process would influence decision-making by comparing Treatments 1 and 3.
In the second part of the experiment, we used a lottery to assess the subjects' risk aversion, which was very similar to the one used by Alfarano et al. (2006). This is a modification of a Holt and Laury (2002) lottery test where one of the options is not probabilistic and increases sequentially in its fixed value and the other is probabilistic but its expected value remains fixed. In this part of the experiment 11 lottery choices are displayed. The risky option, which remains available along the 11 scenarios, is to obtain 48 000 EU or zero EU with 50% probability. The safe option consists of a secure payment which ranges from 4000 EU in the first scenario, to 31 000 EU in the last one. After all choices are made, one of the 11 scenarios is randomly chosen and also the 50% probability situation is solved by a volunteer tossing a coin. 5 Then the payment to each participant in the risky lottery is determined according to these events. An expected rational behaviour would be to choose the risky option in the first scenarios when the riskless offer is low and afterwards, with higher secured yields, switch to the safe option at some point of the decisions chain. 6 Finally, the third part of the experiment consisted of a questionnaire with demographic and idiosyncratic data. The first three questions were meant to reveal the financial knowledge level of the participant. The following four questions evaluated how important investment yields and risks were for the subject and whether they had any asymmetric perception in the evaluation of gains and losses. The last four questions aimed at evaluating subjects' rationality when selecting investments. 7

HYPOTHESES
In the mean-variance framework of choice among financial assets, for a given level of risk, an asset offering a higher expected return would always be preferred over one with a lower expected performance. In our design, the only risk faced by the participants concerns the future evolution of the (computer or human generated, depending on the treatment) simulated stock market revaluation rm, on which the variable part of the structured fund return is based. In this way the underlying risk is kept constant for all the guaranteed products within a given treatment. The alternative investment possibility is a risk-free bond. In this setting, the binary decision of choosing between the two investments should be made in terms of the subjectively estimated expected utility of each alternative according to each individual's level of risk aversion. When one of the investment alternatives unequivocally increases its expected return with respect to the other without varying its risk, it should be preferred by our investors. This can be expressed as appears in our Hypothesis 1: HYPOTHESIS 1. Investment in the structured fund is increasing in the difference between the expected return of the structured fund and that of the risk-free bond.
We understand that each investor may subjectively attach different utility to the same level of expected return. This is due to the fact that not every person is risk neutral. Indeed, in the experimental literature there is ample evidence that people tend to be risk averse even for the relatively small amounts of money they can gain in experiments. As the only risk in our experimental design concerns the structured fund, this will be, in general, the least preferred option for the more risk-averse investors, and vice-versa:

HYPOTHESIS 2. Risk-averse (loving) participants will invest more in the bond (structured fund).
We think that this effect could be so important as to totally nullify the effect of big expected return differentials between the investment options, but only for extremely risk-averse or extremely risk-loving individuals. We introduce expected return differences up to 30% in the design, which are very big for regular investment standards. We do not expect many subjects to show an extreme degree of risk aversion or lovingness. Under these circumstances, the aggregate effect of these few subjects' decisions will, in any case, be very small.

HYPOTHESIS 3. Extremely risk-averse participants will not invest in the structured fund even for high differences in the expected returns.
According to Miller (1956, pp. 89) 'Everybody knows that there is a finite span of immediate memory and that for a lot of different kinds of test materials this span is about seven items in length . . . and there is a span of absolute judgment that can distinguish about 7 categories'. That is, the ability of people to retain the information and compare a large set of options is limited. In our case we presented each subject with 60 binary choices. In Treatment 1 the information was presented sequentially, in cycles with increasing order of expected returns, so that it was easy for the subjects to categorize and compare the different assets across the scenarios. According to the psychological research on the matter, in Treatments 1 and 3, subjects should be able to recall and easily compare at least within each group of 5 scenarios with stable fixed returns for both investments and increasing index-performance-related expected returns. However, in Treatment 2, the sequence of scenarios did not follow any logic and what was 'stored in memory' was a juxtaposition of a steadily increasing number of offers with different expected values. Malhotra (1982) found that respondents experienced information overload when they were presented with 10, 15, 20 or 25 choice alternatives. If the independence of irrelevant alternatives held in our case this would not pose any problem, because all 60 binary choices are independent in our design, in the sense that only one of the scenarios was to be selected in the end, and all other 59 choices would be totally irrelevant for determining the payment to the particular subject. No matter how attractive or unattractive an investment seen in prior scenarios was, that should not have any weight in the binary decision being presented in a particular alternative scenario. However, if the subject tried to retain the information about all the investment options that were presented in order to carry out a global comparison, the subject's memory and judgment would endure a hard test.
HYPOTHESIS 4. The order in which information is presented to our participants (sequential vs random) will generate biases in their decisions related to information processing limitations: (i) a sequential presentation of better alternatives can introduce return chasing, as has been previously observed in the literature, but, on the other hand, and thanks to our design, (ii) it can make the extremely generous offers seem 'too good to be true' and, therefore, they are chosen less.
Our argument is that the memory and judgment limitations, operating when the investment options are presented randomly (Treatment 2), are greatly reduced when these are sequentially ordered in groups of five choices in which the only difference is the increase in the upside market participation (Treatments 1 and 3). This increase may make the guaranteed option more attractive in comparison to the bond than what the difference in expected returns would justify. However, when the upside market participation (which increases from 10 to 110%) goes above 100% it could appear to be 'too good to be true'; that is, the guaranteed investment may seem to be offering too much. In this case, subjects could come to doubt the likelihood of a positive stock market return as suggested in the instructions. 8 In order to alleviate the possible fear of some participants that high stock market revaluations could be less likely to be selected by the computer than they should, in the third treatment we have replaced the black box draw of the normal distribution generated by the computer with a volunteer participant rolling a 10-sided dice offering an equivalent 40% probability of negative revaluation and an equal 12% mean expected revaluation to that of the normal.
All other characteristics of the treatment are as in Treatment 1. What we expect is that the more transparent random generation process used in Treatment 3 causes high upside participation investments to be perceived as credible as small upside participation investments.

HYPOTHESIS 5.
Higher transparency in the random generation process followed for obtaining the market revaluation (human dice roll vs computer draw) will alleviate the bias of not choosing options offering high upside participations.

Aggregate results on guaranteed mutual funds investment
Figure 1 offers us some graphical evidence for Hypotheses 1 and 2. It allows us to infer from the subject's choices that a greatly reduced number of people are highly risk loving or highly risk averse and they stick to their preferred option: the risky or the safe option, respectively, both in the presence of highly positive or highly negative return differentials between the fund and the bond. In fact, there are probably more extremely risk-averse subjects than extremely riskloving subjects (approximately 9 and 1%, respectively). However, most investors (approximately 90%) change their decision in the hypothesized way alongside the evolution of the difference in expected returns between the two assets following a sigmoid logistic shape.
Comparing Treatments 1 and 2 in Figure 1 we can observe that in Treatment 1, when the scenarios are easier to compare (because they were presented in the sequential order shown in Table 1  the guaranteed fund is greater for most expected return differentials (full dots are normally placed higher than hollow dots). Hence, investors have a higher preference for the fund when they can easily compare the independent scenarios and observe that the fund offers increasingly higher expected gains, while the bonds' gains remain constant. This is the first casual evidence for Hypothesis 4.i. As for Treatment 3, it appears that a more transparent way to generate the stock market revaluation consistently results in less investment in the mutual fund when the expected return difference is negative and more investment when it is positive than in the other two treatments.
This observation supports the idea that investors may suffer from a kind of 'past returns' or 'trend' illusion, similar to Chartism, due to which they tend to believe that a good history is in some way a guarantee of a good future performance, even in totally independent realizations such as those presented in our experiment. This result is complementary to the those recently obtained by Choi et al. (2010) and Anufriev et al. (2012), even though our situation is not identical, given that the offers that we present to the investors correspond to alternative worlds that might or might not be realized in the end, and not to real past performance.
This 'trend' effect can also be observed numerically in Table 2a. In order to statistically support our graphical observations above, we have conducted a battery of Kolmogorov-Smirnov tests between the distributions of subjects' proportions of structured fund choice for different groups of scenarios and we have obtained statistically significant evidence that the Treatment 1 distribution stochastically dominates Treatment 2's for the whole sample and for the two 30-scenario subsamples. 9 However, Treatment 3 stochastically dominates Treatment 1, but only for the past 30 scenarios when the fund is relatively less attractive. This indicates that with a more transparent random generation process, subjects decide more in accordance with the expected return difference. The observed pattern shows some evidence in favour of Hypothesis 5, given that when the attractiveness of the fund is greater, more participants trust investing in the fund for Treatment 3 than for Treatment 1.
In Table 2b we compare the median number of scenarios in which subjects invested in the structured fund (instead of the whole distribution of the proportions of investors), obtaining robust results supporting the statistical significance of a positive difference in median investment in the guaranteed fund in Treatment 1 with respect to Treatment 3. The median number of scenarios in which subjects selected the guaranteed fund is 33 out of 60 in Treatment 1, while only in 28 out of 60 in Treatment 2. In fact, performing an additional Mann-Whitney test, we obtain that the probability for a random scenario that a randomly chosen agent from Treatment 1 has selected the guaranteed fund more often than a randomly chosen agent from Treatment 2 is 60%. The tests above offer evidence consistent with our Hypothesis 4.i, confirming the existence of a 'trend' 9 Only when we further break down the sample into the 12 cycles of 5 periods do we obtain that the difference is significant in half of the cycles, very precisely matching what appears in Figure 2.  effect. We observe no significant differences regarding the 'trend' effect between Treatments 1 and 3, as expected.

Table 2b. Median number of scenarios in which agents chose the structured fund and Mann−Whitney test between treatments
If we analyse Figure 2, which describes the evolution along the scenarios of the percentage of investment in the structured fund, behavioural paths can be identified.
The guaranteed return of the mutual fund is −3% in the first group of 5 periods, while the bond ensures a 9% return on the investment for the same time horizon. In the first period, with an additional 10% yield over the stock market revaluation for the mutual fund, only 18% of the participants prefer the risky option, which seems to indicate that a maximum 12% loss is compensated for them by a highly positive expectation on the evolution of the stock market. In Treatment 1, within this first group of 5 scenarios there is a maximum investment in the fund option in the third scenario, where 78.9% of participants decide that a 12% maximum loss is compensated by a 60% upside participation. In the subsequent 4th and 5th scenario we observe a fall in the mutual fund investment: 77.5 and 71.8% of investors decide to invest in the fund for a ρj value of 100 and 110%, respectively. This pattern is not infrequent in Treatment 1: in the second group of 5 scenarios a similar phenomenon is observed; that is, mutual fund investment rises from 21.1% in the first scenario up to 85% in the 4th scenario, where it reaches the maximum, and, finally, in the fifth scenario, when the ρj value goes beyond 100%, investment in the fund drops to 79%. This extreme concavity feature is repeated throughout the whole of Treatment 1, especially in scenarios 1 to 30 where the difference between the guaranteed 3-year return of the bond and the guaranteed part of the mutual fund is narrower than it is for the last 30. This is, in our opinion, the most original result of this experiment. While one would expect a monotonic increase in investment in each 5 scenario cycle together with the increase in the upside participation, we observe that for percentages higher than 100% investment in the structured product, in fact, nearly always decreases in Treatment 1. We call this finding the 'too good to be true' effect, which has some implications for the advertisement of structured products. Offering such high upside participations could, in effect, be conveying to the risk-averse investor the idea that the event of the stock market actually revaluating is highly unlikely, because otherwise such great upside participation would not be offered. In our experimental case, students may doubt whether in the scenarios where the offer is so high the actual probability of a positive revaluation really is 60% as stated in the instructions. However, in Figure 2, we can also observe that the 'too good to be true' effect totally disappears as soon as the subjects are no longer able to easily compare all the possible investments. In Treatment 2, just more of them invest in the fund when the upside participation is 110% than when it is 100%. Seeing all the binary options in random order seems not to make them behave more cautiously for extremely high offers. In addition, introducing a more transparent way of generating the stock market revaluation in Treatment 3 dramatically reduces the 'too good to be true effect', as stated in Hypothesis 5. Also, the percentages of investment in the fund with medium to high upside participation are much bigger than in the other two treatments.
To provide statistical evidence for the 'too good to be true' effect we have conducted a McNemar symmetry test. This test compares whether the number of times that an agent was choosing the guaranteed fund when ρj was 100% and he or she decided to switch his or her selection to the bond when ρj increased to 110% is significantly different from the opposite switch; that is, that an agent was choosing the bond when ρj was 100% and decided to change to the fund for 110%. Our results can be found in Table 3. For the first 30 scenarios of Treatment 1 we find that significantly more times the case was that those choosing the fund switched to the bond, thus statistically supporting the 'too good to be true' effect. For the last 30 scenarios of Treatment 1 there is no significant decrease in fund investment, but also no significant increase (still consistent with our hypothesized effect), while for both the 30 first and the 30 last scenarios of Treatment 2 we observe the opposite phenomenon: that significantly more people switched from the bond to the fund when the upside market participation increased over 100%, as expected if no 'too good to be true' effect applies and investors just follow the guide of the expected return difference. These tests together support our Hypothesis 4.ii that a 'too good to be true' effect arises when the relatively better and worse investment scenarios are made easier to compare.
In Treatment 3 we obtain that there is no significant decrease in the number of participants investing in the fund when the upside participation becomes very high for the first 30 scenarios and, in fact, that there is a significant increase in the last 30 scenarios, thus confirming Hypothesis 5 that transparency about the market revaluation random generation process alleviates the 'too good to be true' effect.
That is, in Treatment 2, when subjects see the 100 and 110% upside participations in random order mixed with the other lower ones (without observing the sequential increase in each 5 scenario group) they do not infer any negative signal in such attractive offers. Thus, spotting 'nearly incredible' offers becomes harder when comparing offers becomes cognitively harder. This fact has implications for financial regulatory authorities. Clearly organizing and categorizing existing investment opportunities could help investors in discriminating reasonable offers from highly unlikely to be fulfilled offers. In addition, exposing dark spots in the information about how the returns are generated can help the investor to trust a given offer less (e.g. a Ponzi scheme). Figure 3 shows the expected return differences between the fund and the bond for each scenario. In this way they can be used as a benchmark for rational risk-neutral decision-makers. As our participants vary in their degree of risk aversion we never observe that all investors follow the clear-cut risk neutral prediction. However, we do observe that the percentage of investors choosing the fund approximately follows the difference between the expected return of the fund and the bond, as proposed by Hypothesis 1. This link is clearly broken only for Treatment 1, in the scenarios where we observe the 'too good to be true' effect.

Econometric analysis
In this subsection we further analyse the statistical significance of our results using panel regression methodology. To obtain a more precise measure of the impact of the guarantee and the stock market upside participation on the demand for the mutual fund investment, we construct a model using as independent variables those appearing in equations 1 and 2: the guaranteed return of the bond (rj), the guaranteed return of the structured fund (gj) and the upside participation offered by the fund (ρj). We have also introduced in the analysis the individual level of risk aversion estimated from our lottery tests (the higher the value the less risk aversion a subject showed in the test). We also employ as a variable the squared term of the upside participation (ρj 2 ) with the aim of capturing, when this quadratic effect is significant, the concavity of the demand of the mutual fund. This concavity must be big for the 'too good to be true' effect to be significant. The obtained data form a panel with 607 individual decisions across 60 periods (287 in Treatment 1, 227 in Treatment 2 and 93 in Treatment 3). Given that we identified that approximately 10% of investors had non-robust answers to the risk aversion test, the respective observations were eliminated from our analysis and we remained with a still relatively large sample of 542 robust individuals (262 for Treatment 1, 205 for Treatment 2 and 75 for Treatment 3) and a total of 32 520 usable observations for our panel data analysis.
Table 4a (Panel A) contains the main results that we obtain by running a probit model for Treatment 1 in the first column, for Treatment 2 in the second column, and, finally, for the difference between the parameters estimated for the two treatments in the third column. Starting with Treatment 1, all variables turn out to be highly significant and they all have the expected sign. For example, an increase of the return (rj) of option A (the bond) has a negative effect on the mutual fund demand, while a higher guaranteed value (gj) of option B (the fund) increases its demand. Also positively, but in a lower proportion, the upside participation (ρj) increases the mutual fund demand. All these three significant results together statistically confirm our Hypothesis 1. The negative coefficient of the squared term of the aforementioned upside participation confirms our preliminary graphical analysis, which indicated a concave shape of the demand for the mutual fund as a function of the upside participation. The effects concerning ρj and ρj 2 deserve a more detailed analysis, which we will undergo when we consider the difference between both treatments (third column).
We also find that on a scale from 1 to 12 of risk attitude (1 is very risk averse and 12 is highly risk lover), one additional level in this scale, that is, being  Standard errors are in parentheses. ***Significant at 1%, **significant at 5% and *significant at 10%.

BIASES IN STRUCTURED FUNDS INVESTMENT
characterized as more risk lover, entails a significantly higher probability of choosing the structured fund. This confirms our Hypothesis 2 that those subjects who are relatively less risk averse invest with higher probability in the risky option.
When we turn to Treatment 2 (second column) we observe that all the mentioned significant effects are robust, but they are smaller, with the exception of the effect of the guaranteed return of the fund. However, are these differences in the size of the coefficients significant? In the third column we check for the significance of the differences between the coefficients estimated for the two treatments and we obtain that those for the bond returns, risk aversion and also the intercept are not significantly different between treatments. The positive effect of the guaranteed return of the fund is slightly greater in Treatment 2. This is true particularly in the first 30 scenarios when the bond return is relatively low, as we can observe in Panels B and C in Table 4a. In those panels we separate the sample into the observations of the first 30 and the last 30 scenarios (when ordered as in Table 1).
The most important differences between the two treatments (third column of Panel A in Table 4a) are, first, that the positive effect of the upside participation on fund demand is significantly reduced to two-thirds in Treatment 2 when the investment options are made harder to compare, thus econometrically confirming the 'trend' effect, and second, that the concavity of the demand function with respect to this upside participation is also significantly halved for Treatment 2, dramatically reducing the 'too good to be true' effect (these results are robust for all scenarios, as we can observe in Panels B and C) in Table 4a. These two observations together further confirm our Hypothesis 4. Table 4b (Panel D) shows the outcome of a probit regression for Treatment 1 in the first column, for Treatment 3 in the second column, and, finally, for the difference between the parameters estimated for the two treatments in the third column. Again, as for Treatments 1 and 2, all variables turn out to be highly significant and they all have the expected sign. There are only some significant differences between Treatments 3 and Treatment 1 that can be found in column 3. The increase of the return (rj) of option A (the bond) has a more negative effect on the mutual fund demand in Treatment 1 than in 3, while consistently a higher guaranteed value (gj) of option B (the fund) increases its demand more in Treatment 3 than in Treatment 1. In addition, the constant is slightly less negative, reflecting a general higher tendency to invest in the fund in Treatment 3. These three differences indicate that risky funds are preferred to the safe bond when the underlying randomness generating process is more transparent. The upside participation shows much lower concavity in Treatment 3 than in Treatment 1, approximately the same as in Treatment 2, confirming a big reduction of the 'too good to be true' effect with higher transparency, as Hypothesis 5 proposes. In contrast, no differences are found in the effect of the upside market participation; that is, the 'trend' effect, which is equally present in both 'ordered' treatments. Risk aversion, as expected, plays a much less fundamental role in Treatment 3, with coefficients much closer to zero than in the other two treatments. Observing Panels E and F in Table 4b we see In order to try to disentangle the effect of risk aversion in the 'too good to be true' effect we have run a Spearman correlation analysis, which we present in Table 5. We have shown above that the exact order in which the sequence of upside participations is displayed encourages the trend phenomenon to appear in the treatment with an easier comparison. However, this does not explain why investment is reduced and not increased for the highest offers. Our Hypothesis 3 was that the highly risk-averse subjects will not invest in the mutual fund even for highly favourable expected return differentials. When the upside participation increases greatly, the fund's expected return will increase accordingly. However, when comparing the options becomes easier, subjects more easily come to believe that a positive revaluation is more unlikely when they are being offered a relatively high upside participation, and, therefore, they perceive higher risk if they do not completely trust the computer generated random draw used in Treatment 1. The more risk averse will not want to invest in the fund under these circumstances.
Given that the 'too good to be true' effect appears in the last period of every 5-period cycle, that is, when the premium goes from 100 to 110%, we analyse investors' behaviour in this scenario interval, identifying those who choose to invest in the mutual fund when they are offered 100% over the stock market revaluation and switch to the safe bond investment option when the upside participation increases to 110%.
For Treatment 1 a highly significant negative correlation is observed between the risk-loving variable and the frequency with which a subject switches from the mutual fund to the safe option in every fifth period. Thus, a more riskaverse attitude is positively correlated with the 'too good to be true' effect (see Table 5).
There is no significant correlation in Treatment 2, however, this result being in concordance with our Hypothesis 4, in the sense that the difficulty of comparing the offers makes it harder for our subjects' minds to spot the extremely high offers and assign them a higher risk. In addition, there is no significant correlation in Treatment 3, consistent with Hypothesis 5 that increased transparency makes subjects trust all offers equally whether more or less risk averse.

CONCLUSIONS
In this paper we experimentally analyse the demand for structured products; in particular, we construct a guaranteed mutual fund that is offered to participant-investors as an alternative to a risk-free bond. Our experimental design allowed us to control for the effect of several variables such as guarantees, upside participation, risk aversion and the informational structure. We obtain that, apart from the expected rational behaviour of participants, consistent with the expected value framework, some behavioural biases arise in Treatment 1, where the investment products are shown sequentially ordered in a way that they can easily be categorized and compared. One of the behavioural biases observed is a 'trend' effect which causes investors to value more positively the structured investment fund when they observe an increase in the expected returns that it offers, even if the final realization of the returns of a given scenario is totally independent of the other scenarios. This illusion is similar to other well-known behavioural biases in the literature, such as the 'illusion of past returns'. We believe this can only be fought by the regulator with greater financial literacy and an insistence that past returns are not a guarantee of future returns.
Another behavioural bias, first documented here, is what we call the 'too good to be true' effect. This refers to participants not investing in extremely high yield opportunities that seem hard to believe. This appears to be a consequence of investors being able to more easily compare the different investment alternatives, thus altering their perceived risk, as the behavioural bias disappears when we present the investment scenarios in random order in Treatment 2. In addition, a modification of the design in Treatment 3, which makes transparent to the subjects the generation of the random market revaluation, keeping the perceived risk constant for all upside participations, results in the 'too good to be true' effect being greatly reduced, without the need to present the scenarios in random order.
The policy implication of our main experimental finding is the importance of increasing the availability of categorized and ordered menus of directly comparable investments so that investors can study before investing. Simplifying the investors' information processing load could reduce the probability of their being lured into dubious extremely high offer investments. Exposing dark spots in the information about how the returns will be generated can inform investors about whether they should be cautious about trusting an offer (e.g. a Ponzi scheme).
Future research could explore the effectiveness of offering information that is ordered, categorized and clearly explained beforehand in fighting the trend bias while at the same time discouraging the 'too good to be true' bias by transparently generating the random market revalorization. In addition, exploring whether introducing a decreasing expected return ordering produces a penalizing effect for the funds would possibly be worth further investigation.