- Email: [email protected]

Risk aversion and under-hedging Tal Shavit a,1 , Uri Benzion b,2 , Ernan Haruvy c,∗ a

c

School of Management, College of Management, 7 Yitzhak Rabin Blvd., Rishon LeZion 75190, Israel b Department of Economics, Ben-Gurion University, Beer-Sheva 84105, Israel School of Management, University of Texas at Dallas, SM 32, P.O. Box 830688, Richardson, TX 75083, USA Received 15 April 2005; received in revised form 16 January 2006; accepted 21 April 2006

Abstract In a series of experiments, subjects allocate an endowment between assets. One of the assets, a bond or a composite asset, is dominated by a combination of two volatile assets. We explore settings and preferences that result in the dominated asset being chosen. The results show that subjects persist in allocating a significant portion of their funds to the dominated asset after 200 rounds. This finding can be explained by risk-averse investors’ inability to treat a combination of assets as a single distribution of payoffs. We find that risk-averse investors are more likely to persist in choosing dominated assets. © 2006 Elsevier Inc. All rights reserved. JEL classiﬁcation: C99; D81; D83 Keywords: Risk; Hedging; Experiments

1. Introduction Experimental studies on boundedly rational behavior in the laboratory have raised several concerns about investors’ ability to identify optimal long run investment strategies. Specifically, past experimental research has examined the issue of investors choosing inferior strategies in asset choice in the context of the equity premium puzzle (Gneezy & Potters, 1997; Gneezy, Kapteyn, & Potters, 2003; Thaler, Tversky, Kahneman, & Schwartz, 1997). In these studies, when given the choice to make one decision for the entire horizon, investors made allocations that were better ∗

Corresponding author. Tel.: +1 972 883 4865; fax: +1 972 883 6727. E-mail addresses: [email protected] (T. Shavit), [email protected] (U. Benzion), [email protected] (E. Haruvy). 1 Tel.: +972 3 963 4111; fax: +972 3 963 4210. 2 Tel.: +972 8 647 2306; fax: +972 4 823 5194. 0148-6195/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jeconbus.2006.04.002

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(payoff maximizing) than their decisions for each of the periods in the investment horizon. The typical explanation hinges on loss aversion being applied to each period as opposed to the entire horizon. This behavioral mode was termed myopic loss aversion (Benartzi & Thaler, 1995; Thaler, Tversky, Kahneman, & Schwartz, 1997). In a series of experiments we show that a similar fallacy applies to the inability to hedge in asset allocation problems. Specifically, combining two volatile yet negatively correlated assets resulting in a low-volatility portfolio is not treated by subjects as equivalent to a single asset, which yields a similar return pattern. Subjects are willing to purchase a single composite asset, which costs them a commission, but appear reluctant or unable to combine the volatile assets to form that same composite mix. The inability to effectively hedge is closely related to failure in self-insurance (e.g., Di Mauro & Maffioletti, 1996) and under-consumption of insurance (Hogarth & Kunreuther, 1989; Kunreuther & Pauly, 2004), particularly if one thinks of put options as insurance against stock losses. However, uncertainty, not risk, is typically responsible for inconsistencies in the pricing of insurance and stock options. In experiments involving professional actuaries pricing insurance (Hogarth & Kunreuther, 1989) and professional option traders pricing stock options (Fox, Rogers, & Tversky, 1996), professionals priced well with risk but appeared to display inconsistencies with uncertainty. Our settings involve risk but not uncertainty. We propose that in our setting, the inability to hedge can be explained by investors’ inability to treat a portfolio as a single distribution of payoffs and ignore the individual assets. We investigate investors’ ability to view asset returns as substitutable. Specifically, we examine whether subjects in the role of investors are able to recognize and avoid dominated strategies in experimental financial markets. We find that subjects are slow or unable to avoid dominated strategies in a portfolio allocation task. Moreover, subjects are willing to pay a substantial premium for a ready made composite portfolio which merely mixes between two other assets. We argue that this finding is important to understanding phenomena such as guaranteed-principal funds where fund managers charge high fees in return for hedging. We present three studies to investigate the portfolio’s allocation. In the first study, in a single period choice task, subjects are asked to choose between two uncorrelated assets, a 50:50 mix between the assets, and a fund which gives a distribution of payoff equal to the previous mix minus commission. Though the last choice is dominated, most subjects make exactly that choice. In the second study, we make allocations more flexible and allow for repeated feedback and learning. In the third study, in the same framework, the underlying assets are negatively correlated. In all three studies, subjects persisted in choosing dominated strategies. We find that subjects behave as if they were receiving disutility from variance in each individual asset as opposed to the combined portfolio. We term this modular risk aversion. This effect can also be thought of as a relative of the isolation effect of Prospect Theory (Kahneman & Tversky, 1979). The isolation effect means that in order to simplify the choice between alternatives, people often disregard the components that the alternatives share and focus on components that distinguish them. Modular risk aversion also closely resembles Thaler’s “mental accounting” (1990). An extension of Kahneman and Tversky’s “framing” principle, known as mental accounting, states that people draw their own frames. Thaler’s focus is on the boundaries between long-term saving, investment and consumption and short-term decisions and accordingly he draws examples from real life where people’s preferences for short-term saving and investment decisions are inconsistent with their long-term preferences. Modular risk aversion, on the other hand, applies to a single investment decision over a portfolio allocation.

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The rest of the paper is organized as follows: Section 2 defines the hypotheses, of our study. Section 3 describes the experimental procedure. Section 4 presents the major results and provides some possible explanations. Section 5 summarizes the relationship between risk aversion and hedging preferences and suggests implications. 2. Hypotheses The null hypothesis of individual rationality is one of the basic building blocks of both classical economic theory and finance theory. Specifically, individuals are assumed to be rational. Hypothesis 1 (The Rational Investor Hypothesis). A decision maker facing k assets would be indifferent between owning the k assets and owning a composite asset with the same payoff distribution. The alternative hypothesis, derived from extending the ideas of the isolation effect and mental accounting, is that individuals have irrational asset-specific risk aversion and that this aversion is not invariant to presentation formats. The modular risk aversion hypothesis is stated below: Hypothesis 2 (The alternative behavioral hypothesis—modular risk aversion). A decision maker facing k assets may not be indifferent between owning the k assets and owning a composite asset with the same payoff distribution. As explained in the introduction, modular risk aversion can be due to the fact that volatility in any of the k assets is unpleasant when observed and less unpleasant when hidden in the total returns of a composite asset. Irrational behavior may be a short-term phenomenon due to confusion or limited computation abilities. It may be that when given time and the right tools, investors may adjust over time in the direction of optimal allocation. Learning theories have been shown to provide explanation to a wide range of puzzles related to investor behavior and investment decisions, from the equity premium puzzle (Barron & Erev, 2003) to asset market bubbles (e.g., Fisher, 1998; Hommes, Sonnemans, Tuinstra, & van de Velden, 2002). Hypothesis 3 (Learning). Individuals can learn over time to reduce their allocations to dominated assets. 3. Experiments We report four studies. Studies 1 and 2 take place in a diversification setting and studies 3 and 4 take place in a hedging setting. The difference lies in the correlation of the primary assets. In a diversification setting, the primary assets are uncorrelated. In a hedging setting, the primary assets are negatively correlated, allowing for an even greater reduction in volatility. 3.1. Study 1—one shot in a diversiﬁcation setting The experiment of study 1 (instructions in Appendix A) gives subjects a choice between two assets, a combination of 50:50 of the same assets (equivalent to owning half a share of asset A and half a share of asset B), and a composite fund which is equivalent to the 50:50 payoff distribution minus a fee of 10 in all positive payoff outcomes. Note that in the negative outcome there is no fee and hence the expected payoff of asset C is 93 and not 90. The assets used in this choice task are given in Table 1.

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Table 1 Assets in studies 1 and 2 Asset A Lose 100 with probability 0.5 Make 300 with probability 0.5 Asset B Lose 100 with probability 0.6 Make 400 with probability 0.4 Asset C Lose 100 with probability 0.3 Make 90 with probability 0.3 Make 140 with probability 0.2 Make 340 with probability 0.2 Asset D Half of asset A and half of asset B (this gives half the prize or loss of asset A and half the prize or loss of asset B)

Note that asset D, which is a 50:50 combination of assets A and B, dominates asset C. However, if subjects are modularly risk averse, they may not wish to take the risk of losses on either asset (asset A or B), and may prefer the asset with the lower risk of observed losses (asset C). 3.1.1. Method The participants were all second and third year undergraduate economics students. Participants were recruited through an announcement on the economics department Internet bulletin board. In the announcement, second and third year economics students who were interested in participating in a computerized economics experiments were invited to sign up by email or SMS. A requirement for participating in the experiment was completion of the course “Statistics for Economics A”—the first statistics course for economics majors, which is a required course in the first year of the economics program. The course covers basic terminology in probability and statistics (e.g., mean, expected value, probability, correlation). We did not require nor collect information on participants’ business training or experience (this is examined in study 4). The students were permitted to use pen and paper or calculators for computations. No other tools were provided or permitted. Sixty participants were given the choice task as shown above. They were asked to choose among these four options. They were told they would be paid their winnings and their losses would be deducted from the show up fee. The show-up fee was 20 New Israeli Shekel and the exchange rate was 1 New Israeli Shekel (the local currency in Israel, hereafter NIS, which is roughly US$ 0.22) for five tokens. 3.2. Study 2—repeated allocation choice in a diversiﬁcation setting Providing repetition and feedback following each choice allows subjects an opportunity to move towards rational choice in response to feedback. To allow subjects to adjust to feedback, we presented the choice in study 1 as a repeated portfolio allocation decision (see Table 1). This presentation allows for adjustment over time. In addition, the allocation framework changes the problem from discrete choice between three alternatives to a continuous allocation choice of three assets.

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3.2.1. Method The participants in the experiment were undergraduate students who had taken a basic course in statistics (recruitment and prerequisite were the same as in study 1 and will remain the same for study 3). Written instructions (see Appendix B) were distributed and read aloud. The experiment was given on a computer interface programmed in an Excel Visual Basic macro. A sample screenshot for a four-asset version (used in experiment 3) is provided in Appendix F. The experiment lasted approximately 1 h. Subjects chose allocations between three assets—the first three assets of study 1. The assets were labeled neutrally as asset A, asset B and asset C. Each subject repeated the portfolio allocation decision 200 times following 10 preliminary rounds for practice. Each round was followed by an on-screen report of each individual asset’s return in that period as well as the return on the portfolio chosen by the subject in that round. The subjects were informed that following the completion of the experiment, only one round would be randomly picked for each subject to determine payment for the experiment (in order to avoid a possible wealth effect). The payment would be 15 NIS, plus the return on the portfolio in the chosen round (exchange rate was 1 NIS for five tokens). 3.3. Study 3—repeated allocation choice in a hedging setting In study 3, we investigate a hedging setting. The difference between this setting and the diversification setting is that two assets (stock and put) are negatively correlated whereas in the diversification setting the assets were independent or positively correlated. This experiment was divided into three treatments. Each subject was assigned to only one of the three treatments. In each treatment, subjects faced repeated allocation decisions over two negatively correlated assets and one or two other assets. Feedback was given following each allocation round. In two treatments there were three assets presented to subjects and in a third treatment there were four assets. Asset A represents a low risk Bond. Asset B represents a stock priced at 70, and asset C represents a put option on the stock with a price is 45, a strike price is 90 and a coupon of 32.3 Asset D represents a composite asset, which is the minimal-risk mixture of assets B and C minus a commission. Asset D could be replicated by combining assets A and B in the right proportions. We refer to this composite as Mix E. Mix E is not one of the alternatives shown on the screen. It represents a self-made hedge, which is the same mixture as asset D but without the commission. The assets are described in Table 2. The computations of the returns from the above assumptions are available in Appendix E. Subjects were able to allocate their funds to any of the above assets in any proportion. As such, asset D is dominated by a self-made hedge (Mix E). The self-made hedge is made by a mixture of 0.608 stock, and 0.392 put option (see Table 3). In comparison, the ready made hedge (asset D) is made by the same mixture with a commission of 0.8%. There were three experimental treatments within this study: • Treatment 3a: allocation between assets A–C. • Treatment 3b: allocation between assets B–D. • Treatment 3c: allocation between assets A–D. 3

Put options generally do not pay a coupon. Hence, this asset can be thought of as a mix of put option and bond.

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Table 2 The asset return distributions Probability

Asset Aa , rate of return

Asset B, rate of return

Asset C, rate of return

Asset D, rate of return

Mix E, rate of return

0.2 0.5 0.3

4% (0.3), 5% (0.4), 6% (0.3) 4% (0.3), 5% (0.4), 6% (0.3) 4% (0.3), 5% (0.4), 6% (0.3)

−30% 10% 30%

62% 0% −29%

5.30% 5.30% 6.10%

6.1% 6.1% 6.9%

Mean return S.D.

5% 0.77%

5.54% 0.37%

6.34% 0.37%

a

8% 20.88%

3.70% 31.80%

Asset A is independent of the other assets. The probabilities for asset A returns are in parentheses.

In each treatment subjects could create Mix E by themselves and choose the amount of allocation to this mix. To describe subjects’ allocation to the different assets as well as the self-made hedge, we subtract the allocation that could be considered a self-made hedge and give only the net allocation to the other assets. We refer to these net allocations as ‘naked stock’ and ‘naked put.’ Note that in contrast to a full hedge, the mix of stock and put (Mix E) does not give the exact same return in each state and so it can be considered only a partial hedge. 3.3.1. Method The recruitment and prerequisites are as in studies 1 and 2. The instructions (see Appendix C) and procedures are as in study 2. Specifically, each subject repeated the portfolio allocation decision 200 times following 10 preliminary rounds for practice. Each round was followed by an on-screen report of each individual asset’s return in that period as well as the return on the portfolio chosen by the subject in that round. In each round, the subjects were asked to allocate the 100 tokens they got among the available assets. 3.4. Study 4—experienced investors The studies discussed so far are with subjects that have a background in statistics but not necessarily in investing. To gauge the external validity of the results, we surveyed MBA students, some of whom had substantial work experience in investment banking. Others had experience in stock investments for themselves. The survey (see Appendix D) gave them an allocation choice between three assets with which they should be familiar. The allocation was to be made at the beginning of the year and the assets kept for the entire year. The first asset is the SPDR exchange traded fund (stock symbol SPY) which is a fund that closely tracks the S&P 500 index. The S&P Table 3 The self-made hedge Probability

0.2 0.5 0.3

Proportion

Asset’s rate of return

Stock (B)

Put (C)

Stock (B)

Put (C)

0.608 0.608 0.608

0.392 0.392 0.392

−30% 10% 30%

62% 0% −29%

The returns are rounded.

Mix E’s rate of return

0.608 (−30%) + 0.392 (62%) ≈ 6.1% 0.608 (10%) + 0.392 (0%) ≈ 6.1% 0.608 (30%) + 0.392 (−29%) ≈ 6.9%

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Table 4 Historical returns shown to participants in study 4 SPY (%)

Put option (%)

XYZ (%)

−10.31 −21.17 22.14 8.15 5.94

95.50 502.69 −100.00 −100.00 −100.00

−8.14 −6.46 17.47 3.91 1.76

500 index is one of the most closely watched indexes among investors and it is reasonable to assume that people with investment experience would be familiar with it. The second is a put option on SPY, with a strike price of 5% below the SPY price at the time of investment. The put option was priced according to the Black–Scholes formula, which may not always be accurate but which is familiar to investors and especially to MBA students. The third asset was the XYZ fund, a fictitious fund we created for the purpose of this survey, but which operates similarly to some Principal Protected Funds. It uses 3% of the fund to buy put options with a strike price of 5% below the SPY price at the beginning of the year. The fund holds the options to expiration date. In addition, it charges a 1% annual management fee. The workings of the fund were explained in detail to the survey participants. In addition, actual historical returns for the past 5 years (based on the performance of the S&P 500) were shown to participants. These returns are also displayed in Table 4. After answering a survey regarding investment risk preferences and investment experience, subjects were asked to choose an allocation between the three funds based on the given historical information. 4. Results 4.1. Study 1 The majority of subjects, 32 in all (53.33%), chose asset C—the dominated choice, while only 13 subjects (21.67%) chose asset D, the dominant asset. The distribution of choices is shown in Table 5. 4.1.1. Discussion We conclude that the rational investor hypothesis (Hypothesis 1) is rejected in favor of the alternative behavioral hypothesis (Hypothesis 2). Individuals prefer a fund that does not show individual asset losses to a combination of assets that yields the same distribution of returns but shows individual asset losses. Table 5 Choices in study 1 Choice

Number making this choice

Percent making this choice (%)

Asset A Asset B Asset C Asset D

7 8 32 13

11.67 13.33 53.33 21.67

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Fig. 1. Average allocation in experiment 2 over 5 blocks of 40 rounds.

4.2. Study 2 Since subjects are now required to distribute their endowment across three assets, as opposed to making a single choice among three alternatives, they are inclined to begin with a roughly uniform distribution among the assets and gradually adjust. Fig. 1 below shows subject allocation over time. Over time, subjects learn to reduce their allocation to the dominated asset (asset C). A comparison of the first 10 periods and the last 10 periods’ allocation to asset C shows that the reduction in allocation to asset C is significant (the mean difference in allocation to asset C is 12.05, with a t-statistic of 2.68, and P-value of 0.0149, 20 d.f.). Hence, we can reject the rational investor hypothesis (Hypothesis 1) since individuals are clearly unable to avoid dominated portfolio allocation choices. The evidence supports Hypothesis 3 that individuals learn over time to reduce dominated portfolio allocation choices. 4.3. Study 3 Fig. 2 shows the actual allocations in the three treatments to self-made hedging, naked stock, naked put option, bond and market hedging averaged over individuals and periods in each of five blocks of 40 periods. Table 6 shows the results for the first and last block in each treatment: In treatments 3a and 3c it appears that subjects reduce their allocation to the bond over time. Although in treatment 3c, they have the possibility of investing in the market hedge, which clearly dominates the bond, they nevertheless allocate in the last block an average of 8.49% of their endowment to the bond. This result provides another rejection of hypothesis 1 and support for Hypothesis 3 that individuals learn over time to reduce dominated portfolio allocation choices. When market hedging is made available (treatment 3c), the allocation to the bond decreases compared to treatment 3a where the market hedging is unavailable. The average allocation to the bond in the last 40 rounds block in treatment 3a is significantly higher than the average allocation to the bond in the last 40 rounds block in treatment 3c (t = 2.15, P = 0.036). Although subjects decrease their investment in the market hedging in treatment 3c, they nevertheless persist in allocating substantial portions to that option (17.08% in the last block). In treatment 3b, we could not reject the hypothesis that subjects did not change their investment in this asset. These results are consistent with Hypothesis 2 since subjects failed to reach the hedging portfolio by themselves.

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Fig. 2. Asset allocation over time in the three treatments.

Finally, to test the conjecture of modular risk aversion as one possibility for the preference for dominated assets, we collected risk attitudes from subjects and compared allocations for subjects with different risk preferences. To obtain risk attitudes, we used the certainly equivalence (CE) approach. We asked the subjects to bid for a lottery in three second price sealed bid auctions. Subjects were provided with initial endowment of 100 tokens and were asked to bid on the following lotteries, presented in Table 7. We used the ratio between the bidding price and the lottery’s expected value as a measure of risk attitude. We group the subjects according to their risk attitudes as revealed in the auction. We group the top half of the subjects in the “high risk averse” group and the bottom half in the “low risk averse” group. In Table 8, we present the results of the regression analysis (for treatments 3b and 3c together). The dependent variable is the allocation to market hedging and the independent variables are two dummy variables for treatment (0 for treatment 3b, 1 for treatment 3c) and

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Table 6 Allocations and allocation ratios—first and last block of each treatment Treatment 3a

Bond Naked stock Naked option Self-made hedge Market hedge Hedging assets Low risk assets Average ratio of self hedging to total low risk assets * **

Treatment 3b

Treatment 3c

First block

Last block

First block

Last block

First block

Last block

22.02 25.5 15.95 36.53 – 36.53 58.55 0.58

17.43* 38.67** 13.78 30.12* – 30.12* 47.55** 0.58

– 36.14 20.23 19.38 24.25 43.63 43.63 0.44

– 40.29 17.99 16.91 24.82 41.73 41.73 0.32**

18.04 16.39 16.75 21.67 27.15 48.82 66.86 0.3

8.49** 35.56** 15.49 23.38 17.08** 40.46* 48.95** 0.41**

Significance at 10% level for difference between the first and last blocks. Significance at the 5% level for difference between the first and last blocks.

Table 7 Lotteries used to capture risk attitudes Probability

Outcome

0.5 0.5 Expected return Standard deviation

Lottery 1

Lottery 2

Lottery 3

80 40 60 20

100 20 60 40

100 50 75 25

risk aversion classification (0 for low risk averse, 1 for high risk averse,). We ran the regression separately for the first 40 rounds, the last 40 rounds, and for all rounds. The results show that on average the allocation to market hedging is higher by 9.96 for the high risk-averse subjects (in all rounds of the regression). There is no significant difference between the two treatments although subjects could allocate to the bond in treatment 3c. Table 8 Regression results Constant

Risk group

Treatment

R2

First block Estimate T-test (P-value)

20.2 T = 5.06 (0.00)

7.93 T = 1.784 (0.08)

3.06 T = 0.68 (0.498)

0.079 F = 1.8 (0.178)

Last block Estimate T-test (P-value)

21.6 T = 4.04 (0.00)

6.42 T = 1.08 (0.28)

−7.6 T = −1.27 (0.21)

0.064 F = 1.42 (0.25)

All rounds Estimate T-test (P-value)

18.96 T = 4.43 (0.00)

9.96 T = 2.1 (0.04)

−1.99 T = −0.418 (0.678)

0.099 F = 2.31 (0.112)

Dependent variable is allocation to market hedging.

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Table 9 Allocations to stock index, put option and XYZ fund Classification

Low risk aversion (N = 31) High risk aversion (N = 31) No personal investment experience (N = 12) Some personal investment experience (N = 50) No investment banking experience (N = 34) Some investment banking experience (N = 28)

Asset allocation XYZ

SPY

PUT

0.36 0.36 0.35 0.36 0.38 0.34

0.46 0.52 0.50 0.49 0.48 0.51

0.17 0.12 0.15 0.14 0.14 0.15

4.4. Study 4 Table 9 shows the mean allocations by investment banking experience, personal investment experience, and risk aversion. Consistent with the previous studies, 35–38% of subjects of all levels of experience chose the dominated fund. None of the classifications had a significant effect on the allocation to any of the assets. The results demonstrate that subjects with investment knowledge and experience facing historical information of the kind typically given in an investment prospectus do not exhibit more or less bias in judgment relative to less experienced subjects. 5. Conclusions The experimental findings indicate that subjects are either unable to or unwilling to pick dominant strategies when such strategies involve the mixing of assets. Although subjects can create a dominant portfolio by the mixing of assets, they allocate substantial amounts to a dominated ready made composite portfolio when one is available. This result is more pronounced when the subjects are highly risk averse, as determined by a lottery auction task. However, when subjects face the ready made portfolio together with the bond (which is clearly dominated by the ready made portfolio) they quickly reduce the allocation to the bond relative to the treatment without the market hedging. That is, when one asset is clearly dominated by another, subjects can and do learn to reduce allocation to the dominated asset. We identified modular risk aversion as one possible explanation, shown very clearly in study 1, but there are of course other possible explanations. The inability of subjects to identify and avoid dominated strategies in the laboratory is consistent with Stahl and Haruvy (2003), and Ben Zion, Haruvy, and Shavit (2004). Stahl and Haruvy (2003) showed that subjects were unable to avoid dominated strategies that were not obvious. In Ben Zion et al. (2004), learning models were provided to show that simple adaptive learning would not lead subjects to optimal choices over time. In contrast to these and other past works, however, we showed that subjects make choices that would appear to indicate a preference for a dominated strategy and that this behavior is persistent over time. We showed that modular risk aversion is related to subjects’ risk preferences as revealed in auction-induced valuations for lotteries. It is important to note that the preference for a dominated ready made hedge over a self-made hedge resembles but cannot be explained by Benartzi and Thaler’s (1995) myopic loss aversion. First, subjects’ earnings were not cumulative (one decision was chosen at random for payment), so there should be no difference between a subject’s one period’s preference and his full horizon’s

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preference. Second, the self-made hedge involves no losses on one’s portfolio in any state of the world and therefore myopic loss aversion does not apply. The hedged portfolio does, however, involve losses in components of one’s portfolio, which myopic loss aversion does not deal with. The finding that decision makers may prefer to pay a fee for a ready made hedge to a selfmade hedge may be related to the popularity of guaranteed-principal funds. The idea behind such funds is that when the stock market goes down, the investor does not lose his principal, but when the stock market goes up, he gets a fraction of the rise, up to some limit. The strategies used to provide guaranteed principal funds are similar to the market hedging mix of this work. While these strategies are clever, they may not justify the high fees that have been described in the press as “exorbitant” (Clash, 2003).4 The reader should be cautioned that the environment faced by participants here is arguably different from that faced by investors. Real investors spend significantly more time on their investment decisions and are exposed to more information and advice than the participants in our experiments. Hence, additional steps may be required before extending the insights obtained here to real investment environments. Appendix A. Translated instructions for study 1 • Welcome to an experiment in decision-making. • In this experiment you will be asked to choose between lotteries. • At the end of the experiment the lottery outcomes will be determined based on random draws by the computer. • The payment for the experiment participation will be 20 NIS + the token payment from your chosen lottery at an exchange rate of 1/5 NIS per token. For example: If the token payment for the lottery you chose is 120 tokens you will get 44 NIS for the experiment (20 + 120 × 1/5). Please choose one of the following lotteries: Choice A: The lottery outcome is as follows: Chance (%)

Outcome

50 50

−100 300

Choice B: The lottery outcome is as follows: Chance (%)

Outcome

60 40

−100 400

4 Clearly, some fees are justified. Gruber (1996) lists four reasons for why individuals might be willing to pay fees for mutual funds: (1) customer service, (2) low transaction costs due to scale, (3) diversification, and (4) professional management. Barclay, Pearson, and Weisbach (1998) note in addition the sensitivity of mutual fund managers to capital gains taxes. Further, there is some evidence, albeit far from consensus, that some mutual fund managers consistently do better, hence justifying higher fees (e.g., Chevalier & Ellison, 1999; Goetzmann & Ibbotson, 1994; Patel, & Zeckhauser, 1993).

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Choice C: The lottery outcome is as follows: Chance (%)

Outcome

30 30 20 20

−100 90 140 340

Choice D: This choice will give you two lottery tickets, the outcomes of which are independently determined. The two lotteries are Chance (%)

Outcome

50 50

−50 150

Chance (%)

Outcome

60 40

−50 200

Appendix B. Translated instructions for study 2 • • • • • • • •

Welcome to an experiment in decision-making. In this experiment you will be asked to allocate tokens among assets. You will participate in 200 rounds. In each round you will get 100 tokens to invest in the assets A–C. You must invest all your tokens in each round. Following each round, you will observe your earnings as well as the return for each asset. Your earning from each asset is the asset’s return multiplied by your allocation to that asset. Prior to the experiment, you will have 10 practice rounds to familiarize you with the interface.

The assets: The assets are described as follows: Asset A: In each round the computer will randomly pick a number from 1 to 10 (with equal chance for all numbers). This number will determine the return for asset A as follows: Selected number

Return (%)

1–50 51–100

−100 300

Asset B: In each round the computer will randomly pick a number (with equal chance for all numbers) from 1 to 100. This number is drawn independently of the number for asset A. The number picked will determine the returns for asset B as follows: Selected number

Return (%)

1–60 61–100

−100 400

Asset C: In each round the computer will randomly pick a number (with equal chance for all numbers) from 1 to 100. This number is drawn independently of the numbers for assets A and B.

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The number picked will determine the returns for asset C as follows: Selected number

Return (%)

1–30 31–60 61–80 81–100

−100 90 140 340

Hypothetical example: Step 1: You have 100 tokens to allocate among A–D. Let us say you selected to allocate 35, 35, and 30 tokens for assets A–C, respectively. Total amount to A Total amount to B Total amount to C

35 35 30

Step 2: The computer draws random numbers: Let us say for A: 12; B: 89; C: 74 Step 3: We will see your allocation and profit for each asset and the profit from your portfolio. Asset A B C Total

Allocation

Return (%)

Profit

Value

35 35 30

−100 400 140

−35 140 42

0 175 72

100

147

147

247

{Total profit calculation: −35 (asset A profit) + 140 (asset B profit) + 42 (asset C profit) = 147}.

* After getting the information on the final value you will start a new round. In the new round you will get initial endowment with no relation to your payoffs in previous rounds. The payoffs in the end of each round are not accumulated. Payment for the experiment participation: At the end of the experiment, one of the rounds you participate in will be randomly selected by the experiment’s software. The payment for the experiment participation will be 15 NIS plus half of the profit at the selected round. Hypothetical example: Let us say the portfolio’s profit at the selected round is 10.33 tokens. The payment for the experiment participation will be 20.2 NIS (15 + 10.33/2 = 20.2). Appendix C. Translated instructions for study 3 • • • • • • • •

Welcome to an experiment in decision-making. In this experiment you will be asked to allocate tokens among assets. You will participate in 200 rounds. In each round you will get 100 tokens to invest in assets A–D. You must invest all your tokens in each round. Following each round, you will observe your earnings as well as the return for each asset. Your earning from each asset is the asset’s return multiplied by your allocation to that asset. Prior to the experiment, you will have 10 practice rounds to familiarize you with the interface.

The assets: The assets are described as follows: Asset A: In each round the computer will randomly pick a number from 1 to 10 (with equal chance for all numbers). This number will determine the return for asset A as follows:

T. Shavit et al. / Journal of Economics and Business 59 (2007) 181–198 Selected number

Return (%)

1–3 4–7 7–10

4 5 6

195

Assets B–D: In each round the computer will randomly pick a number (with equal chance for all numbers) from 1 to 100. This number is drawn independently of the number for asset A. The number picked will determine the returns for assets B–D as follows: Selected number

Asset B return (%)

Asset C return (%)

Asset D return (%)

1–20 21–70 71–100

−30 10 30

62 0 −29

5.3 5.3 6.1

Hypothetical example: Step 1: You have 100 tokens to allocate among A–D. Let us say you selected to allocate 25 tokens for each asset. Total amount to A Total amount to B Total amount to C Total amount to D

25 25 25 25

Step 2: The computer draws random numbers: Let us say for A: 2; B–D: 15. Step 3: We will see your allocation and profit for each asset and the profit from your portfolio. Asset A B C D Total

Allocation 25 25 25 25 100

Return

Profit

4 −30 62 5.3

1 −7.5 15.5 1.33

26 17.5 40.5 26.33

10.33

110.33

10.35

Value

{Total profit calculation: 1 (asset A value) − 7.5 (asset B value) + 15.5 (asset C value) + 1.33 (asset D value) = 10.33}.

* After getting the information on the final value you will start a new round. In the new round you will get initial endowment with no relation to your payoffs in previous rounds. The payoffs in the end of each round are not accumulated. Payment for the experiment participation: At the end of the experiment, one of the rounds you participate in will be randomly selected by the experiment’s software. The payment for the experiment participation will be 15 NIS plus half of the profit at the selected round. Hypothetical example: Let us say the portfolio’s profit at the selected round is 10.33 tokens. The payment for the experiment participation will be 20.2 NIS (15 + 10.33/2 = 20.2) Appendix D. Instructions for study 4 We will now ask you to select an allocation of funds between three assets: (1) the XYZ Principal Protected Fund, (2) the SPY index fund, which tracks the S&P index, (3) a put option at a strike price of the 5% below the SPY at the beginning of the year with 1 year maturity.

196

T. Shavit et al. / Journal of Economics and Business 59 (2007) 181–198

SPY is a real traded index fund and the returns we use here are actual returns for the past 5 years. The put options returns are computed under the assumption that the put options are priced at Black–Scholes prices in the beginning of the year. The XYZ fund is a fictitious fund we created for the purpose of this survey, but it operates similarly to some Principal Protected Funds. It uses 3% of the fund to buy put options with a strike price of 5% below the SPY price at the beginning of the year. The fund holds the options to expiration date. In addition, it charges a 1% annual management fee. Historical returns for the past 5 years are shown below for each asset. Year

SPY (%)

Put option (%)

XYZ (%)

1 2 3 4 5

−10.31 −21.17 22.14 8.15 5.94

95.50 502.69 −100.00 −100.00 −100.00

−8.14 −6.46 17.47 3.91 1.76

Your allocation: SPY index fund Put option on SPY XYZ principal protected fund

% % %

Total

100%

Appendix E. The computations of returns based on the assumptions Assumptions: The stock price is 70. The put option strike price is 90 and the put option price is 45. This put option also gives a coupon of 32 (and hence can be thought of as a combination of put and bond). The payoffs on the stock are assumed to be Probability

Stock

0.2 0.5 0.3

49 77 91

Since the option’s strike price is 90 and it gives a coupon of 32, the return is Probability

Option

0.2 0.5 0.3

(90 − 49) + 32 = 73 (90 − 77) + 32 = 45 0 + 32 = 32

Finally, the return in percentage gain over the initial cost of the asset is: Probability

Stock Option

0.2

0.5

0.3

49/70 − 1 = −30% 73/45 − 1 = 62%

77/70 − 1 = 10% 45/45 − 1 = 0%

91/70 − 1 = 30% 32/45 − 1 = −29%

T. Shavit et al. / Journal of Economics and Business 59 (2007) 181–198

197

Appendix F. Sample screenshot for study 3

References Barclay, M. J., Pearson, N. D., & Wisbach, M. S. (1998). Open-end mutual funds and capital gains taxes. Journal of Financial Economics, 49, 3–43.

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Barron, G., & Erev, I. (2003). Small feedback-based decisions and their limited correspondence to description-based decisions. Journal of Behavioral Decision Making, 16(3), 215–233. Benartzi, S., & Thaler, R. H. (1995). Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics, 110(1), 73–92. Ben Zion, U., Haruvy, E., & Shavit, T. (2004). Adaptive portfolio allocation with options. Journal of Behavioral Finance, 5(1), 43–56. Chevalier, J., & Ellison, G. (1999). Are some mutual fund managers better than others? Cross-sectional patterns in behavior and performance. Journal of Finance, 54(3), 875–899. Clash, J. M. (2003). Guaranteed!. Forbes, 171(12), 18–118. Darryll, H., Patel, J., & Zeckhauser, R. (1993). Hot hands in mutual funds: Short-run persistence of performance, 1974–1988. Journal of Finance, 48, 93–130. Di Mauro, C., & Maffioletti, A. (1996). An experimental investigation of the impact of ambiguity on the valuation of self-insurance and self-protection. Journal of Risk and Uncertainty, 13(1), 53–71. Fisher, E. (1998). Explaining bubbles in experimental asset markets, Ohio State Working Paper. Fox, C. R., Rogers, B. A., & Tversky, A. (1996). Options traders exhibit subadditive decision weights. Journal of Risk and Uncertainty, 13(1), 5–17. Uri, G., Kapteyn, A., & Potters, J. (2003). Evaluation periods and asset prices in a market experiment. Journal of Finance, 58, 821–837. Gneezy, U., & Potters, J. (1997). An experimental test on risk taking and evaluation periods. Quarterly Journal of Economics, 112, 631–645. Goetzmann, W. N., & Ibbotson, R. G. (1994). Do winners repeat? Patterns in mutual fund performance. Journal of Portfolio Management, 20, 9–18. Gruber, M. J. (1996). Another puzzle: the growth in actively managed mutual funds. Journal of Finance, 51(3), 783–810. Hogarth, R. M., & Kunreuther, H. (1989). Risk, ambiguity and insurance. Journal of Risk and Uncertainty, 2, 5–35. Hommes, C., Sonnemans, J. Tuinstra, J. & van de Velden, H. (2002). Expectations and bubbles in asset pricing experiments, Working Paper, University of Amsterdam. Kahneman, D., & Tversky, A. (1979). Prospect theory: Analysis of decision under risk. Econometrica, 47, 263–291. Kunreuther, H., & Pauly, M. (2004). Neglecting disaster: Why don’t people insure against large losses. Journal of Risk and Uncertainty, 28(1), 5–21. Stahl, D. & Haruvy, E. (2003). Level-n bounded rationality and dominated strategies in normal-form games, Working Paper. Thaler, R. H. (1990). Anomalies: Saving, fungibility, and mental accounts. The Journal of Economic Perspectives, 4, 193–205. Thaler, R. H., Tversky, A., Kahneman, D., & Schwartz, A. (1997). The effect of myopia and loss aversion on risk taking: An experimental test. The Quarterly Journal of Economics, 112, 647–661.