Master Thesis
Organisation Economics University of Amsterdam 2014/2015
Naive risk diversification and incentives in loan-based
crowdfunding
15 ECTS
Ben van Tongeren 10677496
2
1. Introduction
Risk diversification is a frequently discussed topic in the finance literature. A phenomenon that is discussed less widely is naive risk diversification. Naive risk diversification refers to investors using heuristics to spread their investments, with the intention to spread their risk. An example of naive risk diversification is the ‘1/n heuristic’. In this heuristic the investment budget is evenly spread over the investment opportunities, also refer to as the ‘1/n strategy’. Naive risk diversification is commonly seen at investors who are not financial experts. Benartzi & Thaler (2001) investigate naive risk diversification in savings plans among university employees and pilots, in particular the 1/n strategy. They find that between the 20 and 35 percent of their respondents pursue the 1/n strategy. Huberman & Jiang (2006) built their paper on Benartzi & Thaler (2001) and find the same results. The problem accompanying the use of the 1/n strategy is the fact that the portfolio of the investor can be off the efficient portfolio frontier and investors thereby get a lower return for the risk they take. This makes the use of the 1/n strategy remarkable, especially when the portfolio decision is important, as is the case in the papers of Benartzi & Thaler (2001) and Huberman & Jiang (2006).
This thesis investigates the use of the 1/n strategy in loan-based crowdfunding. In crowdfunding, not all investors are financial experts either. Crowdfunding websites advice investors to spread their investments over several projects to diversify risk. In this context the 1/n strategy means investors spread their investment budget evenly over several projects. This raises the question how crowdfunding investors spread their risk, if they follow the 1/n strategy and whether this is consistent with the results of Benartzi & Thaler (2001) and Huberman & Jiang (2006).
To investigate this the website geldvoorelkaar.nl is analysed. Geldvoorelkaar.nl is a loan-based crowdfunding website, where the project owner can combine the loan-loan-based model of crowdfunding with reward-based crowdfunding. In addition to rewarding the investor with an interest rate, project owners can also reward the investor with a discount or a free consumption of the product. This is typically done when a certain amount, a target, determined by the project owner, is invested. This feature is interesting because it can influence the use of the 1/n strategy. Another feature of the website geldvoorelkaar.nl, which makes the site useful for this paper, is the insight it gives in investments per investor
3 in a project. By combining different projects, an investment analysis per investor can be made. Through this analysis, I will explore whether investors in loan-based crowdfunding pursue naive risk diversification and whether incentives have an influence on naive risk diversification. This will contribute to the literature by testing whether the results of Benartzi & Thaler (2001) and Huberman & Jiang (2006), on naive risk diversification, hold in loan-based crowdfunding.
Results show, 22.82 percent of the investors in loan-based crowdfunding follow the 1/n strategy. This is in line with the results of Benartzi & Thaler (2001) and Huberman & Jiang (2006). Furthermore, incentives in loan-based crowdfunding decrease the use of the 1/n strategy. This is also according to the expectations, incentives can motivate investors to deviate from the 1/n strategy. Interesting is also the positive correlation between the interest rate of a project and the use of incentives. A negative correlation is expected since these two features can be seen as substitutes. Some investors invested at least once in every classification, in this group only 6.31 percent used the 1/n strategy. This is a remarkable result, but can be explained by optimal portfolio theory.
The set-up of the paper is as follows. Section two will discuss related literature in crowdfunding and the 1/n strategy. Section three will explain the hypotheses and the methodology. In section four the summary statistics of the data set will be provided, as well as the results which will test the hypotheses. In section five the limitations will be discussed and section six will conclude.
2. Related literature
In their literature review, Moritz & Block (2014) divide the crowdfunding literature in three subsections, namely capital-seekers, capital-providers and intermediaries. In this paper I will contribute to the capital-providers literature. Another distinction in the crowdfunding literature is made by Mollick (2014). Mollick (2014) describes four different types of crowdfunding. The difference between these types of crowdfunding is the way in which the owner of a project rewards the investor. A project owner can reward an investor with a product (in the reward-based model), a share (in the equity-based model), an interest rate (in the loan-based model) and the owner can see the investment as a donation (in the
4 patronage model). The focus of this paper will be on the loan-based model, in some cases combined with the reward-based model.
Another phenomenon in finance, which is similar to loan-based crowdfunding, is peer-to-peer lending. The basics are the same, lending and borrowing money through a community without the intervention of a bank. The difference is that in peer-to-peer lending investors bid on a loan and it is meant for established companies. Loan-based crowdfunding is meant for start-ups and early-stage businesses. Another difference is that loan-based crowdfunding can be combined with different types of crowdfunding.
Mollick (2014) has made an early contribution to the crowdfunding literature by exploring the determinants of success of crowdfunding projects. He focusses on the patronage and the reward-based model using data from Kickstarter. He finds that personal network and underlying project quality, such as including a video, posting updates or absence of common spelling mistakes, are determinants of getting a project financed. Determinants of success are not explored in this paper because of the inability to get data on the projects that did not succeed on the website geldvoorelkaar.nl. A shortcoming of Mollick (2014), as well as other papers who use data from Kickstarter, is that they do not have data on investments per investor and thus are not able to explore the dynamics of investors.
An et al. (2014) have found a way to gather information on personal investments on Kickstarter. An et al. (2014) actively followed projects on Kickstarter and the tweets about these projects on Twitter. They managed to gather data on investors and find an average of three projects backed per investor. However, this data could contain measurement bias. Investors could invest in a project without mentioning it on Twitter. On geldvoorelkaar.nl data on investment per backer is also directly observable.
‘1/n Strategy’
Geldvoorelkaar.nl advices backers to spread their investments over several projects1. My interest is in how backers spread their investments over several projects. Benartzi & Thaler (2001) and Huberman & Jiang (2006) find evidence for the 1/n strategy. Benartzi & Thaler (2001) test investment decisions of university employees and pilots in their pension plans and start with a survey where they ask the respondents to allocate their retirement contributions between two funds, Fund A and Fund B. Fund A and Fund B differ between
1 ‘Note: Geldvoorelkaar.nl advises you to spread your investment over several projects and only invest a responsibly amount of your total wealth through this platform.’
5 three conditions. In condition one, Fund A invested in stocks and Fund B invested in bonds. In condition two, Fund A again invested in stocks, but Fund B was a ‘balanced fund’, investing half of its assets in stock and half in bonds. In the last condition, Fund A was a balanced fund and Fund B was a bond fund. Through this survey they find that in condition one 34 percent of the respondents invested 50-50 between the funds, in condition two this was 21 percent and in the final condition 28 percent choose to divide their investment equally between the two funds. This means between 21 and 34 percent of the respondents pursue naive risk diversification.
However, a shortcoming of this set-up is that respondents are not incentivized when making the decision on asset allocation, which could bias the results upward. In a more realistic setting respondents might consider the asset allocation more carefully. Benartzi & Thaler (2001) also investigate a different interpretation of the 1/n strategy, where it is not about the question how many respondents choose the 1/n strategy but about how the choice for asset allocation depends on the available funds. In this different setting, university employees can choose between one stock fund and four bond funds. Benartzi & Thaler (2001) find these university employees invest 34 percent of their money in stocks. Pilots, on the other hand, can choose between five stock funds and one bond fund and results show pilots invest 75 percent of their money in stocks, which supports their claim on the 1/n strategy. To exclude risk-seeking behaviour of pilots driving the results, Benartzi & Thaler (2001) ran an extra experiment among university employees, where they had to make the asset-allocation decision in one of the two conditions. Findings were in line with the 1/n strategy.
Huberman & Jiang (2006) built their paper on Benartzi & Thaler (2001) and try to test their results with a different dataset. The focus of Huberman & Jiang (2006) is also on the 1/n strategy, but they clearly make a distinction in the meaning of the 1/n strategy. The first way they define the 1/n strategy is the relationship between the n’s chosen by the respondents and the n’s offered by the plans. Benartzi & Thaler (2001) find a positive relation, the more funds offered in a plan, the more funds respondents choose. However, Huberman & Jiang (2006) did not find a significant relationship between the amount of funds offered and the amount of funds chosen. The second way they define the 1/n strategy is the same as Benartzi & Thaler (2001) mainly do. The more equity funds are offered in the plans, the more equity funds are chosen by the respondents. Again, Benartzi & Thaler (2001) find a positive and significant relationship, where Huberman & Jiang do not find
6 any convincing evidence for this notion. The third and last interpretation of the 1/n strategy is more of interest for this thesis. Participants tend to spread their investments evenly over the funds chosen. Overall, 23.39 percent of the participants uses the 1/n strategy. This is consistent with the results of Benartzi & Thaler (2001). However, this percentage differs between groups. Huberman & Jiang (2006) divide the respondents by the amount of funds the respondents invest in.
Huberman & Jiang (2006) choose a different way to test whether respondents significantly belong to the group of respondents that use the 1/n strategy. In this thesis, respondents will be categorized by the variance of their investment, which will be extensively discussed later in this thesis. Huberman & Jiang (2006) use the Herfindahl index to check whether an investor significantly belongs to the 1/n category. This is a strong and inventive point of their paper. In this thesis, the Herfindahl index will be used to test the results for robustness.
Since investors in crowdfunding are not all financial experts and they are advised to spread their investments over several projects, the 1/n heuristic can also be at work in loan-based crowdfunding. A difference with Benartzi & Thaler (2001) is the opportunity to invest in a different kind of financial products, namely stocks and bonds. On geldvoorelkaar.nl investors only have the opportunity to invest in loan-based crowdfunding.
3. Methodology
In this section the methodology of this thesis will be discussed. First, a description of the data set will be provided. Then the hypotheses will be formulated and the methodology for testing these hypotheses will be explained.
Data set
The data set for the analysis is constructed with use of a data crawler, from the website import.io. With this data crawler I gathered the data from the website geldvoorelkaar.nl. The variables in the data set are the project number, risk classification, interest rate, a dummy for the use of incentives, a dummy for start-ups and the investors. The data set
7 contains 532 projects2 and 6026 investors and has a timespan from February 2011 till March 2015. In total €45.732.700,- is invested. Investors who invested only once are neglected for the analysis on the 1/n strategy, because they automatically use the 1/n strategy and this will bias my results. This restriction results in 4321 investors.
The risk classification variable is the variable which indicates the riskiness of the project. This variable can have the value 1, 2, 3 , 4, 5 and 5s, where 1 refers to the lowest risk (and 5 to the highest risk). 5s means the funding of the project is meant for a start-up company. Because of problems of dealing with the value 5s in Stata, I created a dummy variable for this value and replaced the value 5s for 5. The reason for combining classification 5 and 5s, is that on the website the riskiness of classification 5 and 5s are the same, but the reason for this riskiness is different3.
The interest rate variable is the variable that indicates the interest rate an investor gets per year when he invests in the project. The value range of this variable is 4 till 12 percent with increments of 0.5 and two exceptions of 3.8 and 5.7 percent
The incentive variable is a binary variable which equals 1 if the project makes use of an incentive and 0 otherwise. To construct this variable I extracted all the text per project from the website and saved it in an excel file. To determine whether the project used incentives I search in the excel file for the words ‘incentive’, ‘favour in return’, ‘discount’, ‘bonus’, ‘free’ and ‘reward’ as indicators of the use of incentives. I also search for the headers ‘other info’ and ‘what can we offer you’4, because these headers can indicate the use of incentives as well. With hits on these words I read the text on the project page and if they used an incentive I marked the project as a 1. All projects that did not gave a hit where marked as a 0. The downside of this approach is the fact that this variable can contain measurement bias, there could be projects that used an incentive but is recorded as if it did not use an incentive. To check whether there is measurement bias I checked a random sample of 20 projects which were recorded as no incentives, I find no use of incentives in these projects so I assume the measurement bias is negligible.
All the other variables are the ID-numbers of the investors. In these rows the investments per project are displayed and the projects which the investor did not invest in are marked as missing values.
2 I left two projects outside the analysis, because these projects where donation-based projects, which is outside the scope of this paper.
3 5 = very speculative (loan maximum 100% of pay off capacity)
5s = very speculative (payoff capacity unknown because of start-up status)
4 The Dutch words I search for were: ‘incentive’, ‘tegenprestatie’, ’korting’, ‘gratis’, ‘bonus’, ‘beloning’, ‘overige informatie’ & ‘wat kunnen wij u bieden’.
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Risk diversification
Because not every investor on geldvoorelkaar.nl is a financial expert, the website advices the investors to spread their investment budget over different projects in order to diversify their risk. Following Benartzi & Thaler (2001), the hypothesis is that investors follow the ‘1/n strategy’, which implies that investors spread their investment budget equally over projects. Benartzi & Thaler (2001), find that the percentage of respondents in their survey pursuing the 1/n strategy is 21, 28 or 34 percent, depending on the condition. Huberman & Jiang (2006) find evidence of 23.39 percent of the participants pursuing the 1/n strategy. Comparing their data with the data in this thesis, two factors can affect these results. Geldvoorelkaar.nl advices to invest in several projects, which can cause a higher use of the 1/n strategy. Geldvoorelkaar.nl also has more investment opportunities, this can have two effects. First, as discussed in Huberman & Jiang (2006), this can lead to an increase in the use of the 1/n strategy. Because of too much investment opportunities it is more likely for investors to use a heuristic. Second, it can lead to a decrease in the use of the 1/n strategy, because investors have more opportunities to deviate.
To test this hypothesis, I calculate the variances of the investments per investor. A variance of zero indicates the investor has invested the same amount in every project and thus pursing the 1/n strategy. However, there are also investors who are close to using the 1/n strategy and can be seen as using the 1/n strategy.
This group will be defined by the Mean Absolute Deviation (MAD)5. This measure is an indicator for the variance of the investments, but is relative to the total investments of an investor. The advantage of this feature is the comparability of investors, regardless of their investment budget. Another advantage is the fact that this measure can be expressed as a percentage of the total investments. In this way the group of investors that are close to pursuing 1/n can be indicated within a 5 percent level, as well as a 10 percent level.
Incentives
5
9 The second interest of this thesis is the combination of loan-based and reward-based crowdfunding. Project owners are allowed to use incentives in addition to the interest rate they give for the loan. These incentives can influence the investing behaviour of investors. Investors are, for example, more willing to deviate from the 1/n strategy to meet the target of the project owner in order to get a reward.
Following this reasoning the use of incentives will decrease the use of the 1/n strategy, resulting in the second hypothesis. To test this hypothesis, the same approach will be used as is used to test the first hypotheses, except the incentivized projects will be excluded of the analysis. The projects with incentives are excluded instead of the projects that did not use incentives, because this generates a larger data set. This results in an analysis of the use of the 1/n strategy in all projects and in projects that did not use an incentive. Comparing these group can confirm or reject the second hypotheses.
4. Results
In this section the results will be discussed. First, to give an insight in the data set, the summary statistics of the data set will be provided. The distribution of the variables, correlation between the variables and a first glance of the effect of incentives in loan-based crowdfunding will be explored. Then the results of the main focus of this thesis will be presented and the hypotheses will be tested.
Summary Statistics
Figures 1a, b, c and d show the distributions of the variables classification, interest rate, start-up and incentive, respectively. The high risk classification (classification 5) is the most frequent classification. This makes sense, since crowdfunding is often a way to get a project financed when the proper financial institutions find it too risky. Almost half of the class 5 projects are start-up projects (46,49 percent). The interest rate is that is mostly used is 8 percent. Higher interest rate are modal, which makes sense because of the abundance of high risk projects. Investors should be rewarded for taking risks. To confirm this notion, table 1 shows the correlation between the variables. The correlation between the interest rate and classification is, as expected, positive and moderately high. The same holds for the correlation between the interest rate and start-up. Because of the uncertainty a start-up
10 brings along the investor should be rewarded for taking the risk to invest in it, resulting in a higher interest rate. 159 (29,89 percent) projects make use of an incentive. The use of incentives will be discussed intensively later in this section.
An interesting statistic is the positive correlation between the interest rate and the use of incentives. A high interest rate and the use of incentives can both attract investors. It would be too much of the same thing to use them both, so in that sense they are substitutes and therefor a negative relationship is expected. This could be the result of herding behaviour by project owners, they use incentives because other projects owners use incentives as well. Herding behaviour is extensively investigated in the peer-to-peer literature (Berkovich, 2011; Herzenstein et al., 2011; Lee & Lee, 2012; Zhang & Liu, 2012), except from the perspective of capital-providers instead of capital-seekers.
Figure 2 shows the amount of investments per investor. 1705 (28,29 percent) investors invested only in one project, 642 (10,65 percent) investors invested in two projects and 440 (7,30 percent) invested in three projects. Interesting is the fact that one investor invested in 193 projects.
Figure 1a: Classification. This figure illustrates the distribution of the number of projects per classification. 53 75 92 41 271 0 50 100 150 200 250 300 1 2 3 4 5 A m o u n t o f p ro je cts Classification
CLASSIFICATION
11 Figure 1b: Interest Rate. This figure illustrates the distribution of the number of projects per interest rate.
Figure 1c: Dummy for start-up. This figure illustrates the number of start-up projects.
1 12 1 8 1 1 40 6 70 28 206 42 84 4 27 1 0 50 100 150 200 250 3,8 4 4,5 5 5,5 5,7 6 6,5 7 7,5 8 8,5 9 9,5 10 12 A m o u n t o f p ro je cts Interest Rate
INTEREST RATE
406 126 0 50 100 150 200 250 300 350 400 450 0 1 A m o u n t o f p ro je ctsDummy for Start-up
12 Figure 1d: Dummy for incentive. This figure illustrates the number of incentivized projects.
Incentive Interest rate Classification Start-up
Incentive 1
Interest rate 0.1911 1
Classification 0.213 0.5258 1
Start-up 0.2448 0.2463 0.4803 1
Table 1: Correlation matrix. This table illustrates the correlations between the variables.
373 159 0 50 100 150 200 250 300 350 400 0 1 A m o u n t o f p ro je cts
Dummy for the use of incentives
13 Figure 2: Amount of Investments per Investor. This figure illustrates the distribution of the amount of investments per investor.
To get a first glance of the influence of incentives in loan-based crowdfunding I neglect the projects that did use incentive and compare the summary statistics of all the projects with the summary statistics of the group of projects who did not use incentives. This results in 373 observations. The first variable to compare is the classification variable. A comparison between the two groups is made in Table 2. The distribution is skewed to the left when incentives are neglected, which implies that the use of incentives is more abundant in high risk classifications. This makes sense, projects with a high risk are more likely to use an incentive to induce investors to invest. However, a t-test does not confirm the difference in means. 1.705 642 440 324 181 85 65 36 27 23 8 6 6 5 3 2 0 200 400 600 800 1.000 1.200 1.400 1.600 1.800 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 A m o unt o f i nve st o rs
Amount of investmens per investor
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Classification All No incentive t-statistic
1 9.96% 12.33% 0.82 2 14.10% 16.35% 3 17.29% 19.03% 4 7.71% 8.05% 5 50.94% 44.24% Total 100.00% 100.00%
Table 2: Classification distribution. This table illustrates the comparison of the classification distribution between all projects and projects that did not use an incentive.
Interest Rate All No Incentive
3.8 - 5 4.14% 5.90%
5.5 - 6.5 9.03% 10.19%
7 - 8.5 65.03% 66.22%
9 - 12 21.80% 17.69%
Total 100.00% 100.00%
Table 3: Interest Rate distribution. This table illustrates the comparison of the interest rate distribution between all projects and projects that did not use an incentive.
The interest rates of the two groups show the same phenomenon. Table 3 shows interest rates are skewed to the left when incentivized projects are neglected, meaning that projects with incentives have higher interest rates. This is an interesting result, since a negative correlation between interest rates and the use of incentives is expected. As discussed before, interest rate and the use of incentives can be seen as substitutes.
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Start-up All No Incentive
0 76.32% 83.11%
1 23.68% 16.89%
Total 100.00% 100.00%
Table 4: Start-up distribution. This table illustrates the comparison of the start-up distribution between all projects and the projects that did not use an incentive.
Table 4 shows the comparison between the percentage of start-up when all projects are considered and when only projects are considered that did not use incentives. The results shows a positive correlation between start-ups and the use of incentives. This is according to the expectation. As mentioned before, to induce investors to invest in a start-up project it is more likely to use an incentive in comparison with regular projects.
1/n Strategy
The previous section gives insight in the variables of the data set and gives a first glance of the dynamics between loan-based and reward-based crowdfunding. However, the main interest of this paper is the naive risk diversification and the 1/n strategy specifically. In this section the hypotheses on the 1/n strategy will be tested and the research question will be answered.
First, the percentages of investors that actually use the 1/n strategy will be explored. This group is determined by calculating the variance of their investments. As mentioned before, investors who only invested once will be neglected. This results in 4321 observations. This is consistent with Figure 2, which shows 1705 investors only invested once. Second, the MAD per investor will be calculated at a 5 percent and 10 percent level. This gives a group of investors that is close to pursuing the 1/n strategy. Third and last, the Herfindahl index6 will be presented, to check for robustness.
6
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Condition % 1/n MAD<5% MAD<10% Herfindahl One year
All 22.82% 23.49% 25.41% 23.03% 25.46% No Incentive 25.13% 25.63% 27.25% 25.49% 28.23% No Start-up 22.76% 23.30% 24.91% 23.00% 25.38% Class = 1 27.90% 28.05% 29.38% 28.94% 34.04% Class = 2 27.05% 27.37% 28.51% 27.75% 32.61% Class = 3 27.11% 27.41% 29.30% 27.81% 31.73% Class = 4 34.72% 35.00% 36.57% 35.73% 36.83% Class = 5 27.27% 27.78% 29.47% 27.64% 30.65% All classes 6.31%
Table 5: Percentage of 1/n strategy. This table illustrates the percentage of investors that follow the 1/n strategy.
Table 5 shows the percentage of investors following the 1/n strategy per condition. The first condition is the condition where all the projects are analysed. In this condition 22.82 percent of the investors followed the 1/n strategy. The percentage is approximately the same when considering investors that are close to using the 1/n strategy. This is consistent with the results of Benartzi & Thaler (2001) and Huberman & Jiang (2006) and confirms the first hypotheses. Between 22.82 and 25.41 percent of the investors in loan-based crowdfunding pursue the 1/n strategy.
The second condition is the condition where projects with incentives are neglected. Table 5 shows 25.13 percent of the investors follow the 1/n strategy. The difference between the first two conditions remains approximately the same when considering investors close to using the 1/n strategy. A t-test confirms these two conditions are significantly different at a 5 percent level (t-statistic = -2.9). This confirms the second hypotheses. Incentives decrease the use of the 1/n strategy in loan-based crowdfunding.
In the third row of Table 5 the condition where start-up projects are neglected is presented. The first and third condition are significantly the same at a 5 percent level (t-statistic = 0.26), which indicates that start-up have no influence on the use of the 1/n strategy in loan-based crowdfunding. This is according to the expectation, since investors know beforehand that crowdfunding is a way of financing new businesses. The other conditions are conditions where only projects are examined within a certain classification. When projects
17 are ordered by classification the use of the 1/n strategy is increased. This makes sense, because according to portfolio theory you must invest equally in equally risky projects. The Herfindahl index is calculated to check the robustness of the MAD. A t-test shows the Herfindahl condition and the condition MAD<5% are significantly the same in the means at a 5 percent level (t-statistic = 0.09). The MAD<10% condition is significantly the same in the mean as the Herfindahl condition as well (t-statistic = -0.75).
Another interesting result that can be explained by optimal portfolio theory, is the use of the 1/n strategy of investors that invest in at least one project of every classification, which are 919 (21.27 percent) investors. Interesting is the percentage of investors that invest in at least one project of every classification and pursuing the 1/n strategy. This is only 6.31 percent, 58 out of the 919 investors, as is shown in Table 5. This is according to the expectations, investors investing in every classification are likely to pursue a diversification strategy. When pursuing a diversification strategy it is also likely to invest unequal amounts in different classifications.
5. Limitations
Because of the scope of this thesis I only have insight in the investment budget of the investors on the website geldvoorelkaar.nl. Investors might have other financial products they invest in and pursuing the 1/n strategy on a larger scale. On the other hand, they might pursue the 1/n strategy on geldvoorelkaar.nl, but on a larger scale they consider portfolio theory.
The timespan of the dataset is also an issue. Early investors might have pursued the 1/n strategy, but over the years their investment budget could have been increased or decreased. This could bias the results, since the investors are using the 1/n heuristic but are not recorded as such. Therefore I performed a robustness test to check whether this time component influenced the results downwards. I performed the same tests as in the original analysis, but only with the projects that were launched in the last year of the data set. Results show the use of the 1/n strategy is increased when only the last year of the data set
18 is analysed at a 10 percent significance level7 (t-statistic = -1.93). This means the results are biased downwards when the total data set is analysed, due to increasing opportunities for investors to deviate from the 1/n strategy.
The results of my paper will be generalizable to other loan-based crowdfunding sites, since the same concept is at work and investors have the same intentions. The results will not be generalizable to other models of crowdfunding. Mainly because the intentions of investors in the other models will differ from the loan-based crowdfunding model (Lin at al., 2014).
6. Discussion
Benartzi & Thaler (2001) and Huberman & Jiang (2006) made an early contributions to the literature on the 1/n strategy. In this paper I contribute to that literature by examining the use of 1/n strategy in loan-based crowdfunding in combination with incentives. For this analysis the website geldvoorelkaar.nl is used.
First, the summary statistics give an interesting result. There is a positive correlation between the interest rate and the use of incentives, where a negative correlation is expected. This could be a sign of herding behaviour by the project owners. Furthermore, high classification projects and high interest rates are abundant. This is according to the expectations because crowdfunding is a platform to finance early business. A first glance on the use of incentives confirm the correlations between classification, interest rate and the use of incentives.
The tests for the 1/n strategy confirm the hypotheses and answer the research question. The first hypotheses is confirmed by checking the variances of the investment of the investors. Between 22.82 and 25.41 percent of the investors in loan-based crowdfunding pursue the 1/n strategy, which is in line with the findings of Benartzi & Thaler (2001) and Huberman & Jiang (2006). The second hypothesis is confirmed by significantly showing the difference between the condition where all projects are analysed and the condition where only projects where analysed that did not use an incentive. Incentives decrease the use the 1/n strategy in loan-based crowdfunding.
7
19 The results of this thesis are in line with papers of Benartzi & Thaler (2001) and Huberman & Jiang (2006). Investors in loan-based crowdfunding make use of the 1/n heuristic. The use of incentives by investor influences the use of this heuristic. Investors change their strategy when incentives are used in loan-based crowdfunding.
DeMiguel et al. (2009) put the importance of diversification in perspective. They test 14 sophisticated diversification models, where they use the 1/n strategy as benchmark model. DeMiguel et al. (2009) conclude that none of the sophisticated models significantly outperforms the 1/n strategy. They stretch these results by indicating that it is more likely for the 1/n strategy to outperform other strategies when n is large, because this improves the potential for diversification.
It will be interesting for future research to investigate what determines the use of the 1/n strategy in loan-based crowdfunding and check if the results of are in line with Huberman & Jiang (2006) or Benartzi & Thaler (2001).
7. Appendix
MAD
To determine the investors that are close to using the 1/n strategy, the Mean Absolute Deviation per investor is calculated. The MAD can be calculated by adding all the absolute deviations from the mean and divide this by the amount of observations.
(1)
For this thesis the MAD is interesting when it is slightly changed, namely by not dividing by the amount of observations but by dividing by the total investment of an investor.
20 (2)
This results in a percentage of the absolute deviation relative to the total investment of the investor. Now all investors that did not use the 1/n strategy, but fall into a certain percentage level (5 or 10 percent) can be determined.
An example: Investor number: 1817 Amount of investments: 8 Total investment: €8600 Mean: €1075 Investments: €1000, €1000, €1000, €1000, €1100, €1100, €1200, €1200 MAD = (|1000-1075|+|1000-1075|+|1000-1075|+|1000-1075|+|1100-1075|+|1100-1075|+|1200-1075|+|1200-1075|)/8600 * 100% = 6.98%
Investor 1817 pursues the 1/n strategy in a 10 percent level.
Herfindahl index
To check for the robustness of the results of the MAD, the Herfindahl index is calculated. The Herfindahl index is also used by Huberman & Jiang (2006) to determine how many respondents fall inside the significance range and can be seen as pursuing the 1/n strategy.
The index is originally used in competition law and is determined to measure the size of firms relative to the industry. It can be seen as a measure of competition. Huberman & Jiang (2006) applied the formula to check is investors that are close to using 1/n can be seen as 1/n by calculating a significance range and check if the index falls inside this range. The Herfindahl index is calculated as follows:
21 (3)
S is the share of the total investment.
To check whether the index falls in the range a significance range must be determined. The upper bound is calculated by the following formula:
(4)
For this index is a 20 percent level used, just as Huberman & Jiang (2006) did. The lower bound is simply 1/n. This formula gives a problem when the investor invests only once but these investors are left out of the analysis in the first place.
Now can be simply determined if the index per investor falls within the significance range.
One year
To test for the robustness of the results only the last year of the data set is analysed. The analysis is the same as in the 1/n condition, so an analysis of variances.
Condition % 1/n MAD<5% MAD<10% Herfindahl One year
All 22.82% 23.49% 25.41% 23.03% 25.46% No Incentive 25.13% 25.63% 27.25% 25.49% 28.23% No Start-up 22.76% 23.30% 24.91% 23.00% 25.38% Class = 1 27.90% 28.05% 29.38% 28.94% 34.04% Class = 2 27.05% 27.37% 28.51% 27.75% 32.61% Class = 3 27.11% 27.41% 29.30% 27.81% 31.73% Class = 4 34.72% 35.00% 36.57% 35.73% 36.83% Class = 5 27.27% 27.78% 29.47% 27.64% 30.65%
Table 6: Percentage of 1/n strategy. This table illustrates the percentage of investors that follow the 1/n strategy.
22 Table 6 shows a significant difference at a 5 percent level between the condition where the total data set is used and the condition where the only the last year is used.
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