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The disposition effect, performance, stop loss orders and education
Journal Pre-proof The disposition effect, performance, stop loss orders and education Tõnn Talpsepp, Tarvo Vaarmets
PII: DOI: Reference:
S2214-6350(19)30086-3 https://doi.org/10.1016/j.jbef.2019.100240 JBEF 100240
To appear in:
Journal of Behavioral and Experimental Finance
Received date : 21 April 2019 Revised date : 1 September 2019 Accepted date : 19 September 2019 Please cite this article as: T. Talpsepp and T. Vaarmets, The disposition effect, performance, stop loss orders and education. Journal of Behavioral and Experimental Finance (2019), doi: https://doi.org/10.1016/j.jbef.2019.100240. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
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The disposition effect, performance, stop loss orders and education*
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Tõnn Talpsepp†, Tarvo Vaarmets‡ Current version: August 21, 2019
Abstract
The paper studies how simulated stop loss orders affect the disposition effect and performance
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by running simulations using a complete transaction dataset from Nasdaq Tallinn which includes all investors in the market. We combine transaction data with detailed educational registry data about individual investors. We show that stop loss orders reduce the disposition effect but only to a certain extent, and they can be harmful to performance at the same time. We
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study how educational factors moderate the association of performance and the disposition
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effect, with mixed results.
Keywords: disposition effect, performance, stop loss orders, education, mental abilities JEL classification: G02, G11
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We are grateful to Kalle Viks and Nasdaq OMX Tallinn Stock Exchange, Marko Mölder and Estonian Ministry of
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Education and Science, Lauri Veski and Innove, Aime Lauk and Statistics Estonia for the data and their supportive attitude and efforts for processing our data requests. †
Corresponding author, Tallinn University of Technology, Department of software sciences; Estonian
Entrepreneurship University of Applied Sciences; Aalto University, Department of Finance; address: Akadeemia tee 15A, 12618 Tallinn, Estonia; [email protected]. Declarations of interest: none. ‡
Department of economics and finance, Tallinn University of Technology, Akadeemia tee 3, 12618 Tallinn,
Estonia. Declarations of interest: none. 1
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1. Introduction It is difficult to underestimate the impact of the disposition effect on the behaviour and performance of investors. The disposition effect was first documented by Shefrin & Statman (1985) and is defined as the tendency of investors to “sell winners too early and ride losers too
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long”. While there is a broad consensus about the existence of the disposition effect and the effects of various factors, the reasons for the effect and its impacts are not so unequivocal. Most of the literature uses the prospect theory developed by Kahneman & Tversky (1979) to explain the disposition effect but e.g. Barberis & Xiong (2009), Kaustia (2010), Hens & Vlcek (2011) and Meng & Weng (2017) provide some alternative explanations. This suggests that we still do not know everything about this bias and further research is necessary. Furthermore, access to the more detailed data allows to reveal new information. The disposition effect is a
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costly bias for investors. Odean (1998) concludes that the disposition effect steals more than 4% of investors’ returns. Several other studies (Goulart, Costa, Andrade, & Santos, 2015; Seru, Shumway, & Stoffman, 2010) also demonstrate the costliness of the disposition effect.
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Previous empirical and experimental studies have identified the bias in a large number of markets. To name a few, Odean (1998) identifies the existence of the disposition effect for individual investors, Shapira & Venezia (2001) confirm and show that the same is true for institutional investors, which is supported by further evidence from Coval & Shumway (2005)
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and Locke & Mann (2005). Grinblatt & Keloharju (2001) provide additional details about trading behavior. Feng & Seasholes (2005) and Seru et al. (2010) highlight the importance of experience and learning. More recently Chang, Solomon, & Westerfield (2016) study the effect of cognitive dissonance, Heimer (2016) the peer pressure and Frydman & Camerer (2016) neural factors. A few studies like Goo, Chen, Chang, & Yeh (2010), Grinblatt, Keloharju, & Linnainmaa (2012) and Vaarmets, Liivamägi, & Talpsepp (2018) have highlighted mental
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abilities and education as factors influencing the disposition effect. Recent studies (Fischbacher, Hoffmann, & Schudy, 2017; Richards, Rutterford, Kodwani, & Fenton-O’Creevy, 2017) show that using stop loss orders can reduce the disposition effect. In this paper we study how simulated stop loss orders affect the disposition effect and performance, and how such effects are moderated by education and intelligence. The motivation for the analysis is derived from the experimental work of Fischbacher et al. (2017), who show that 2
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using stop loss orders decreases the disposition effect, and from Vaarmets et al. (2018), who show that more intelligent investors can learn faster, which results in a lower disposition effect. This raises the questions of whether the performance of investors would benefit from the use of stop loss orders, and whether the benefits of stop loss orders depend on the cognitive abilities of
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investors. We expect simulated stop loss orders to decrease the disposition effect, but we are more interested in the viability of stop loss orders and the resulting consequences on performance along with comparing and identifying feasible stop loss levels in a real transaction data set. Another unique feature of the current study is to check for possible moderating effects of cognitive and educational factors. Our results can contribute to the debate on the feasibility and the applicability of implementing automatic stop loss orders by investors themselves or their
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advisors.
Our first contribution lies in checking the hypothesis of whether simulated forceful stop loss orders would decrease the disposition effect and increase returns in actual stock market trading data. Such a check is important because investors would only be willing to use stop loss orders
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if doing so does not hurt performance. Secondly, we check how cognitive abilities moderate the impact of stop loss orders on the disposition effect and performance. Thirdly, we show that performance is clearly linked to the disposition effect and education and mental abilities have
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limited impact in restraining the direct cost of the disposition effect. We use stock market transaction records from 2004 to 2012 that contain all the trades made in Nasdaq Tallinn during that period, the number of which is about 1.3 million. We analyse all investors (including both institutions, corporations and individuals1) in Nasdaq Tallinn and provide a more detailed view on individual investors for whom we are able to combine the
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The data set enables to distinguish between individual, corporate, institutional client and nominee accounts,
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investment funds and government related entities. As the number of accounts associated with financial institutions and government is very small, we cannot draw any significant conclusions from analysing such accounts separately. Corporate accounts can represent both small and large companies and thus can fall under both sophisticated and non-sophisticated investors depending on the corporate and ownership structure. We are more interested in individual accounts for whom we can obtain additional data about the individual. We explicitly mention individual investors when presenting results about a subsample of individual investors and use the whole set of investors otherwise. 3
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transaction records with educational data from the Estonian Ministry of Education and Science. Educational data includes information about individuals’ high school exam results, university degrees and subjects. Using the Estonian dataset allows us to build the study using a complete stock market transaction dataset that is free of selection bias.
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We run simulations of what would have happened if investors’ positions had been closed at certain threshold levels such as a loss of 5% or 10%. As the simulations are retrospective, they cannot consider the consequences and effects that such forceful position closures would have had on the subsequent trading decisions of investors2. For each trading day and each simulated scenario we measure whether each investor is in loss or profit with each of their trades, and record if a selling or buying decision is made. That yields over three hundred million records, of which we are mainly interested in about 3.4 million observations where selling decisions were
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recorded.
We find that stop loss orders invert the disposition effect in the simulated data when stop loss levels are close to the reference price, say at 5%, but they do not seem to decrease the disposition effect particularly when the stop loss limit is further away, say at 15%. In the
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subsample of individual investors, stop loss orders have small positive effects on performance for investors with lower cognitive abilities, but there is no statistically significant effect for an average investor and a slightly negative effect for smarter investors when stops are close to the reference price. Stop loss orders seem to affect performance negatively when the stops are loss level.
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further away from the reference price and the negative effect starts to decrease from the 20-25%
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If for example a person opens a position in stock A and the market price then falls below the threshold level (e.g.
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5% below the purchase price), our simulation automatically sells the whole position with the closing price of the day. If that person adds to the position of stock A after a simulated stop loss is executed, our simulation regards the purchase as a new position with a new reference price. When a person is forced out of the stock position, their subsequent trading decisions would take the liquidation of the stock position into account, which cannot be the case for our simulated data. Investors making up the majority of the sample do not seem to open new stock positions actively after selling their initial positions. Very active traders with many trades would just see their trades to be with somewhat shorter in duration in the simulated data as they frequently choose new stocks anyway. 4
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2. Data and methodology The stock market dataset contains all the transactions from 2004-2012 made in the Nasdaq Tallinn stock exchange, which is the only trading venue in Estonia. Nasdaq Tallinn is a small exchange with market capitalization of around 3 billion euros during the sample period and with an average of around 600 trades a day, which imposes clear liquidity constraints on active
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trading due to the small size of the stock market3. The total number of market participants during the period was 33,843, of whom about two thirds were individual investors (see descriptive statistics in Table 1). We have detailed educational data available for 10,555 investors, which includes a very large proportion of investors under 35 years of age at the sample end date. These data include information about individuals’ exam results, university degrees and subjects. Students need to take the exams to graduate high school and the results determine university entrance. We use the exam results together with other educational variables
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as a proxy for the level of mental abilities4. We divide exam results into equal quartiles such that students with the highest scores belong to the highest quartile (e.g. Maths Q4), and students with lower math abilities to the lowest quartile.
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We use a Cox proportional hazard model like in Feng & Seasholes (2005) and Seru et al. (2010) to measure the disposition effect. We follow the same definitions and setup as used in previous studies using Nasdaq Tallinn data, such as by Talpsepp (2011) and Talpsepp, Vlcek, & Wang (2014). We calculate the probability of selling a stock at time t conditional on holding a stock
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until time t-1, using both fixed and time-varying covariates. We estimate the coefficients and from the maximum likelihood equation: ℎ 𝑡, 𝑋, 𝑍
ℎ t exp 𝑋𝛽
𝑍𝛾
𝜀
where h is the hazard rate, X and 𝑍 are vectors of fixed and time-varying covariates and ℎ is the baseline hazard. We report hazard ratios which are equal to exp() and exp() from the regressions.
The average number of trades per year for our sample is 4.9 and the median number of trades per year is 2. The
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implied average number of trades per year in the dataset used by Odean (1998) and Barber & Odean (2001) is around 5.5 per year. Similar figures have been reported for Finland and Israel, although the number is clearly higher for individual investors e.g. in Turkey probably mostly due to cultural differences. 4
A number of studies find that results of academic tests are closely correlated with mental abilities. See e.g. meta-
analysis by Kuncel, Hezlett, & Ones (2004), Duckworth & Seligman (2005), and Sackett, Borneman, & Connelly (2008). 5
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Individual
Number of investors Number of trades
Corporate
Client accounts
Investment Government funds related
Total
28 957
4 792
43
24
27
33 843
553 848
536 194
236 252
1 053
332
1 327 679
294 357
262 282
119 504
401
190
676 734
Number of sells
259 491
273 912
116 748
652
142
650 945
4.1
9.2
137.6
8.7
3.4
4.9
Average number of trades per year
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Number of buys
Number of investors with bachelor's degree
6 182
Number of investors with master's or higher degree
608
Number of investors without university degree
3 765
Number of investors with education in humanitarian science
529
Number of investors with education in real sciences
1 244
Number of investors with education in social sciences
5 132
Number of investors with exam results
6 851
4 648
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Including investors who have taken maths exam
The table reports the number of investors belonging to each category and the number of trades they made during the sample period along with the average number of trades per year. The lower pane presents the number of investors
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for whom we have educational data available.
Figure 1. The figure presents the total number of individual investors (with grey) belonging to each age bracket and the number of individual investors (with red) for whom we have educational data available. 6
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We calculate the trading loss indicator (TLI) for each stock position for each trading day. The TLI takes the value of 1 if a position is in loss and 0 otherwise. The hazard ratio for a TLI shows whether investors are more willing to sell losing stocks than winning stocks. We interact the TLI with other covariates in the model and the hazard ratios of the interaction terms show whether a
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covariate increases or reduces the disposition effect. As pointed out by Feng & Seasholes (2005), the advantages of using survival analysis comes from taking into account the price path of the stock in a statistical model for how long stocks are held, and using all trading days in comparison with only data of sell decisions, which is typical for ratio analysis. We follow the same approach as used by Vaarmets et al. (2018) and make a comparison with the average purchase price5 and the current market price of the stock to check whether an investor incurs a loss or profit for a particular position.
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We measure performance in various ways. We report the results for money-weighted annualised returns and risk adjusted returns (RAP) by following the methodology of Modigliani & Modigliani (1997). The use of money-weighted returns considers the effect of the investing part of the funds to other assets (including cash) at times when investors do not prefer to keep their
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investments in stock. However, we obtain similar results when we use either time-weighted returns (investment funds are required to report their performance with using time-weighted returns according to GIPS standards) or monetary returns without annualization. In our main scenario we also adjust the returns with risk to consider possible variations in the level of risk in
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order to compare also investor risk-adjusted performance. Various measurements of returns are necessary as investors sell decisions may depend on their own perceived performance and due to complexity of calculating returns, we cannot be sure which type of calculation is used by investors in their mental accounts, which may affect their trading behaviour and susceptibility to the disposition effect.
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3. Results
We study the relation between the disposition effect and performance by dividing investors into ten deciles according to their risk adjusted performance (RAP). The results show (see Figure 2)
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We follow the conventional approach to measure the disposition effect, although some alternatives have also been
proposed for special cases (Sarmiento, Rendón, Sandoval, & Cayon, 2019). 7
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that the disposition effect decreases monotonically as performance improves. These results are
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in line with previous studies (Locke & Mann, 2005; Seru et al., 2010).
Figure 2. The figure presents hazard ratios of the Cox proportional hazard model for regressions run for each decile of investors grouped by their stock market performance. The figure plots hazard ratios for the TLI. Hazard ratios of less than 1 indicate the disposition effect (the lower the ratio, the stronger the disposition effect). Hazard ratios of
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more than 1 indicate the reverse of the disposition effect. Performance decile 1 contains investors with the lowest risk-adjusted returns and decile 10 investors with the highest risk-adjusted returns.
Our dataset lets us study whether factors related to education and cognitive abilities moderate the relationship between performance and the disposition effect. We run the Cox proportional
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model with fixed covariates that include the ex-post performance quartile and variables related to education and academic results along with time-varying covariates measuring experience and portfolio size. We use indicator educational variables and present results separately for regressions using different educational indicators (see Table 2). We include interaction terms to capture the moderating effects of educational variables. A
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higher level of education and certain types of education (a degree in real sciences) generally decreases the disposition effect (as measured with the variable TLI*EDUC), but the moderating effect of educational variables in the highest performance quartile can also be negative (variables TLI*RAP*EDUC), meaning they can also increase the disposition effect. When we look at subsamples based on the mathematics exam results (see Pane B of Table 2), the impact of the disposition effect on performance (variable TLI*RAP) varies more for investors in the 8
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lower quartiles for maths abilities than for investors with higher maths abilities. Given that other standardised exam scores give similar results, the indication is that investors with lower academic abilities may be more vulnerable to negative impacts on their performance. We run simulations by introducing automatic stop loss orders at different stop loss levels of 5%,
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10%, 15%, 20% and 25% below the reference price. Those simulated automatic stop loss orders completely liquidate the single stock position when the stock price falls below the threshold. We generate new datasets for each of the simulations and calculate hazard ratios for the TLI. Figure 3 reports the results of the survival analysis at different stop loss levels from the simulated data, along with horizontal lines showing the hazard ratio values when there are no stop loss transactions, as found in the actual data. Stop loss orders at 5% below the reference price reverse the disposition effect (hazard ratios for a TLI>1). At 15% level all groups once
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again exhibit the disposition effect (TLI<1) and the disposition effect becomes even worse than the actual level without the simulated stop loss transactions when the simulated stop loss orders are 20% below the reference price.
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The results indicate that reacting relatively early to losing positions (i.e. selling the position before the actual stock price falls approximately 10% below the reference price) would help to reduce the disposition effect. On the other hand, if investors hold on to losing positions and let position returns fall deeper into negative territory (i.e. more than 10% below the reference
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price), we see the disposition effect. Based on our simulations, the inflection points of being influenced (or not being influenced) by the disposition effect is around 10% below the reference price. Investors with lower academic or mental abilities seem to benefit most from the impact of simulated stop loss orders. As investors with lower cognitive abilities tend to achieve lower average returns compared to investors with higher abilities (Talpsepp, Liivamägi, & Vaarmets, 2019), they may also experience deeper relative losses. Therefore, cutting these losses early may
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help them more to reduce the disposition effect.
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Masters' or doctoral
Humanitarian
degree
science
Bachelor's degree Haz. Ratio
TLI
z-stat Haz. Ratio
Real science
z-stat Haz. Ratio
z-stat Haz. Ratio
0.467***
-20.54 0.47***
-22.68 0.486***
Q2
0.666***
-18.05 0.668***
-17.93 0.666***
Q3
0.625***
-24.57 0.626***
-24.44 0.625***
-24.54 0.624***
-24.63
Q4
0.832***
-10.02 0.835***
-9.89 0.828***
-10.32 0.83***
-10.16
Q2
1.317***
6.66 1.333***
9.25 1.336***
9.28 1.359***
9.62
Q3
1.594***
12.52 1.535***
15.08 1.542***
15.33 1.603***
16.08
Q4
1.775***
15.50 1.633***
17.53 1.634***
17.51 1.693***
18.34
EDUC
0.968***
-2.74 0.813***
-8.11 1.146***
5.97 0.954***
-2.83
TLI*EDUC
1.018***
0.62 1.078***
1.15 0.723***
-4.54 1.169***
3.99
pro of
RAP
Q2
1.027
0.61 0.998
Q3
0.963
-0.93 1.231**
Q4
0.88***
-3.18 0.974
Subsample: TLI
Maths Q1
-0.02 1.118
2.42 1.247**
-0.29 1.167*
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Pane B
-18.06 0.665***
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TLI*RAP
TLI*RAP*EDUC
-21.59 0.464***
z-stat
Maths Q2
-23.00 -18.09
1.16 0.919
-1.37
2.10 0.836***
-3.33
1.81 0.779***
-4.15
Maths Q3
Maths Q4
0.441***
-7.54 0.522***
-5.30 0.499***
-6.65 0.459***
-7.59
Q2
0.78***
-3.91 0.758***
-4.34 0.77***
-3.75 0.552***
-9.01
Q3
0.587***
-9.34 0.666***
-7.14 0.615***
-8.63 0.565***
-10.41
Q4
1.049
0.93 0.773***
-4.68 0.831***
-3.38 0.861***
-2.89
1.213**
2.14 1.14
1.50 1.467***
3.97 1.583***
4.85
1.761***
6.82 1.633***
6.04 1.791***
7.03 2.149***
9.44
2.043***
9.09 1.941***
7.88 1.9***
7.76 2.221***
10.22
TLI*RAP Q2 Q3 Q4
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RAP
***significant at the 1% level; **significant at the 5% level; *significant at the 10% level The table reports results from the Cox proportional hazard model, showing the hazard ratios, z-values and
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significance levels. TLI represents the Total Loss Indicator, taking the value one if the position is in loss and the value zero otherwise. The results are reported only for variables showing education and performance (RAP), and control variables are omitted. Variables are interacted with TLI to capture the disposition effect. Pane A shows the results of individually run regressions by using different educational variables (EDUC) for the whole sample, while Pane B shows the results of regressions run for subsamples obtained by dividing investors into quartiles based on their maths exam results. Quartile 1 (Q1) has the lowest maths scores and quartile 4 (Q4) has the highest scores.
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Figure 3. The figure presents the hazard ratios of the Cox proportional hazard model for regressions run to simulate stop loss transactions at different levels for all investors; investors in the top quartile for their average exam score; and investors in the bottom quartile for their average exam score. The horizontal lines show the hazard ratios when the stop loss orders were not simulated. Hazard ratios of below 1 indicate the disposition effect, and the disposition effect.
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lower the ratio, the stronger the disposition effect. Hazard ratios of more than 1 indicate the reverse of the
Figure 4 reports the results for what happens to investors’ returns when simulated stop loss transactions are introduced. The population of investors, including both institutions and private individuals, and the subsample of investors in the highest quartile for the average score of the standardised exams has a lower median return in all cases when stop loss orders are used compared to when they are not used. When returns are annualised (money-weighted returns –
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MWR), the returns become more variable for close stops at the 5% level, because the price can move down by 5% in a relatively short period, which magnifies the annualised returns. We also calculate holding period returns (HPR), where the distribution of returns seems more favourable for investors, as it is difficult to lose much in absolute terms because of the automatic stops, especially for investors who do not trade frequently.
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Once again, investors with lower academic abilities seem to benefit more from the simulated stop loss transactions, at least in their HPR, as their median HPR with stop loss levels of 5% and 10% is higher than the HPR without the simulated orders. However, their 75th percentile annualised return and the return distribution in general indicate weaker performance than in any
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other group. In all cases where simulated stop loss transactions were used, the median performance was worst when the stop loss transactions were executed at 15% below the reference price, which is the average purchase price. Performance worsens from the levels of 5% to 15% and it starts to
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improve slowly when simulated stop loss orders were placed further away than 15% level.
Figure 4. The bottom and top of the boxes indicate the first and the third quartiles of returns. HPR is the holding period return and MWR is the annualised money-weighted return. The line inside the box shows the median return and the ends of the whiskers present the 10th and the 90th percentiles of the returns. The dotted red line shows the median return for data when stop loss orders were not used.
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4. Conclusion We find that forcing the use of stop loss orders reduces the disposition effect, but this decrease is more profound for investors with lower mental abilities. This is consistent with lower average performance, which investors with lesser cognitive abilities tend to achieve compared to other
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investors. Lower performance also relates to bigger losses and cutting these losses early can decrease the disposition effect. However, in our simulated scenarios, stop loss transactions generally lead to lower returns compared to when they are not used at all, but the downside variability of holding period returns becomes smaller. If investors measure their performance in annualised returns, the benefit of using stop loss orders to tackle the negative effects of the disposition effect may be clearly limited. If investors base their decisions on the absolute amount of money won or lost, there would be some performance benefits from using stop loss orders. We find that investors with lower academic abilities may be more vulnerable to the
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negative performance associated with the disposition effect. The moderating effects of educational factors on the connection between performance and the disposition effect are mixed. Our results provide insights into the feasibility of implementing automatic stop loss orders by investors or investment advisors who also benefit from considering sociodemographic factors of
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their clients.
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Sackett, P. R., Borneman, M. J., & Connelly, B. S. (2008). High stakes testing in higher education and employment: appraising the evidence for validity and fairness. American Psychologist, 63(4), 215. Sarmiento, J., Rendón, J., Sandoval, J. S., & Cayon, E. (2019). The disposition effect and the relevance of the reference period: Evidence among sophisticated investors. Journal of Behavioral and Experimental Finance. Seru, A., Shumway, T., & Stoffman, N. (2010). Learning by Trading. Review of Financial Studies, 23(2), 705–739. Shapira, Z., & Venezia, I. (2001). Patterns of behavior of professionally managed and independent investors. Journal of Banking & Finance, 25(8), 1573–1587. Shefrin, H., & Statman, M. (1985). The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence. The Journal of Finance, 40(3), 777–790. Talpsepp, T. (2011). Reverse disposition effect of foreign investors. Journal of Behavioral Finance, 12(4), 183–200. Talpsepp, T., Liivamägi, K., & Vaarmets, T. (2019). The Effect of Academic Abilities and Education on Performance in the Stock Market. Talpsepp, T., Vlcek, M., & Wang, M. (2014). Speculating in gains, waiting in losses: A closer look at the disposition effect. Journal of Behavioral and Experimental Finance, 2, 31– 43. Vaarmets, T., Liivamägi, K., & Talpsepp, T. (2018). How does learning and education help to overcome the disposition effect? Review of Finance, forthcoming.
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PII: DOI: Reference:
S2214-6350(19)30086-3 https://doi.org/10.1016/j.jbef.2019.100240 JBEF 100240
To appear in:
Journal of Behavioral and Experimental Finance
Received date : 21 April 2019 Revised date : 1 September 2019 Accepted date : 19 September 2019 Please cite this article as: T. Talpsepp and T. Vaarmets, The disposition effect, performance, stop loss orders and education. Journal of Behavioral and Experimental Finance (2019), doi: https://doi.org/10.1016/j.jbef.2019.100240. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
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The disposition effect, performance, stop loss orders and education*
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Tõnn Talpsepp†, Tarvo Vaarmets‡ Current version: August 21, 2019
Abstract
The paper studies how simulated stop loss orders affect the disposition effect and performance
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by running simulations using a complete transaction dataset from Nasdaq Tallinn which includes all investors in the market. We combine transaction data with detailed educational registry data about individual investors. We show that stop loss orders reduce the disposition effect but only to a certain extent, and they can be harmful to performance at the same time. We
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study how educational factors moderate the association of performance and the disposition
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effect, with mixed results.
Keywords: disposition effect, performance, stop loss orders, education, mental abilities JEL classification: G02, G11
*
We are grateful to Kalle Viks and Nasdaq OMX Tallinn Stock Exchange, Marko Mölder and Estonian Ministry of
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Education and Science, Lauri Veski and Innove, Aime Lauk and Statistics Estonia for the data and their supportive attitude and efforts for processing our data requests. †
Corresponding author, Tallinn University of Technology, Department of software sciences; Estonian
Entrepreneurship University of Applied Sciences; Aalto University, Department of Finance; address: Akadeemia tee 15A, 12618 Tallinn, Estonia; [email protected]. Declarations of interest: none. ‡
Department of economics and finance, Tallinn University of Technology, Akadeemia tee 3, 12618 Tallinn,
Estonia. Declarations of interest: none. 1
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1. Introduction It is difficult to underestimate the impact of the disposition effect on the behaviour and performance of investors. The disposition effect was first documented by Shefrin & Statman (1985) and is defined as the tendency of investors to “sell winners too early and ride losers too
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long”. While there is a broad consensus about the existence of the disposition effect and the effects of various factors, the reasons for the effect and its impacts are not so unequivocal. Most of the literature uses the prospect theory developed by Kahneman & Tversky (1979) to explain the disposition effect but e.g. Barberis & Xiong (2009), Kaustia (2010), Hens & Vlcek (2011) and Meng & Weng (2017) provide some alternative explanations. This suggests that we still do not know everything about this bias and further research is necessary. Furthermore, access to the more detailed data allows to reveal new information. The disposition effect is a
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costly bias for investors. Odean (1998) concludes that the disposition effect steals more than 4% of investors’ returns. Several other studies (Goulart, Costa, Andrade, & Santos, 2015; Seru, Shumway, & Stoffman, 2010) also demonstrate the costliness of the disposition effect.
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Previous empirical and experimental studies have identified the bias in a large number of markets. To name a few, Odean (1998) identifies the existence of the disposition effect for individual investors, Shapira & Venezia (2001) confirm and show that the same is true for institutional investors, which is supported by further evidence from Coval & Shumway (2005)
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and Locke & Mann (2005). Grinblatt & Keloharju (2001) provide additional details about trading behavior. Feng & Seasholes (2005) and Seru et al. (2010) highlight the importance of experience and learning. More recently Chang, Solomon, & Westerfield (2016) study the effect of cognitive dissonance, Heimer (2016) the peer pressure and Frydman & Camerer (2016) neural factors. A few studies like Goo, Chen, Chang, & Yeh (2010), Grinblatt, Keloharju, & Linnainmaa (2012) and Vaarmets, Liivamägi, & Talpsepp (2018) have highlighted mental
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abilities and education as factors influencing the disposition effect. Recent studies (Fischbacher, Hoffmann, & Schudy, 2017; Richards, Rutterford, Kodwani, & Fenton-O’Creevy, 2017) show that using stop loss orders can reduce the disposition effect. In this paper we study how simulated stop loss orders affect the disposition effect and performance, and how such effects are moderated by education and intelligence. The motivation for the analysis is derived from the experimental work of Fischbacher et al. (2017), who show that 2
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using stop loss orders decreases the disposition effect, and from Vaarmets et al. (2018), who show that more intelligent investors can learn faster, which results in a lower disposition effect. This raises the questions of whether the performance of investors would benefit from the use of stop loss orders, and whether the benefits of stop loss orders depend on the cognitive abilities of
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investors. We expect simulated stop loss orders to decrease the disposition effect, but we are more interested in the viability of stop loss orders and the resulting consequences on performance along with comparing and identifying feasible stop loss levels in a real transaction data set. Another unique feature of the current study is to check for possible moderating effects of cognitive and educational factors. Our results can contribute to the debate on the feasibility and the applicability of implementing automatic stop loss orders by investors themselves or their
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advisors.
Our first contribution lies in checking the hypothesis of whether simulated forceful stop loss orders would decrease the disposition effect and increase returns in actual stock market trading data. Such a check is important because investors would only be willing to use stop loss orders
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if doing so does not hurt performance. Secondly, we check how cognitive abilities moderate the impact of stop loss orders on the disposition effect and performance. Thirdly, we show that performance is clearly linked to the disposition effect and education and mental abilities have
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limited impact in restraining the direct cost of the disposition effect. We use stock market transaction records from 2004 to 2012 that contain all the trades made in Nasdaq Tallinn during that period, the number of which is about 1.3 million. We analyse all investors (including both institutions, corporations and individuals1) in Nasdaq Tallinn and provide a more detailed view on individual investors for whom we are able to combine the
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The data set enables to distinguish between individual, corporate, institutional client and nominee accounts,
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investment funds and government related entities. As the number of accounts associated with financial institutions and government is very small, we cannot draw any significant conclusions from analysing such accounts separately. Corporate accounts can represent both small and large companies and thus can fall under both sophisticated and non-sophisticated investors depending on the corporate and ownership structure. We are more interested in individual accounts for whom we can obtain additional data about the individual. We explicitly mention individual investors when presenting results about a subsample of individual investors and use the whole set of investors otherwise. 3
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transaction records with educational data from the Estonian Ministry of Education and Science. Educational data includes information about individuals’ high school exam results, university degrees and subjects. Using the Estonian dataset allows us to build the study using a complete stock market transaction dataset that is free of selection bias.
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We run simulations of what would have happened if investors’ positions had been closed at certain threshold levels such as a loss of 5% or 10%. As the simulations are retrospective, they cannot consider the consequences and effects that such forceful position closures would have had on the subsequent trading decisions of investors2. For each trading day and each simulated scenario we measure whether each investor is in loss or profit with each of their trades, and record if a selling or buying decision is made. That yields over three hundred million records, of which we are mainly interested in about 3.4 million observations where selling decisions were
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recorded.
We find that stop loss orders invert the disposition effect in the simulated data when stop loss levels are close to the reference price, say at 5%, but they do not seem to decrease the disposition effect particularly when the stop loss limit is further away, say at 15%. In the
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subsample of individual investors, stop loss orders have small positive effects on performance for investors with lower cognitive abilities, but there is no statistically significant effect for an average investor and a slightly negative effect for smarter investors when stops are close to the reference price. Stop loss orders seem to affect performance negatively when the stops are loss level.
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further away from the reference price and the negative effect starts to decrease from the 20-25%
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If for example a person opens a position in stock A and the market price then falls below the threshold level (e.g.
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5% below the purchase price), our simulation automatically sells the whole position with the closing price of the day. If that person adds to the position of stock A after a simulated stop loss is executed, our simulation regards the purchase as a new position with a new reference price. When a person is forced out of the stock position, their subsequent trading decisions would take the liquidation of the stock position into account, which cannot be the case for our simulated data. Investors making up the majority of the sample do not seem to open new stock positions actively after selling their initial positions. Very active traders with many trades would just see their trades to be with somewhat shorter in duration in the simulated data as they frequently choose new stocks anyway. 4
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2. Data and methodology The stock market dataset contains all the transactions from 2004-2012 made in the Nasdaq Tallinn stock exchange, which is the only trading venue in Estonia. Nasdaq Tallinn is a small exchange with market capitalization of around 3 billion euros during the sample period and with an average of around 600 trades a day, which imposes clear liquidity constraints on active
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trading due to the small size of the stock market3. The total number of market participants during the period was 33,843, of whom about two thirds were individual investors (see descriptive statistics in Table 1). We have detailed educational data available for 10,555 investors, which includes a very large proportion of investors under 35 years of age at the sample end date. These data include information about individuals’ exam results, university degrees and subjects. Students need to take the exams to graduate high school and the results determine university entrance. We use the exam results together with other educational variables
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as a proxy for the level of mental abilities4. We divide exam results into equal quartiles such that students with the highest scores belong to the highest quartile (e.g. Maths Q4), and students with lower math abilities to the lowest quartile.
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We use a Cox proportional hazard model like in Feng & Seasholes (2005) and Seru et al. (2010) to measure the disposition effect. We follow the same definitions and setup as used in previous studies using Nasdaq Tallinn data, such as by Talpsepp (2011) and Talpsepp, Vlcek, & Wang (2014). We calculate the probability of selling a stock at time t conditional on holding a stock
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until time t-1, using both fixed and time-varying covariates. We estimate the coefficients and from the maximum likelihood equation: ℎ 𝑡, 𝑋, 𝑍
ℎ t exp 𝑋𝛽
𝑍𝛾
𝜀
where h is the hazard rate, X and 𝑍 are vectors of fixed and time-varying covariates and ℎ is the baseline hazard. We report hazard ratios which are equal to exp() and exp() from the regressions.
The average number of trades per year for our sample is 4.9 and the median number of trades per year is 2. The
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implied average number of trades per year in the dataset used by Odean (1998) and Barber & Odean (2001) is around 5.5 per year. Similar figures have been reported for Finland and Israel, although the number is clearly higher for individual investors e.g. in Turkey probably mostly due to cultural differences. 4
A number of studies find that results of academic tests are closely correlated with mental abilities. See e.g. meta-
analysis by Kuncel, Hezlett, & Ones (2004), Duckworth & Seligman (2005), and Sackett, Borneman, & Connelly (2008). 5
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Individual
Number of investors Number of trades
Corporate
Client accounts
Investment Government funds related
Total
28 957
4 792
43
24
27
33 843
553 848
536 194
236 252
1 053
332
1 327 679
294 357
262 282
119 504
401
190
676 734
Number of sells
259 491
273 912
116 748
652
142
650 945
4.1
9.2
137.6
8.7
3.4
4.9
Average number of trades per year
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Number of buys
Number of investors with bachelor's degree
6 182
Number of investors with master's or higher degree
608
Number of investors without university degree
3 765
Number of investors with education in humanitarian science
529
Number of investors with education in real sciences
1 244
Number of investors with education in social sciences
5 132
Number of investors with exam results
6 851
4 648
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Including investors who have taken maths exam
The table reports the number of investors belonging to each category and the number of trades they made during the sample period along with the average number of trades per year. The lower pane presents the number of investors
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for whom we have educational data available.
Figure 1. The figure presents the total number of individual investors (with grey) belonging to each age bracket and the number of individual investors (with red) for whom we have educational data available. 6
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We calculate the trading loss indicator (TLI) for each stock position for each trading day. The TLI takes the value of 1 if a position is in loss and 0 otherwise. The hazard ratio for a TLI shows whether investors are more willing to sell losing stocks than winning stocks. We interact the TLI with other covariates in the model and the hazard ratios of the interaction terms show whether a
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covariate increases or reduces the disposition effect. As pointed out by Feng & Seasholes (2005), the advantages of using survival analysis comes from taking into account the price path of the stock in a statistical model for how long stocks are held, and using all trading days in comparison with only data of sell decisions, which is typical for ratio analysis. We follow the same approach as used by Vaarmets et al. (2018) and make a comparison with the average purchase price5 and the current market price of the stock to check whether an investor incurs a loss or profit for a particular position.
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We measure performance in various ways. We report the results for money-weighted annualised returns and risk adjusted returns (RAP) by following the methodology of Modigliani & Modigliani (1997). The use of money-weighted returns considers the effect of the investing part of the funds to other assets (including cash) at times when investors do not prefer to keep their
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investments in stock. However, we obtain similar results when we use either time-weighted returns (investment funds are required to report their performance with using time-weighted returns according to GIPS standards) or monetary returns without annualization. In our main scenario we also adjust the returns with risk to consider possible variations in the level of risk in
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order to compare also investor risk-adjusted performance. Various measurements of returns are necessary as investors sell decisions may depend on their own perceived performance and due to complexity of calculating returns, we cannot be sure which type of calculation is used by investors in their mental accounts, which may affect their trading behaviour and susceptibility to the disposition effect.
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3. Results
We study the relation between the disposition effect and performance by dividing investors into ten deciles according to their risk adjusted performance (RAP). The results show (see Figure 2)
5
We follow the conventional approach to measure the disposition effect, although some alternatives have also been
proposed for special cases (Sarmiento, Rendón, Sandoval, & Cayon, 2019). 7
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that the disposition effect decreases monotonically as performance improves. These results are
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in line with previous studies (Locke & Mann, 2005; Seru et al., 2010).
Figure 2. The figure presents hazard ratios of the Cox proportional hazard model for regressions run for each decile of investors grouped by their stock market performance. The figure plots hazard ratios for the TLI. Hazard ratios of less than 1 indicate the disposition effect (the lower the ratio, the stronger the disposition effect). Hazard ratios of
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more than 1 indicate the reverse of the disposition effect. Performance decile 1 contains investors with the lowest risk-adjusted returns and decile 10 investors with the highest risk-adjusted returns.
Our dataset lets us study whether factors related to education and cognitive abilities moderate the relationship between performance and the disposition effect. We run the Cox proportional
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model with fixed covariates that include the ex-post performance quartile and variables related to education and academic results along with time-varying covariates measuring experience and portfolio size. We use indicator educational variables and present results separately for regressions using different educational indicators (see Table 2). We include interaction terms to capture the moderating effects of educational variables. A
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higher level of education and certain types of education (a degree in real sciences) generally decreases the disposition effect (as measured with the variable TLI*EDUC), but the moderating effect of educational variables in the highest performance quartile can also be negative (variables TLI*RAP*EDUC), meaning they can also increase the disposition effect. When we look at subsamples based on the mathematics exam results (see Pane B of Table 2), the impact of the disposition effect on performance (variable TLI*RAP) varies more for investors in the 8
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lower quartiles for maths abilities than for investors with higher maths abilities. Given that other standardised exam scores give similar results, the indication is that investors with lower academic abilities may be more vulnerable to negative impacts on their performance. We run simulations by introducing automatic stop loss orders at different stop loss levels of 5%,
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10%, 15%, 20% and 25% below the reference price. Those simulated automatic stop loss orders completely liquidate the single stock position when the stock price falls below the threshold. We generate new datasets for each of the simulations and calculate hazard ratios for the TLI. Figure 3 reports the results of the survival analysis at different stop loss levels from the simulated data, along with horizontal lines showing the hazard ratio values when there are no stop loss transactions, as found in the actual data. Stop loss orders at 5% below the reference price reverse the disposition effect (hazard ratios for a TLI>1). At 15% level all groups once
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again exhibit the disposition effect (TLI<1) and the disposition effect becomes even worse than the actual level without the simulated stop loss transactions when the simulated stop loss orders are 20% below the reference price.
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The results indicate that reacting relatively early to losing positions (i.e. selling the position before the actual stock price falls approximately 10% below the reference price) would help to reduce the disposition effect. On the other hand, if investors hold on to losing positions and let position returns fall deeper into negative territory (i.e. more than 10% below the reference
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price), we see the disposition effect. Based on our simulations, the inflection points of being influenced (or not being influenced) by the disposition effect is around 10% below the reference price. Investors with lower academic or mental abilities seem to benefit most from the impact of simulated stop loss orders. As investors with lower cognitive abilities tend to achieve lower average returns compared to investors with higher abilities (Talpsepp, Liivamägi, & Vaarmets, 2019), they may also experience deeper relative losses. Therefore, cutting these losses early may
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help them more to reduce the disposition effect.
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Masters' or doctoral
Humanitarian
degree
science
Bachelor's degree Haz. Ratio
TLI
z-stat Haz. Ratio
Real science
z-stat Haz. Ratio
z-stat Haz. Ratio
0.467***
-20.54 0.47***
-22.68 0.486***
Q2
0.666***
-18.05 0.668***
-17.93 0.666***
Q3
0.625***
-24.57 0.626***
-24.44 0.625***
-24.54 0.624***
-24.63
Q4
0.832***
-10.02 0.835***
-9.89 0.828***
-10.32 0.83***
-10.16
Q2
1.317***
6.66 1.333***
9.25 1.336***
9.28 1.359***
9.62
Q3
1.594***
12.52 1.535***
15.08 1.542***
15.33 1.603***
16.08
Q4
1.775***
15.50 1.633***
17.53 1.634***
17.51 1.693***
18.34
EDUC
0.968***
-2.74 0.813***
-8.11 1.146***
5.97 0.954***
-2.83
TLI*EDUC
1.018***
0.62 1.078***
1.15 0.723***
-4.54 1.169***
3.99
pro of
RAP
Q2
1.027
0.61 0.998
Q3
0.963
-0.93 1.231**
Q4
0.88***
-3.18 0.974
Subsample: TLI
Maths Q1
-0.02 1.118
2.42 1.247**
-0.29 1.167*
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Pane B
-18.06 0.665***
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TLI*RAP
TLI*RAP*EDUC
-21.59 0.464***
z-stat
Maths Q2
-23.00 -18.09
1.16 0.919
-1.37
2.10 0.836***
-3.33
1.81 0.779***
-4.15
Maths Q3
Maths Q4
0.441***
-7.54 0.522***
-5.30 0.499***
-6.65 0.459***
-7.59
Q2
0.78***
-3.91 0.758***
-4.34 0.77***
-3.75 0.552***
-9.01
Q3
0.587***
-9.34 0.666***
-7.14 0.615***
-8.63 0.565***
-10.41
Q4
1.049
0.93 0.773***
-4.68 0.831***
-3.38 0.861***
-2.89
1.213**
2.14 1.14
1.50 1.467***
3.97 1.583***
4.85
1.761***
6.82 1.633***
6.04 1.791***
7.03 2.149***
9.44
2.043***
9.09 1.941***
7.88 1.9***
7.76 2.221***
10.22
TLI*RAP Q2 Q3 Q4
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RAP
***significant at the 1% level; **significant at the 5% level; *significant at the 10% level The table reports results from the Cox proportional hazard model, showing the hazard ratios, z-values and
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significance levels. TLI represents the Total Loss Indicator, taking the value one if the position is in loss and the value zero otherwise. The results are reported only for variables showing education and performance (RAP), and control variables are omitted. Variables are interacted with TLI to capture the disposition effect. Pane A shows the results of individually run regressions by using different educational variables (EDUC) for the whole sample, while Pane B shows the results of regressions run for subsamples obtained by dividing investors into quartiles based on their maths exam results. Quartile 1 (Q1) has the lowest maths scores and quartile 4 (Q4) has the highest scores.
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Figure 3. The figure presents the hazard ratios of the Cox proportional hazard model for regressions run to simulate stop loss transactions at different levels for all investors; investors in the top quartile for their average exam score; and investors in the bottom quartile for their average exam score. The horizontal lines show the hazard ratios when the stop loss orders were not simulated. Hazard ratios of below 1 indicate the disposition effect, and the disposition effect.
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lower the ratio, the stronger the disposition effect. Hazard ratios of more than 1 indicate the reverse of the
Figure 4 reports the results for what happens to investors’ returns when simulated stop loss transactions are introduced. The population of investors, including both institutions and private individuals, and the subsample of investors in the highest quartile for the average score of the standardised exams has a lower median return in all cases when stop loss orders are used compared to when they are not used. When returns are annualised (money-weighted returns –
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MWR), the returns become more variable for close stops at the 5% level, because the price can move down by 5% in a relatively short period, which magnifies the annualised returns. We also calculate holding period returns (HPR), where the distribution of returns seems more favourable for investors, as it is difficult to lose much in absolute terms because of the automatic stops, especially for investors who do not trade frequently.
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Once again, investors with lower academic abilities seem to benefit more from the simulated stop loss transactions, at least in their HPR, as their median HPR with stop loss levels of 5% and 10% is higher than the HPR without the simulated orders. However, their 75th percentile annualised return and the return distribution in general indicate weaker performance than in any
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other group. In all cases where simulated stop loss transactions were used, the median performance was worst when the stop loss transactions were executed at 15% below the reference price, which is the average purchase price. Performance worsens from the levels of 5% to 15% and it starts to
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improve slowly when simulated stop loss orders were placed further away than 15% level.
Figure 4. The bottom and top of the boxes indicate the first and the third quartiles of returns. HPR is the holding period return and MWR is the annualised money-weighted return. The line inside the box shows the median return and the ends of the whiskers present the 10th and the 90th percentiles of the returns. The dotted red line shows the median return for data when stop loss orders were not used.
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4. Conclusion We find that forcing the use of stop loss orders reduces the disposition effect, but this decrease is more profound for investors with lower mental abilities. This is consistent with lower average performance, which investors with lesser cognitive abilities tend to achieve compared to other
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investors. Lower performance also relates to bigger losses and cutting these losses early can decrease the disposition effect. However, in our simulated scenarios, stop loss transactions generally lead to lower returns compared to when they are not used at all, but the downside variability of holding period returns becomes smaller. If investors measure their performance in annualised returns, the benefit of using stop loss orders to tackle the negative effects of the disposition effect may be clearly limited. If investors base their decisions on the absolute amount of money won or lost, there would be some performance benefits from using stop loss orders. We find that investors with lower academic abilities may be more vulnerable to the
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negative performance associated with the disposition effect. The moderating effects of educational factors on the connection between performance and the disposition effect are mixed. Our results provide insights into the feasibility of implementing automatic stop loss orders by investors or investment advisors who also benefit from considering sociodemographic factors of
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their clients.
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References
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