Do individual investors gamble to recoup losses?

ABSTRACT

This study presents novel empirical insights into the speculative behaviours of individual investors within the stock market. Using detailed data on individual investors’ stock portfolios, we find that investors are more likely to invest in lottery stocks and to invest a larger proportion of their stock portfolio in lottery stocks after experiencing a large loss. These results are consistent with Thaler and Johnson’s (1990) experimental findings, showing that investors, when faced with losses, tend to increase their risk appetite, displaying a preference for investment options that present a perceived opportunity to recoup losses.

KEYWORDS:

• Individual investors
• gamble
• stocks
• risk-taking

JEL CLASSIFICATION:

• G11
• G14
• G15
• H31

I. Introduction

In their seminal paper in Econometrica, Kahneman and Tversky (1979) address the role of prior gains and losses when individuals make risky decisions, stating that ‘a person who has not made peace with his losses is likely to accept gambles that would be unacceptable to him otherwise’ (Kahneman and Tversky 1979, 287). In this paper, we study whether this statement accurately describes how investors behave when investing in equities. We use detailed data on individual investors’ stock portfolios to examine whether investors are more likely to invest in lottery stocks after experiencing a large loss in their stock portfolio.

We find that investors who experience a large loss are more likely to invest in lottery stocks and are more likely to increase the proportion of lottery stocks in their stock portfolios. These effects are most pronounced for investors exposed to the largest losses (i.e. investors with portfolio returns below the 10^th percentile and investors with portfolio returns equal to or larger than −50%). Further, since the proportion of lottery stocks in the portfolio changes automatically depending on the performance of the stocks in the portfolio, we test the robustness of the results by focusing on investors that have actively traded new lottery stocks. The results from this analysis provide similar results: investors who have experienced the largest losses subsequently invest a larger proportion of their portfolio in new lottery stocks.

The findings are important because they demonstrate that predictions based on experimental studies are borne out in the behaviour of investors in real life. More specifically, we build on Thaler and Johnson’s (1990) and Imas’ (2016) findings showing how prior gains and losses affect risky choices. Analogous to our findings, Thaler and Johnson (1990) document that, subsequent to a loss, individuals increase their risk taking and prefer investment alternatives that offer a chance to break-even. Further, Imas (2016) find that there is a difference between unrealized and realized gains and losses, where individuals take on greater risk when experiencing unrealized losses. Our results support the findings by Imas (2016), where investors that have experienced large unrealized losses are more likely to invest in lottery stocks.

The findings also add to the body of research on investors’ gambling behaviour in the stock market. Liu et al. (2022) find that gambling preferences significantly influence investors’ trading activities. Additionally, Cookson (2018) and Chen et al. (2021) show that individuals often substitute between gambling and investments. It has also been observed that short-term stock market returns increase when market lottery preferences are high (e.g. Zhang et al. 2021) and that the demand for lottery-type stocks increases during economic downturns (Kumar 2009). Our findings contribute to this literature by demonstrating that the demand for lottery stocks is, at least in part, driven by investors’ portfolio losses, which tend to increase during economic downturns.

The rest of the paper is organized as follows. In Section II, we describe the data and the main variables used. In Section III, we test whether investors invest more in lottery stocks when exposed to a large loss in their stock portfolios. Section 4 provides a conclusion.

II. Data

The paper utilizes data from Statistics Sweden (SCB), covering individual investors’ stock and mutual fund holdings, other assets (e.g. bank holdings, real estate, debt securities), and taxable income. It also includes individual characteristics such as gender, education, and occupation. The data spans two cohorts born in 1963 and 1973,¹ observed annually from 1999 to 2007, with individuals aged 36–44 and 26–34, respectively. The sample includes 74,118 stockowners and 449,843 individual-year observations.

Following Kumar (2009), lottery stocks are identified based on below-median prices and above-median idiosyncratic volatility and skewness. The idiosyncratic volatility is the variance of the residual obtained by fitting a four-factor model to the daily returns time series. Like Cronqvist and Siegel (2014) we obtain the idiosyncratic volatility using the world market return, the squared world market return, the local Swedish market return, and the squared local market return. The idiosyncratic skewness is obtained by fitting a two-factor model to the daily stock returns time series. The two factors are the excess market return and the squared excess market return. The idiosyncratic volatility and skewness are computed using the previous 12 months of daily returns data. The main dependent variable is the proportion of lottery stocks in the investor’s stock portfolio.

Descriptive statistics

In Table 1, descriptive statistics are presented. The investors in the sample are unlikely to own lottery stocks, where the mean (median) portfolio weight is 2% (0%). Further, the standard deviation is 11%, suggesting that there are some investors who invest a relatively large proportion of their portfolios in lottery stocks. There is also a large difference in the stock portfolio returns between investors in the period: the mean is −11%; whilst the median is 5%.

Table 1. Descriptive statistics.

	Mean	SD	P25	Median	P75
Lottery stock weight in portfolio	0.02	0.11	0.00	0.00	0.00
Stock portfolio return	−0.11	0.60	−0.35	0.05	0.25
Disposable income (in SEK)	237774.77	547544.20	157000.00	205400.00	265000.00
Real estate wealth (in SEK)	950415.23	1899694.16	0.00	532400.00	1220780.00
Financial wealth (in SEK)	310425.20	1997314.55	33933.00	105345.00	276394.00
Total liability (in SEK)	458579.55	756195.03	80054.00	299600.00	622529.00
Gender (1 = male, 0 = female)	0.63	0.48	0.00	1.00	1.00
Educational attainment (1= less than 9 years of schooling, 6 = PhD)	3.87	1.06	3.00	4.00	5.00
Finance professional dummy (1 = work in financial industry, 0 = otherwise)	0.03	0.18	0.00	0.00	0.00
Entrepreneur dummy (1 = entrepreneur, 0 = otherwise)	0.05	0.21	0.00	0.00	0.00
Unemployed dummy (1 = unemployed, 0 = otherwise)	0.09	0.28	0.00	0.00	0.00
Children dummy (1 = children, 0 = otherwise)	0.59	0.49	0.00	1.00	1.00
Partner dummy (1 = partner, 0 = otherwise)	0.40	0.49	0.00	0.00	1.00
Lagged annual stock market return	0.05	0.32	−0.22	0.15	0.24
Cohort 1963 dummy (1 = born 1963, 0 = otherwise)	0.55	0.50	0.00	1.00	1.00
Risky Share	0.63	0.35	0.32	0.71	1.00
Gambling per capita in region (in SEK)	1533.59	407.45	1186.51	1470.72	1854.04
Number of observations	449,843
Number of individuals	74,118

Descriptive statistics are calculated over the period 2000–2007.

III. Results

We test if investors are more likely to invest in lottery stocks after significant losses in their portfolios by estimating the following model:

(1) $\mathit{Lottery}\mathit{weigh}{t}_{\mathit{i},\mathit{t}}={\beta }_0+{\beta }_1\mathit{Large}\mathit{los}{s}_{\mathit{i},\mathit{t}-1}+X_{\mathit{i},\mathit{t}}+{\theta }_i+{\delta }_t+{\phi }_{\mathit{i},\mathit{t}}+{\epsilon }_{\mathit{i},\mathit{t}.}$(1)

The dependent variable is the portfolio weight invested in lottery stocks. $\mathit{Large}\mathit{los}{s}_{\mathit{i},\mathit{t}-1}$ is measured using four different dummy variables, taking the value of one if: i) portfolio returns are below the 10th percentile; returns are equal to or exceed ii) −10%; iii) −30%; vi) −50%. $X_{\mathit{i},\mathit{t}}$ contains the individual-level controls presented in Table 1. Since gambling attitudes can differ between regions (Ji et al. 2021) we also control for regional gambling expenditure per capita. ${\theta }_i$ are municipality fixed effects, ${\delta }_t$ are year fixed effects, and ${\phi }_{\mathit{i},\mathit{t}}$ are individual fixed effects. Standard errors are clustered at the individual level.

The results in Table 2 show that investors who have experienced large losses in their portfolio in the preceding year tend to increase the proportion of lottery stocks in their portfolios. These effects are most pronounced for investors with the largest losses in their portfolios. Investors that experience losses that are equal to or larger than 50% increase their portfolio weight in lottery stocks by, on average, 1.5% points.

Table 2. Portfolio weight in lottery stocks.

	(1)	(2)	(3)	(4)
Lagged stock portfolio return in the 10^th percentile dummy	0.007***	-	-	-
	(0.001)	-	-	-
Lagged negative stock portfolio return ≥ −10% dummy	-	0.007***	-	-
	-	(0.001)	-	-
Lagged negative stock portfolio return ≥ −30% dummy	-	-	0.012***	-
	-	-	(0.001)	-
Lagged negative stock portfolio return ≥ −50% dummy	-	-	-	0.015***
	-	-	-	(0.001)
Constant	0.003	0.003	0.002	0.003
	(0.008)	(0.008)	(0.008)	(0.008)
Time-varying individual controls	Y	Y	Y	Y
Year FE	Y	Y	Y	Y
Community FE	Y	Y	Y	Y
Individual FE	Y	Y	Y	Y
Adjusted R^2 Number of observations	0.008	0.009	0.010	0.010
	414,660	414,660	414,660	414,660

The table shows the results from OLS regressions. The dependent variable is the weight of lottery stock in the investor’s stock portfolio. The specification includes time-varying individual controls, individual fixed effects, community fixed effects, and time fixed effects. Standard errors are clustered at the individual level are reported in parentheses. Significance levels: ***p < 0.01 **p < 0.05 *p < 0.10.

Robustness analyses

Table 2 indicates that investors increase their allocation to lottery stocks after experiencing significant portfolio losses in the previous year. However, as discussed by Calvet et al. (2009), portfolio changes are influenced by both active decisions and passive market conditions. To address this, we conduct three robustness tests to examine whether investors actively choose to invest in lottery stocks after a portfolio loss.

First, we assess whether investors are more inclined to buy lottery stocks following significant portfolio losses in the preceding year by estimating the following probit model:

(2) $Pr\left(\mathit{Bu}{y}_{\mathit{i},\mathit{t}}=1\right)={\beta }_0+{\beta }_1\mathit{Large}\mathit{los}{s}_{\mathit{i},\mathit{t}-1}+X_{\mathit{i},\mathit{t}}+{\theta }_i+{\delta }_t+{\epsilon }_{\mathit{i},\mathit{t}.}$(2)

The dependent variable, $\mathit{Bu}{y}_{\mathit{i},\mathit{t}}$, is 1 if an investor invests in lottery stocks, 0 otherwise. $\mathit{Large}\mathit{los}{s}_{\mathit{i},\mathit{t}-1}$ is proxied for using the same portfolio variables as in Table 2. $X_{\mathit{i},\mathit{t}}$ contains the individual-level controls, ${\theta }_i$ are municipality fixed effects, and ${\delta }_t$ are year fixed effects. Table 3 presents the average marginal effects. The results show a significant increase in the probability of investors purchasing lottery stocks after experiencing large losses in the previous year. On average, the likelihood of investing in lottery stocks rises by 3% points when facing portfolio declines equal to or larger than 50%.

Table 3. Activity investing in lottery stocks.

	(1)	(2)	(3)	(4)
Lagged stock portfolio return in the 10^th percentile dummy	0.035***	-	-	-
	(0.001)	-	-	-
Lagged negative stock portfolio return ≥ −10% dummy	-	0.016***	-	-
	-	(0.001)	-	-
Lagged negative stock portfolio return ≥ −30% dummy	-	-	0.031***	-
	-	-	(0.001)	-
Lagged negative stock portfolio return ≥ −50% dummy	-	-	-	0.030***
	-	-	-	(0.001)
Time-varying individual controls	Y	Y	Y	Y
Year FE	Y	Y	Y	Y
Community FE	Y	Y	Y	Y
Pseudo R^2	0.061	0.057	0.061	0.060
Number of observations	409,356	409,356	409,356	409,356

The table shows the average marginal effects from probit regressions. The dependent variable takes the value one if the investor actively purchases lottery stocks during the year, zero otherwise. The specification includes time-varying individual controls, community fixed effects, and time fixed effects. Standard errors clustered at the individual level are reported in parentheses. Significance levels: ***p < 0.01 **p < 0.05 *p < 0.10.

Further, we calculate the active and passive changes in lottery stock weight following Calvet et al. (2009). Passive change is the weight at year-end without trading lottery stocks, while active change is the actual trading-induced change in weight. Table 4 presents regression results similar to Table 2, but with active change in the lottery stock weight as the dependent variable. We present separate results for investors who owned lottery stocks in the previous year and those who did not.

Table 4. Active change of lottery stocks.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Lagged stock portfolio return in the 10^th percentile dummy	0.040***	-	-	-	0.003***	-	-	-
	(0.004)	-	-	-	(0.000)	-	-	-
Lagged negative stock portfolio return ≥ −10% dummy	-	0.041***	-	-	-	0.002***	-	-
	-	(0.004)	-	-	-	(0.000)	-	-
Lagged negative stock portfolio return ≥ −30% dummy	-	-	0.041***	-	-	-	0.003***	-
	-	-	(0.004)	-	-	-	(0.000)	-
Lagged negative stock portfolio return ≥ −50% dummy	-	-	-	0.043***	-	-	-	0.003***
	-	-	-	(0.004)	-	-	-	(0.000)
Constant	0.142***	0.104***	0.107***	0.111***	0.003*	0.002	0.002	0.003
	(0.034)	(0.035)	(0.034)	(0.034)	(0.002)	(0.002)	(0.002)	(0.002)
Time-varying individual controls	Y	Y	Y	Y	Y	Y	Y	Y
Year FE	Y	Y	Y	Y	Y	Y	Y	Y
Community FE	Y	Y	Y	Y	Y	Y	Y	Y
Adjusted R^2	0.053	0.053	0.052	0.053	0.004	0.004	0.004	0.004
Number of observations	22,749	22,749	22,749	22,749	347,992	347,992	347,992	347,992

The table shows results from OLS regressions. The dependent variable is the weight of active change in lottery stocks in the investor’s stock portfolio. Column (1) – (4) shows the results for investors that owned lottery stocks in t-1. Column (5) – (8) shows the results for investors that did not own any lottery stocks in t-1. The specification includes time-varying individual controls, community fixed effects, and time fixed effects. Standard errors clustered at the individual level are reported in parentheses. Significance levels: ***p < 0.01 **p < 0.05 *p < 0.10.

The results indicate that investors facing significant portfolio declines actively increase their allocation to lottery stocks. These results are stronger for prior lottery stock owners compared to non-lottery stock owners, implying a stronger tendency among prior owners to invest in lottery stocks post-decline.

Finally, the results in the main analysis could be influenced by ‘mental accounting’.² To investigate this, Table 5 re-examines the results in Table 2 and test whether investors increase their allocation to lottery stocks when losses occur in the non-lottery part of their portfolios. This is done by excluding lottery stocks from the return calculations. Despite smaller coefficients, Table 5 still shows significant results, suggesting that investors increase their investment in lottery stocks even when losses occur in the non-lottery part of their portfolios.

Table 5. Active change of lottery stocks when the loss appears in the non-lottery part of the portfolio.

	(1)	(2)	(3)	(4)
Lagged stock portfolio return in the 10^th percentile dummy	0.004***	-	-	-
	(0.000)	-	-	-
Lagged negative stock portfolio return ≥ −10% dummy	-	0.002***	-	-
	-	(0.000)	-	-
Lagged negative stock portfolio return ≥ −30% dummy	-	-	0.003***	-
	-	-	(0.000)	-
Lagged negative stock portfolio return ≥ −50% dummy	-	-	-	0.003***
	-	-	-	(0.000)
Constant	0.003***	0.004***	0.004***	0.004***
	(0.001)	(0.001)	(0.001)	(0.001)
Time-varying individual controls	Y	Y	Y	Y
Year FE	Y	Y	Y	Y
Community FE	Y	Y	Y	Y
Adjusted R^2	0.005	0.004	0.004	0.004
Number of observations	414,634	414,634	414,634	414,634

The table shows the results from OLS regressions. The portfolio loss is calculated for the non-lottery part of the stock portfolio in the preceding year. The dependent variable is the active change in the portfolio weight of lottery stocks. The regressions include time-varying individual controls, community fixed effects, and time fixed effects. Standard errors clustered at the individual level are reported in parentheses. Significance levels: ***p < 0.01 **p < 0.05 *p < 0.10.

IV. Conclusions

We use detailed data on individual investors’ stock portfolios to study whether investors are more likely to invest in lottery stocks if they have experienced a large loss in their stock portfolios during the preceding year. In doing so, we are able to examine whether experimental findings of Thaler and Johnson (1990) and Imas (2016) can explain individual investor financial decisions by using real portfolio data. Our findings suggests that individual investors are more likely to invest in lottery stocks and allocate a larger part of their stock portfolios to such holdings when they have experienced a large decline in the value of their stock portfolio. This effect is particularly pronounced among investors with the largest losses. However, the size of this effect is relatively modest, indicating that while investors are more inclined to invest in lottery stocks after experiencing a significant portfolio decline, they typically allocate only a small portion of their portfolios to these stocks.

Acknowledgements

Financial support from the Wallander, Browald and, Tom Hedelius Foundation is gratefully acknowledged. I thank Jörgen Hellström, Markku Kaustia, Elizabeth O’Nions, and Valia Velli for useful comments on an earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/13504851.2024.2371511

Additional information

Funding

The work was supported by the Jan Wallanders och Tom Hedelius Stiftelse samt Tore Browaldhs Stiftelse.

Notes

¹ The choice of cohorts was made with respect to considerations outside the scope of the current paper. Furthermore, the choice of study period is determined by the abolishment of the wealth tax in Sweden in 2007. Before this time, financial institutions, i.e. all Swedish banks, brokerage firms, and other financial firms, were required by law to report to the Swedish Tax Authority information about investors’ portfolios (i.e. stocks, bonds, mutual funds, and other securities) owned at December 31. After 2007, the data were not available.

² As discussed by Frydman et al. (2018) a central question in the mental accounting literature involves how individuals group outcomes together. Investors might use different mental accounts when assessing the lottery and non-lottery parts of their portfolios, potentially leading them to invest in lottery stocks only when losses occur in the lottery part.