Do Large Losses Loom Larger than Gains? Salience, Holding Periods, and the Disposition Effect

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1 Do Large Losses Loom Larger than Gains? Salience, Holding Periods, and the Disposition Effect Preliminary Draft: November 2017 Abstract Individual investors are more likely to sell stocks with nominal gains and losses that are large relative to their brokerage portfolio value due to their salience. For holding periods up to one year, individuals are more likely to sell stocks with large (i.e., salient) nominal losses than large gains, which attenuates the disposition effect. The pervasive effect of salience is observed across taxable and tax-deferred accounts and across different investors. It is weaker for stocks with high valuation uncertainty. Investors prone to realizing their larger nominal losses underperform relative to other investors. The effect of nominal losses remains significant after controlling for the rankings of losses within a portfolio. Keywords Individual investors Disposition effect Reference point Salience Recency bias JEL Classification G02 G11 1

2 Introduction How do gains and losses affect investors decisions to sell stocks? Behavioral finance research has identified numerous departures from the prescriptions of modern portfolio theory. Prior literature has extensively discussed investors tendency to hold losers and sell winners, known as the disposition effect (Shefrin and Statman, 1985). More recently, Kaustia (2010) shows that the probability of selling a stocks jumps at zero return, Ben-David and Hirshleifer (2012) find that the magnitude of percentage returns affects the sale decision, and Hartzmark (2015) finds that stocks with extreme (highest or lowest) percentage returns within a portfolio are more likely to be sold. We extend this line of research by showing that individual investors are (1) more likely to sell stocks with large nominal gains and losses and (2) not hesitant to realize large nominal losses compared to gains of the same magnitude (and therefore not exhibiting the disposition effect) for stocks acquired within the last twelve months. Positions with large gains or losses are likely to be more salient and most easily available for recall, consistent with the effect of salience on judgment (Taylor and Thompson 1982) and the availability heuristic (Tversky and Kahneman 1973), respectively. As a result, such positions are likely to attract more attention, be researched more and monitored more frequently, and therefore more likely to be sold than otherwise similar positions with smaller gains or losses. Nominal value changes may be as important as or more important than percentage returns, especially to retail investors. While reviewing percentage returns on individual positions is consistent with narrow framing (Kahneman and Lovallo 1993, Tversky and Kahneman 1981) or mental accounting (Thaler, 1985), the tendency of many individual investors to engage in the extreme form of narrow framing by evaluating each investment position in isolation may be reduced when they simultaneously observe (e.g., on an account statement or snapshot) gains and losses on the entire portfolio as well as on individual positions. Viewing the composition, value, and value changes of the whole brokerage portfolio simultaneously with values, gains, and losses of individual positions within 2

3 the portfolio invites the investor to consider his or her total brokerage portfolio value in addition to stock-specific reference points such as acquisition prices or recent peak prices when deciding which stocks to sell. Consistent with this conjecture, Shavit et al. (2010) show in an experimental setting that investors look at monetary value changes longer than at percentage changes. We posit that stock positions with large nominal gains and losses are more salient, and, as a result, are more likely to be sold. A nominal gain or loss depends on both the percentage return since acquisition and the initial amount invested in the stock. A large positive (negative) percentage return on a position with a small initial investment results in a small nominal gain (loss) relative to the overall portfolio value. On the other hand, a small percentage return on a large position may result in a relatively large dollar gain (loss), drawing more attention from the investor. Of course, what one person perceives as a significant nominal gain or loss may appear miniscule to another. We therefore normalize nominal gains and losses incurred on each position by dividing their absolute values over the value of an investor s common stock portfolio held at a large US discount brokerage (the data used by Barber and Odean (2000) and many others). We refer to this measure of gains (losses) interchangeably as a nominal gain (loss) or a normalized nominal gain (loss) hereafter. Normalizing nominal gains and losses by investor portfolio values allows us to study the effects of gains and losses across time and investors. Our study documents two new stylized facts about individual investors behavior. First, we find that absolute values of nominal gains and losses are positively related to the probability of selling a stock. An increase in absolute nominal loss (gain) equal to one percent of the portfolio value increases the probability of selling a stock by 0.55 (0.33) percent. The propensity to realize large nominal losses attenuates the disposition effect the general tendency to hold on to losers relative to winners (Sherfin and Statman, 1985; Odean, 1998). While previous studies used percentage returns when modeling stock selling decisions, we show that nominal gains and losses are as important if not 3

4 more important than percentage returns in individuals stock selling decisions. The higher propensity to realize larger normalized nominal gains and losses suggests that investors pay attention to nominal values of individual positions and that they may weigh nominal gains and losses against their brokerage portfolio values. This result holds across different account types (margin and non-margin, taxable and tax-deferred), holding periods, and investors. Individuals may compare the gains and losses to their total wealth when making stock selling decisions, and the brokerage account value may appear important simply because it is highly correlated with net worth. To alleviate this concern, we run our tests for subsamples of investors with different portfolio value ranges. The results are similar across portfolio sizes. We also obtain similar results when we use an investor s average brokerage portfolio value throughout the entire sample period as a base for computing normalized nominal gains and losses instead of the previous day s portfolio value. Second, at short holding periods (up to one year), the disposition effect is eliminated when normalized nominal gains and losses are large. In general, investors are more likely to realize gains than losses (the disposition effect) and more likely to sell more recently acquired stocks (the recency effect). However, people more readily realize large nominal losses then gains of the same size on stocks when holding periods are short (roughly up to a year). The opposite is true for longer holding periods: large gains are more likely to be realized than large losses. Small losses are always less likely to be realized than small gains. Tax incentives cannot entirely explain why people are more likely to realize larger shorter-held losses than shorter-held gains of the same size because we also observe this pattern in tax-deferred accounts. Our finding in the context of the holding period and salience provides some insight into our understanding of determinants of the disposition effect. Dhar and Zhu (2006) find that higher trading frequency is associated with a lower disposition effect and attribute it to investors learning from experience. While that might well be the case for some investors, we believe that portfolio turnover is not necessarily a proxy for investor sophistication. Investors appear to more 4

5 easily cut large nominal losses on recently acquired positions than on ones held for a long time, and frequent traders simply tend to have shorter holding periods. Thus, frequent traders would exhibit a lower disposition effect. In sum, compared to nominal gains of the same size, investors more easily cut large nominal losses on recently acquired stocks (holding periods roughly up to one year) than on ones held longer. This pattern holds even for tax-deferred accounts, ruling out tax-loss selling as the sole explanation. We are not aware of any studies that would explain this phenomenon. We conclude that, while large gains and losses are both salient for investors, recency makes large losses even more salient than gains of the same size. 1 While normalized nominal gains and losses affect stock selling decisions, we find that investors are less likely to realize large nominal losses on stocks with high valuation uncertainty than on other stocks. This finding is consistent with Kumar s (2009a) findings that behavioral biases are stronger for stocks in uncertain environments. The possibility of price recovery for stocks with high valuation uncertainty may prompt investors to hold on to such stocks even when they accumulate large nominal losses. Hartzmark (2015) finds the rank effect in stock sales: stocks with highest and lowest percentage returns within a portfolio are more likely to be sold. It is therefore possible that the effect of nominal gains and losses disappears when their ranks are controlled for. When we control for the rank of nominal value changes within a portfolio, our normalized nominal gain measure loses significance, but the normalized nominal loss measure remains significant in the regressions for the 1 Recently acquired positions by individuals receive greater attention in comparison to longer held positions (Ben- David and Hirshleifer, 2012; Nofsinger and Varma, 2013), which could contribute to the realization of large recent losses. Chakrabarty, Moulton, and Trzcinka (2017) find evidence of the recency driving short-term institutional trades, which tend to be loss-making. 5

6 probability of a stock sale. It suggests that the size of a loss has influence on stock selling decisions beyond the ranking of losses within the portfolio. Propensities to realize gains and losses, including large ones, vary across investors. Such propensities may be affected by common investor disciplines, e.g., cut your losses or take your profits, and may affect portfolio performance. We compare risk-adjusted performance of investors who are more prone (above median) to realizing nominal gains and/or losses to those less prone to do so. Investors who tend to realize larger normalized nominal losses underperform as a group: their risk-adjusted gross returns are lower than for investors with a lower propensity to realize abovemedian losses. Thus, realizing larger losses does not, on average, results in superior performance. 1. Data and Methodology We use a data set containing stock trading activity of 77,995 households at a large discount brokerage from January 1991 through November This data set, described in detail in Barber and Odean (2000), contains about 1.9 million trades. We look at portfolios of stocks held by investors on any date on which they sell at least one stock (a household-sell date). 2 We exclude portfolios with positions acquired prior to January 1, 1991, as we do not have any purchase information on these positions. The data set is sufficiently rich as it covers a large cross-section of investors and provides demographic information on investors. We require that a portfolio have at least two positions on any sale date to ensure there are different positions to choose from. This filter results in a loss of 2 Sale refers to either a complete or partial sale of a position. We combine multiple sales of the same stock on the same day using the weighted average price. Only stocks with information in the CRSP database on a sell date are included in our analysis. Gains and losses for positions with multiple acquisition dates are computed using the first-in, first-out method (FIFO). The results are not sensitive to the method of computing gains and losses. We make appropriate adjustments for stock splits. We exclude short sales, which account for a miniscule portion of the total transactions, and aggregate positions across multiple accounts under the same household identifier. The transaction data show some unsold stocks that were acquired during the sample period but failed to appear on successive monthly portfolio statements. We include these positions as part of the portfolio only on household-sell dates that are prior to the last date these positions appear on the monthly position statement. For positions with multiple acquisition dates, we compute holding periods weighted by the number of shares acquired on each date. 6

7 mere 28,609 observations out of more than 1.9 million, as our sample is dominated by individuals holding multiple stocks on a given household-sell date. The key variables in our analysis are the normalized absolute dollar gain (Norm$Gain) and the normalized absolute dollar loss (Norm$Loss), computed as an absolute value of an accumulated dollar gain (loss) on a given stock position divided by the total value of all stocks in the brokerage portfolio at the end of the previous day, expressed in percent. 3 We use absolute values to facilitate the interpretation of the results. Table 1 summarizes our sample, which consists of approx million positions held by 28,096 households on 198,647 unique household-sell dates. Across all household-sell dates, the median number of positions with gains or losses is six, the median number of positions with gains is three, the same as the median number of positions with losses. Table 1 presents descriptive statistics for nominal gains and losses, percentage returns, and holding periods across all household-sell dates. The median nominal gain (loss) is 3.0 percent (2.7 percent) of the portfolio value, and the median holding period is just below eight months, computed based on all open positions on all household-sell dates. [Insert Table 1 here] When reviewing a portfolio held in a brokerage account, an investor can easily observe accumulated gains and losses on open positions. Similar to Hartzmark (2015), we study the determinants of households decisions to sell stocks on days with stock sales. This approach allows us to model sale decisions that could be driven by various factors and makes no assumptions regarding the investor s trading frequency. 4 We employ the following logistic regression: 3 As a robustness check, in our unreported results we also considered the average portfolio value across all sell dates for our investors and our key findings remain unchanged. 4 This approach differs from that of Ben-David and Hirshleifer (2012), who estimate the probability of selling a stock on any day with an open position, an approach suited to analyzing investors who monitor their brokerage accounts on a daily basis. 7

8 Ln[ρ i,h,t (1 ρ i,h,t )] = α 0 + α 1 Loss i,h,t + β 1 Norm$Gain i,h,t + β 2 Norm$Loss i,h,t N + δ 1 HPGain i,h,t + δ 2 HPLoss i,h,t + j=1 ω j Control i,j,t (1), where ρ is the probability of selling stock i by household h on day t on which at least one stock is sold by the given household. Norm$Gain and Norm$Loss were defined above; Loss is a dummy variable equal 1 if a position has accumulated a loss and 0 otherwise; HPGain (HPLoss) is the holding period, in months, for stocks sold for a gain (loss), and 0 otherwise. The controls are at the stock level and include the following: RetPrevDay_High, RetPrevDay_Low, Cap_Decile, High_Vlty, Div_Stk and Tech_Stk. RetPrevDay_High and RetPrevDay_Low are indicator variables for stocks that had a previous day return in the top and the bottom decile of all CRSP stocks, respectively. Positions with extreme previous day returns attract more attention from investors observing daily changes in values, as well as the media, which is likely to increase their salience and, with that, the probability of sale. 5 Cap_Decile is the market capitalization decile based on all CRSP stocks on the previous trading day, with 1 denoting the smallest and 10 denoting the largest capitalization deciles. High_Vlty is an indicator for stocks in the top volatility decile of all CRPS stocks over the previous six calendar months. Small cap stocks and highly volatile stocks may be associated with a lower probability of selling because they may be harder to value (Kumar 2009a). We present additional tests of the effect of valuation uncertainty on stock sales in the context of nominal gains or losses later in the paper. Div_Stk is an indicator for stocks that paid dividends any time during the previous 12 month. Dividend stocks may be bought for income and may represent more established companies, which may result in a lower probability of sale. Tech_Stk is an indicator for technology company stocks, which tended to attract more attention from the media 5 Barber and Odean (2008) report that individual investors buy more attention-grabbing stocks (e.g., stocks with high absolute previous day returns) than they sell them. They argue that the buying is affected more than selling for attentiongrabbing stocks, since investors can choose from thousands of stocks to buy while only a few stocks to sell. While we agree, we hypothesize that, in a set of stocks held by an individual, stocks with extreme one-day returns are likely to attract more attention and be sold. 8

9 and investors during the sample period and thus could be sold more frequently. 6 For all our regression results, we present marginal effects, in percent, calculated at the mean values of other variables, alongside the coefficient estimates. Standard errors are clustered at the household level. Our study emphasizes the effects of nominal gains and losses on stock positions relative to an investor s portfolio value. We create two separate variables, Norm$Gain and Norm$Loss, to allow for different effects of gains and losses on the probability of stock sales. That is, we would like to see if a gain on a stock equal to a given percentage of the portfolio value affects the probability of selling to the same extent as a loss of the same magnitude. We use absolute values of these variables and hypothesize that, consistent with salience of larger gains and losses, Norm$Gain and Norm$Loss will have positive coefficients, implying that stocks with nominal gains or losses that are large in the portfolio context will have a higher probability of sale. 7 We expect a negative coefficient for the Loss dummy, implying that investors are in general less likely to sell losers than winners, consistent with the disposition effect. We also expect negative parameters for HPGain and HPLoss, implying that individuals are more likely to sell stocks they purchased more recently, a manifestation of the recency effect (Nofsinger and Varma 2013; Chakrabarty, Moulton, and Trzcinka, 2017). We create separate holding period variables for gains and losses to compare how holding periods affect the probability of selling winners versus losers. 6 We require at least one month of non-missing data for our calculation of volatility. Changing this requirement to one year of non-missing data does not impact our results. 7 We compute the nominal gains and losses and (in subsequent tests) other measures of return based on capital gain/loss returns. Using total returns instead, which account for both capital gains/losses and dividends, does not affect the results. The realized gains and losses are after commissions. 9

10 2. Salience of nominal gains and losses 2.1. The effects of nominal gains and losses on stock sales Table 2 reports the first of the two main results of the study; it presents the output of four regressions. Regression 1 employs only the Loss dummy and the normalized nominal gains (Norm$Gain) and losses (Norm$Loss), while Regression 2 also includes the controls (this is Equation 1). To compare the impact on selling decisions of nominal gains and losses to that of percentage returns, Regression 3 uses percentage returns on a stock since acquisition for gains (Ret%Gain) and losses (Ret%Loss) in place of the nominal gains and losses in Equation (1), and Regression 4 has both nominal gains and losses and percentage returns for gains and losses. Both are absolute values and defined separately for gains and losses to test for asymmetric effects of gains and losses. The Loss dummy has a negative coefficient in all four regressions, indicating that stocks with accumulated losses are less likely to be sold, consistent with the disposition effect. The marginal effect for the Loss dummy in Regression 2 implies that, holding all other variables at their mean levels, a losing stock is about 5.45 percent less likely to be sold than a non-losing stock on a day when at least one stock in the portfolio is sold. [Insert Table 2 here] Consistent with our main hypothesis, we find that the estimated parameters for nominal gains and losses expressed relative to the brokerage portfolio value, Norm$Gain and Norm$Loss, are positive and significant, regardless of other explanatory variables included in the regressions. Also, the coefficient for Norm$Loss is statistically higher than its Norm$Gain counterpart. The marginal effects in Regression 2 indicate that a one percent increase in the normalized nominal gain (Norm$Gain) and loss (Norm$Loss) increases the likelihood of sale by 0.33 and 0.55 percent, respectively. Interpreting the results in the context of the odds ratios yields an even stronger economic significance: a one percent increase in normalized nominal losses and gains is associated with the increase in odds of a 10

11 sale by 4.50 and 2.63 percent, respectively. Thus, individuals are more likely to sell their relatively more salient positions that are associated with larger nominal gains and losses. Also, after controlling for a general disposition for realizing gains, increasing nominal losses has a stronger effect on the probability of sale than increasing nominal gains. We show in Section 3 that this asymmetry holds only for shorter holding periods (roughly up to one year). The percentage return variables coefficients in Regression 3 are statistically and economically insignificant, and the explanatory power of that regression (measured by the pseudo R-squared) is much lower than that of Regression 2. This difference in explanatory power suggests that nominal gains and losses scaled by the portfolio value may contain more information that retail investors consider relevant in selling decisions than percentage returns. When we include both normalized nominal gains and losses and percentage returns on a stock in Regression 4, the former retain significance, while the percentage returns become statistically but not economically significant and have negative signs, which is inconsistent with the hypothesis that stocks with higher returns are more salient and more likely to be sold. Having established that nominal gains and losses are better predictors of selling decisions than percentage returns, we focus our discussion on Regression 2 (Equation 1) hereafter. The coefficients for HPGain and HPLoss are negative, supporting the recency effect. Individuals are more likely to sell more recently acquired stocks (Ben-David and Hirshleifer, 2012), and to repurchase more recently sold stocks (Nofsinger and Varma, 2013). Such stocks may be more available for recall, consistent with the effects recency plays in revival of thoughts (James, 1892) and memory (Ebbinghaus, 1913) and with the availability heuristic of Tversky and Kahneman (1973). Holding all other variables at their mean levels, an increase in the holding period of one month is associated with a decrease in the probability of sale of 0.36 percent for winners and 0.26 percent for losers. Technology company stocks and stocks with extreme previous day returns are more likely to 11

12 be sold, while dividend stocks, small cap stocks, and high-volatility stocks are less likely to be sold. The findings regarding small cap and high-volatility stocks are consistent with Kumar (2009a). We explore the impact of hard-to-value stocks in more detail in Section 4. The presence or absence of any of the control variables does not affect the main results Account types and tax considerations The results for nominal gains and losses may be driven by investor behavior in non-retirement accounts where people may be taking a shorter-term view of their investments or taking more risk. In Table 3, we report the regression coefficient estimates for retirement (tax-deferred) accounts in column 1 and non-retirement (taxable) accounts in column 2. The marginal effects of one-percent increases in the Norm$Gain and Norm$Loss variables for non-retirement (retirement) accounts is 0.56 (0.48) and 0.33 (0.42) percent, respectively. As before, the results hold consistently, with a higher propensity for selling positions with larger nominal gains and losses. In taxable accounts, the probability of sale goes up more with a one-percent increase in the normalized nominal loss than in the normalized nominal gain: the difference in the coefficients of Norm$Gain and Norm$Loss is negative and significant. In tax-deferred accounts, this difference is insignificant. That is, keeping the holding period constant, the probability of a stock sale is equally sensitive to the magnitudes of gains and losses in tax-deferred accounts, but more sensitive to the magnitude of losses than gains in taxable accounts. Tax considerations likely play a role here: in taxable accounts, realizing large gains notably increases taxable income, while realizing large losses results in notable tax savings. [Insert Table 3 here] For taxable accounts, we test if the preference for selling large nominal losses is driven by tax-loss selling at the end of the year. Regression 3 in Table 3 restricts the sample to stock sales in taxable accounts for the months January through November, while Regression 4 only includes December 12

13 sales. We find a much lower impact of the Loss dummy for December because tax-loss selling dampens the disposition effect (Odean, 1998). Also consistent with tax-loss selling, we find a much stronger preference for realizing large nominal losses than gains in December: the marginal effects for Norm$Gain and Norm$Loss in Regression 4 are 0.26 and 0.83 percent, respectively, with the difference being statistically significant. For sales during January through November (Regression 3), the preference for realizing large nominal gains and losses remains strong, with marginal effects of Norm$Gain and Norm$Loss of 0.34 and 0.51 percent, respectively, and the difference being statistically significant. While tax-loss selling peaks in December, it is observed throughout the year (Ivković, Poterba, and Weisbenner 2005) Investor characteristics Not all investors may react to gains and losses similarly. Feng and Seasholes (2005) conclude that sophistication and trading experience eliminate the tendency to hold on to losses and reduce the propensity to realize gains. Barber and Odean (2001) find that men, who tend to be more overconfident investors than women, trade excessively and realize poorer net returns as a result. Dhar and Zhu (2006) report that higher investor sophistication (measured by income and professional occupation) as well as trading frequency are associated with a weaker disposition effect. Therefore, as the next step we present in Table 4 the output of estimating Equation (1) for investors with different characteristics. While we use all of the variables from Equation (1), including the controls, we only report and discuss the output for the first three the normalized nominal gain and loss variables and the Loss dummy. 8 In unreported results, we exclude margin accounts, where selling may be driven by margin calls. The results for nominal gains and losses do not change. 13

14 Panel A of Table 4 classifies investors by gender and age. Men tend to trade more frequently than women (Barber and Odean 2001). Our results suggest that men show a stronger sign realization preference: the marginal effect of the Loss dummy is larger for males than females (-7.03 vs percent). However, men are more sensitive to the magnitude of accumulated losses than women: an increase of 1 percent in the normalized nominal loss (gain) is associated with a 0.55 (0.32) percent increase in the likelihood of sale by men, with the difference being significant. For women, larger nominal gains and losses are also associated with higher probabilities of sale (by 0.31 and 0.38 percent, respectively), but the difference between the effects of nominal gains and losses is not significant. Thus, salience of gains and losses matters to both male and female investors. Because men dominate the sample with ten times more sales than women, the men s higher sensitivity to nominal losses drives the results for the entire sample. Older investors (50 years and older) react to nominal gains and losses similarly to younger investors, but older investors appear less hesitant to realize losses in general, reflected in the lower marginal effect of Loss, percent, compared to percent for younger investors. 9 Thus, the disposition effect is weaker for older investors, consistent with Dhar and Zhu (2006). [Insert Table 4 here] Panel B of Table 4 reports the results for the sample split based on the portfolio turnover and diversification. Investors with low (below median) and high (above median) portfolio turnover, measured as the average portfolio turnover over the 71-month period (similarly to Barber and Odean 2000), exhibit similar reactions to nominal gains and losses: both are more likely to sell a big loser than a big winner (after controlling for the general disposition effect measured by the parameter of Loss, which appears to be somewhat stronger for high-turnover investors). Dhar and Zhu (2006) find that investors who trade frequently are more likely to sell their losers, which reduces the disposition effect. 9 In regressions with interaction effects (not reported) this difference is statistically significant at the 1% level. 14

15 They view frequent trading to be a sign of experience. Our findings in Section 3 provide an alternate explanation rooted in the greater propensity to sell large nominal loss positions that were acquired recently. Next, we report in Panel B the results for investors with more versus less diversified portfolios, measured by the average end-of-month number of stocks held by the household in the brokerage account. The level of diversification may partially reflect investor sophistication. In our restricted sample of households that hold at least two stocks on a sale date, the median (mean) number of stocks on a household-sell date is 6 (9.74). 10 Goetzmann and Kumar (2008) report that the median (mean) number of stocks owned by the unrestricted sample of households at the same brokerage house is three (four). We classify a household as undiversified if its portfolio s median number of stocks throughout the entire 71-month data period is three or fewer and diversified if the median is four or more. We find that the general reluctance to sell losers is stronger for undiversified investors: the marginal effect of the Loss dummy is percent for them and percent for the more diversified investors. 11 For undiversified investors, the probability of sale increases when nominal gains or losses increase, similarly to more diversified investors. However, the sensitivities to increases in both nominal gains and losses are statistically the same in the undiversified subsample, while more diversified investors are more sensitive to increases in nominal losses than gains. It suggests that undiversified investors exhibit a stable disposition effect across gains and losses of different sizes, while more diversified investors exhibit a diminishing disposition effect as nominal gains and losses increase due to the higher probability of realizing large losses compared to large gains. It may indicate that 10 Our sample s means and medians are computed across household-sell dates rather than just households (if a household sells any number of stocks on a given date, it is counted as one household-sell date), and households with more stocks in their portfolios tend to trade more and thus account for the majority of household-sell dates. 11 In unreported results we find the difference to be statistically significant at the 1% level. 15

16 diversified investors use a simple decision rule of cutting their largest losses due to limits to the cognitive resources they have to expand to monitor numerous stock positions. To test the impact of limited attention on stock sales, we explore the effects of a relatively large number of positions on the decision to sell. In unreported results (available upon request), we compare the effects of salience on household-sell dates with 10 or more stocks to household-sell dates with less than 10 stocks and find economically insignificant differences. In taxable accounts we observe a marginally higher sensitivity to the size of a loss for accounts with more positions, particularly for the shorter-term nominal losses, and a lower sensitivity to nominal gains. This is consistent with the tax-related incentives to realize short-term losses and defer realization of gains. We find no significant effect of the number of positions on the probability of large loss realization in tax-deferred accounts. We conclude that the focus on larger (more salient) nominal gains and losses is not exclusive to investors who may pay limited attention to individual positions due to a large number of stocks they hold. Panel C of Table 4 presents the results for different portfolio value ranges (measured as the average portfolio value prior to the date of sale). Investors with larger portfolios (over $100,000) represent 11 percent of accounts, but they are responsible for a disproportionately large portion (62 percent) of stock sales. Compared to investors with portfolio values below $100,000, investors with larger portfolios show a lower disposition effect (the marginal effect of the Loss dummy becomes less negative as the average portfolio value goes up) and lower sensitivity to nominal gains (the marginal effect of Norm$Gain declines as the portfolio value goes up). The lower sensitivity to nominal gains may be consistent with large investors being more tax savvy and delaying realization of large capital gains (Ivković, Poterba, and Weisbenner, 2005). Similarly to investors with smaller portfolios, they are more likely to sell a large loser than a small one: the coefficients of Norm$Loss are positive across the 16

17 four portfolio size classifications; they are statistically larger than their Norm$Gain counterparts for the largest three portfolio size ranges. 12 Overall, the probability of sale increases with nominal gains and losses for investors with all the different characteristics examined in this section. The higher sensitivity to changes in nominal losses than gains is exhibited by investors who are male, more diversified, and have portfolios with higher values; these groups dominate the trading activity in the sample. 3. Salience and holding periods Investors may react differently to gains and losses depending on how long they have held their positions. Thus, we examine in this subsection how nominal gains and losses affect stock sale probabilities across the holding period spectrum. 13 In Figure 1 we plot the marginal effects from the estimation of Equation 1 for the normalized nominal gain and loss variables (Norm$Gain and Norm$Loss) alongside the marginal effect for the losses in general (the Loss dummy) across different holding periods ranges, from below 15 days to over 30 months. The estimates were generated from separate regressions for each holding period range. In the shortest holding period ranges, while normalized nominal losses have a much stronger impact on the probability of sale than normalizes gains, although the general aversion towards realizing losses is stronger as well. For holding periods of 15 days or less, the marginal effect of a one-percent increase in the normalized nominal loss is 3.66 percent, which attenuates the 8.19 percent lower likelihood of realizing any loss in general. All else equal, increasing a normalized nominal gain by one percent of the portfolio value is associated with a 12 Knowing both the investor s portfolio value and total net worth would be ideal. However, while net worth figures are available for many accountholders, we use the portfolio value as an approximation of wealth. The reported net worth figures may not be very clean measures of wealth because they are (1) self-reported, and thus may be computed differently by different investors, (2) reported only once and not updated, and (3) not reported by all investors, and thus subject to self-selection. Regressions based on net worth ranges yield similar results. 13 Because our sample period covers just over five years and we can only analyze round-trip transactions, we may not capture the determinants of selling decisions for stocks with very long holding periods. However, retail investors tend to have relatively short holding periods for directly purchased stocks. 17

18 negligible marginal effect of 0.03 percent, though the estimates for the loss-related variables (i.e., Norm$Loss and the Loss dummy) show that smaller nominal gains are in general more likely to be realized than smaller losses. The findings for the shortest holding period range of up to 15 days are particularly striking: the marginal effects imply that a normalized nominal loss equal to (greater than) 2.34 percent would have the same (higher) probability of realization compared to the normalized nominal gain of the same size, eliminating the disposition effect. As the holding period lengthens, the impact of the magnitude of nominal losses on the probability of sale first falls steeply and then continues to decline steadily. As a result, the difference between the marginal effects of normalized nominal gains and losses shrinks; it is statistically insignificant for holding periods over 18 months. [Insert Figure 1 here] The results in Figure 1 help us visualize effects of salience of gains and losses in discrete time intervals. To examine the effects of salience (size of gains and losses relative to the portfolio value) with continuous changes in the holding period, we estimate Equation 1 on our full sample with additional interactions between the normalized nominal value changes and the holding period, Norm$Gain*HP and Norm$Loss*HP. Columns 1, 2 and 3 in Table 5 display the results for all, taxable, and tax-deferred accounts, respectively. The control variables are not presented in the interest of brevity. The results across all estimations are similar. As before, we observe the effect of incurring a loss (the coefficient of Loss is negative and significant) and the effect of salience on stock sales (the coefficients of Norm$Gain and Norm$Loss are positive and significant), with a stronger effect of nominal losses than gains. The recency effect is also evident: both HPGain and HPLoss variables have negative parameters. However, the estimated coefficients of the interaction Norm$Gain*HP is positive, while that of Norm$Loss*HP is negative. That is, the probability of realizing nominal losses falls faster than that of realizing nominal gains of the same size as the holding period lengthens. [Insert Table 5 here] 18

19 To visualize the effect of salience on stock selling decisions across holding periods, we plot in Figure 2 the predicted probabilities of sale based on the estimates presented in columns 2 and 3 of Table In Panel A (taxable accounts) we observe that the largest normalized gains and losses (along the left and right edges of the plot, respectively) are more likely to be realized than smaller ones. The probability of sale as a function of the holding period has a very steep for extreme losses (the right edge of the plot), while the slope for very large gains (the left edge of the plot) is virtually flat. The latter may be due to tax incentives: realizing large losses often reduces taxable income, while realizing large gains increases it. The plots in Panel B of Figure 2 (tax-deferred accounts) reconfirm our findings. In the absence of tax incentives, more recently purchased stocks are more likely to be sold for any given level of gains or losses, consistent with the impact of recency. [Insert Figure 2 here] When normalized nominal gains and losses are small, losses are less likely to be realized than gains in both taxable and tax-deferred accounts, especially at short holding periods. Thus, the disposition effect is most pronounced for smaller nominal gains and losses and longer holding periods. 15 The novel result of our analysis is that investors do not hesitate to realize large losses (relative to the portfolio value) soon after acquisition when compared to gains of the same size, but as time passes, large losses become less likely to be realized relative to gains of the same size. Thus, quickly accumulating a nominal loss that is large in the portfolio context is more likely to trigger a sale than quickly accumulating a gain of the same size or incurring the same large loss after holding a stock for a longer period of time. Tax considerations cannot entirely explain the higher probability of selling 14 We assume the fifth market capitalization decile (Cap_Decile = 5) and set the rest of the control variables to zero. 15 We have also estimated regressions for (i) narrower holding period ranges in Figure 1 and (ii) with dummy variables for three ranges of holding periods below one month, one to twelve months, and over twelve months in place of the continuous HP variable. We obtain similar results; they are available upon request. 19

20 large losers relative to winners with short holding periods because we also observe this pattern in taxdeferred accounts. Recently acquired positions in general are likely to receive greater attention due to the recency bias (Ben-David and Hirshleifer, 2012), making avoidance of recent losses more difficult. Chakrabarty, Moulton, and Trzcinka (2017) find that professional investment managers, when faced with a sharp fall in a stock price shortly after buying the stock, tend to overreact and close out the position, or, in practitioner vernacular, abandon his thesis, leading to a short-duration trade, although they may have done better if they held on longer to their positions. Our results for individuals are consistent with Chakrabarty, Moulton, and Trzcinka (2017) as we find that retail investors are more likely to abandon their large nominal losers in the short-term, eliminating the disposition effect. Dhar and Zhu (2006) attribute the lower disposition effect of frequent trades to the influence of experience gained through frequent trading. However, if it were the case, we would observe a smaller (in absolute value) marginal effect of the Loss dummy, of the Norm$Loss variable, or both for high-turnover investors. By explicitly studying the time dimension of stock holdings, we argue that high-turnover investors are more likely to have shorter holding periods, and investors tend to realize large nominal losses on recently acquired positions, resulting in the reduction of the disposition effect at short holding periods. We thus provide an alternative explanation for the link between high turnover and the lower disposition effect without making assumptions about investor experience or sophistication. We conclude that large nominal losses are more salient than gains of the same size for recently acquired stocks, but the difference in salience of large losses and gains of the same size diminishes with the passage of time. Why this is the case is an open question. Chang, Solomon, and Westerfield (2016) provide some insight by suggesting that the disposition effect may be rooted in cognitive dissonance (Festinger, 1962) a conflict between two cognitive elements (e.g., a person s belief that 20

21 he or she is a good investor and the fact that a stock they purchased has incurred a loss). However, Festinger (1962) notes the magnitude of the dissonance (i.e., discomfort) cannot exceed the resistance to change of the cognitive elements involved. Our finding that people are more likely to overcome the disposition effect by selling recently acquired stocks with large accumulated losses suggests that the salience of such losses may be sufficient to break the resistance to sell the losing stock. However, this is only a speculation because theory of cognitive dissonance does not predict what effect recency would have on the extent of the dissonance (discomfort) and on the ability to break the resistance to act (i.e., to overcome the discomfort). More research, especially experimental, is needed to confirm or refute this conjecture, which is beyond the scope of the present study. 4. Salience and stock valuation uncertainty We have established so far that individuals stock selling decisions are affected by normalized nominal gains and losses and that at short holding periods they are more sensitive to changes in losses than gains. However, uncertainty associated with a stock price may affect future stock price expectations, in turn affecting investor selling decisions. In this section we explore if stock price uncertainty influences investors responses to gains and losses. For example, investors with the prospect theory utility function may feel they have little to lose if the stock price continues to go down after accumulating a large nominal loss, but would like to avoid regret if the price recovers after the stock is sold. The possibility of a price recovery for a volatile stock may prompt an investor to hold it longer than a less volatile stock. To examine the effects of valuation uncertainty on selling decisions, we include different measures of uncertainty into our regressions, one at a time. We label this set of uncertainty measures VAR. It includes: (1) the high volatility dummy (High_Vlty), (2) the high idiosyncratic volatility variable (High_Idiosyn), (3) the low market capitalization dummy (Low_Cap), and (4) the lottery-type 21

22 stock dummy (Lottery_Stock). 16 Our measures of total and idiosyncratic volatility are calculated over the last six calendar months for all stocks in the CRSP database with at least one month of nonmissing data. As defined earlier for Equation (1), High_Vlty is 1 for stocks in the highest standard deviation decile and 0 otherwise. High_Idiosyn is 1 for stocks in the highest idiosyncratic volatility decile. Idiosyncratic volatility is the standard deviation of the residual from the Carhart (1997) four-factor model. Low_Cap is 1 for stocks in the lowest market cap decile at the end of the previous day. Lottery_Stock is 1 for lottery-type stocks, classified as such using the methodology in Kumar (2009b). 17 We include in our regressions the interactions of the valuation uncertainty measure with the Loss dummy (Loss*VAR) and the normalized nominal gain and loss variables (Norm$Gain*VAR and Norm$Loss*VAR). These interactions allow us to detect if the presence of losses and the salience of gains and losses affect the probability of sale differently for stocks with high valuation uncertainty and all other stocks. The output is in Table 6. While we use the holding period variables and the control variables in the estimation (see Equation 1), we do not report their parameters in the interests of brevity. 18 [Insert Table 6 here] The effects of losses in general (Loss) and of the magnitudes of normalized nominal gains and losses (Norm$Gain and Norm$Loss) are similar to those reported in our earlier tests. In Regression 1, where we use past return volatility (VAR=High_Vlty) to measure valuation uncertainty, we observe that uncertainty impacts investors responses to the size of normalized nominal losses but not 16 Instead of using extreme decile dummies, in our unreported results we also used alternative classification using actual decile rankings. Our conclusions are robust to these alternate classifications. 17 At the end of each month, Kumar (2009b) identifies stocks on the major exchanges (NYSE/NASDAQ/AMEX) with prices in the bottom 50th percentile, idiosyncratic volatility in the top 50th percentile and idiosyncratic skewness in the top 50th percentile as lottery type stocks. To check the robustness of our results, we also use the 33rd percentile benchmark, which results in a fewer number of stocks being identified as lottery stocks. Our results are insensitive to this alternate definition of lottery type stocks. 18 We drop control variables that are similar to the measures of uncertainty being considered in the regression. For example, in Regression 3, we drop the Cap_Decile variable because we use Cap_Low as a measure of uncertainty. 22

23 normalized nominal gains. The marginal effect of the interaction Norm$Loss*High_Vlty indicates that increasing a normalized nominal loss by one percent for a highly volatile stock reduces the probability of sale by an additional 0.33 percent. This cuts by about a half the marginal effect of 0.62 percent associated with the Norm$Loss variable itself. Perhaps the greater prospects of recovering losses in volatile stocks dampen individual investors propensity to sell positions with large nominal losses. This explanation is also supported by observing the marginal effect of percent for the interaction of High_Vlty with Loss, which indicates that the general disposition to avoid selling losing positions is even stronger in the presence of greater uncertainty. It is consistent with Kumar (2009a), who shows that individual investors demonstrate a stronger disposition effect for hard-to-value stocks. The disposition effect may be stronger for high-volatility stocks due to investors overconfidence, belief in mean reversion of stock prices, gambling tendencies such as the desire to break even, or reference points being affected by valuation uncertainty. Our results in column 2, with valuation uncertainty measured by idiosyncratic volatility (High_Idiosyn), mirror the results in column 1. Column 3 considers low market capitalization (Low_Cap) as another proxy for valuation uncertainty: smaller companies may be younger, less established businesses with greater idiosyncratic risk and relatively little media and analyst coverage. Similarly to high volatility and high idiosyncratic volatility (columns 1 and 2), low capitalization is associated with a reduced propensity to realize large nominal losses: the marginal effect of the interaction term Norm$Loss*Low_Cap is percent, offsetting more than a half of the marginal effect of Norm$Loss of 0.57 percent. A perceived shot at very large gains may tempt people to invest in stocks with lottery-like payoffs. Kumar (2009b) studied retail investors preference for lottery stocks. In specification 4, we employ the lottery stock dummy (defined in footnote 19) as a proxy for valuation uncertainty. Investors may expect losses on such stocks and may therefore react less to the presence and the magnitude of losses. Consistent with this hypothesis, the disposition effect is stronger for lottery-type 23

24 stocks than other stocks: the marginal effect of the Loss*Lottery_Stock interaction is percent. The sensitivities to changes in nominal gains and losses are also lower for lottery-type stocks: the marginal effects of the interactions Norm$Gain* Lottery_Stock and Norm$Loss* Lottery_Stock are and percent, respectively. They represent reductions of the impact of normalized nominal gains (losses) on the probability of sale by two-thirds, or 0.24 out of 0.36 percent (slightly less than a half, or 0.28 out of 0.65 percent). Overall, the relation between valuation uncertainty and the probability of selling losing stocks for retail investors is inverse, consistent with Kumar (2009a). As to gains, this relation is not consistent across different measures of stock valuation uncertainty. 5. Nominal Gains and Losses and the Rank Effect Hartzmark (2015) also studies stock selling decisions in the context of the overall brokerage portfolio. Using the same data set, he uncovers the rank effect - stocks with highest and lowest percentage or dollar changes in a household s portfolio are more likely to be sold than other stocks held in a household s portfolio. In this section, we test whether the impact of larger nominal gains and losses on the probability of sale is due to the extreme rankings of such gains and losses within the portfolio. To have meaningful rankings, we restrict our sample for the tests in this section to portfolios with at least five open positions on a sale day. Table 7 presents the output of four alternative regressions. Regression 1 is a rerun of Equation 1 for the sample we employ in this section. We observe similar results as in Table 2, except the marginal effect of the nominal gains is lower. In Regression 2, we add four dummy variables for the highest (Norm$Best), second highest (Norm$Best2), second lowest (Norm$Worst2), and lowest (Norm$Worst) nominal changes in position values since acquisition. [Insert Table 7 here] 24

25 In Regression 2, the marginal effects of the highest and lowest (best and worst) nominal value changes on the probability of sale is and 7.26 percent, respectively. They are 4.70 and 3.12 percent for the second best and second worst position ranks, respectively. Adding the four dummies for the extremely ranked nominal gains and losses results in the coefficient of Norm$Gain becoming negative and the coefficient of Norm$Loss remaining positive albeit smaller than in Regression 1. This is a natural consequence of the high influence of rankings because positions with the four extreme changes in nominal value are also much more likely to be sold. The fact that the impact of normalized nominal losses on the probability of sale remains positive and significant even after controlling for extremely ranked value changes suggests that the magnitude of nominal losses affects selling decisions beyond the rank effect. In Regression 3, we follow Hartzmark (2015) by introducing four dummy variables for the best two and the worst two percentage returns instead of the nominal gains or losses normalized by portfolio values. The marginal effects are similar to those in Regression 2. Finally, we combine the dummies for the best two and the worst two nominal value changes and percentage returns in Regression 4. While both sets of rank-related dummy variables retain their significance, the extremely ranked nominal value changes have a somewhat higher impact on the likelihood of sale. The correlations between rankings based on percentage returns and those based on normalized nominal value changes are positive but not close to perfect. 19 Thus, the results suggest separate rank effects for nominal value changes and percentage returns within a given portfolio. 19 For household-sell dates with at least 5 positions, the correlation between Norm$Best and Ret%Best, Norm$Best2 and Ret%Best2, Norm$Worst2 and Ret%Worst2 and Norm$Worst and Ret%Worst are 0.68, 0.48, 0.40 and 0.55, respectively. These correlations decrease further for households with more positions on a given sell date, while our key findings remain unchanged. For example, for household-sell dates with at least 10 positions, the correlations between Norm$Best and Ret%Best, Norm$Best2 and Ret%Best2, Norm$Worst2 and Ret%Worst2, and Norm$Worst and Ret%Worst are 0.63, 0.39, 0.31, and 0.46, respectively. 25

26 6. Large Loss Realization and Portfolio Performance Does the tendency to realize large nominal gains or losses affect performance? We examine investor portfolio performance based on the observed propensities to realize large nominal gains and losses in this section. We classify households based on the probability to realize large nominal gains (PLG) and losses (PLL). To compute these probabilities, we begin by classifying nominal gains and losses as large and small. When computing PLG (PLL), we consider only household-sell dates with at least two positions with gains (losses). We classify a gain (loss) as large if its absolute value is larger than the absolute value of the median gain (loss) on all gain (loss) positions on a given household-sell date. The probability of realizing large gains (losses) on each household-sell date is the number of above-median losses (gains) realized divided by the sum of the numbers of above-median realized and unrealized losses (gains). Next, we average the probabilities of realizing large gains (losses) for each household across all sale dates to arrive at the household s probability of realizing large gains (losses). Table 8 presents gross monthly returns, both raw and abnormal, based on the market model, the Fama-French three-factor model, and the Carhart four-factor model, in percent, for households in different terciles of PLG (Panel A) and PLL (Panel B). No investor group earns significant abnormal returns. Investors in the high PLL tercile earn significantly lower CAPM and four-factor alphas than their counterparts in the low PLL tercile. [Insert Table 8 here] To examine in greater detail the effect of loss realization patterns on portfolio performance, we next double sort households by PLL and turnover. We present the gross returns for these groups of households in Table 9. The differences between the gross CAPM and four-factor alphas of households in the high and the low PLL terciles are negative and significant for investors in the middle and the high turnover terciles. Thus, investors who trade relatively frequently and tend to realize their 26

27 larger nominal losses underperform. While the exact source of underperformance is not clear (unlike net returns, gross returns should not be affected by turnover), realizing one s larger losses may be a naïve trading strategy and a sign of low investor sophistication. [Insert Table 9 here] 7. Conclusion Why do individual investors sell the stocks they sell? The literature suggests that investors behavior may depend on accumulated gains and losses on investments. The few studies that have examined investors reactions to gains and losses (e.g., Ben-David and Hirshleifer 2012; Kaustia 2010) measured gains and losses with percentage returns on positions since acquisition. We extend this line of research by hypothesizing that nominal gains and losses are at least as important as percentage returns and by testing this proposition. Using individual investor stock trading data from a large US discount brokerage (e.g., Barber and Odean 2000), we model the likelihood of stock sales by households. Normalizing nominal gains and losses by the household s brokerage portfolio value, we find that larger normalized nominal gains and losses, but not necessarily higher absolute percentage returns, are associated with higher probabilities of stock sales by households. This result holds consistently across different account types, holding periods, and investor characteristics. Salience of large nominal gains and losses is the likely explanation of this effect. When viewing their stock portfolios, investors are more likely to focus on positions with large accumulated nominal gains or losses. As a result, the investors spend more time and effort thinking about or researching such positions, increasing the likelihood of further actions, including sales. Consistent with the importance of nominal gains and losses, Shavit et al. (2010) find in experimental setting that people spend more time looking at nominal value changes than percentage returns. 27

28 We use a household s brokerage portfolio value to normalize nominal gains and losses. Doing so allows us to compare the effect of gains and losses across investors and time periods and implies that the portfolio value is important for retail investors when they decide which stocks to sell. Since investors are able to simultaneously observe gains and losses on separate positions as well as the entire portfolio value and changes in it, they are unlikely to engage in the extreme form of narrow framing looking at positions in isolation without regard to the rest of the portfolio and instead are likely to weigh gains and losses on individual positions against the portfolio value. This hypothesis is consistent with Hartzmark s (2015) finding that return rankings within a given portfolio affect the probability of a stock sale. The higher sensitivity to changes in nominal losses than gains is exhibited by investors who are male, more diversified, and have portfolios with higher values; these groups dominate the trading activity in the sample. The higher probability of sale associated with large normalized nominal losses is partially offset for stocks with high valuation uncertainty, consistent with the finding of Kumar (2009a) that such stocks are subject to a stronger disposition effect. The effect of nominal losses on the probability of sale remains significant after controlling for the rank effect detected by Hartzmark (2015). Finally, investors who are more prone to realizing their larger nominal losses tend to underperform other investors. Being greatly affected by salience of losses may be a sign of low investor sophistication, which may be related to the underperformance. Our second major finding is that the likelihood of realizing nominal gains versus losses depends on investment holding periods. While the probability of a stock sale is in general inversely related to the holding period for both gains and losses (a manifestation of the recency effect), large nominal losses are more likely to be realized than nominal gains of the same size at holding periods up to one year. Shefrin and Statman (1985) show that investors tend to realize their winners over losers, the phenomenon known as the disposition effect. Our finding implies that there is no 28

29 disposition effect when gains and losses are large relative to the portfolio size and holding periods are short. This effect cannot be explained by tax incentives (e.g., short-term losses having a higher taxreducing potential under some circumstances than long-term losses) because we also observe it in taxdeferred accounts. For holding periods longer than one year, large normalized nominal gains are more likely to be realized than losses of the same size, consistent with the disposition effect. Small gains are more likely to be realized than losses of the same size across the entire spectrum of holding periods, also consistent with the disposition effect. We conclude that large nominal losses are more salient than gains of the same size for recently acquired stocks, but the difference in salience of large losses and gains of the same size diminishes with the passage of time. 29

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32 ME for Norm$Gain & Norm$Loss (Salience) ME for Loss Dummy (Diposition Effect) Figure 1 Marginal effects of Nominal Gains/Losses and Disposition Effect ME of Norm$Gain ME of Norm$Loss ME for Loss Dummy days days 1-3 mths 3-6 mths 6-9 mths 9-12 mths mths mths mths > 30 mths

33 Figure 2 Salience, holding periods, and the probability of sale 33