Tests of the disposition effect amongst UK managed funds

Transcription

1 Tests of the disposition effect amongst UK managed funds By Da Silva Rosa, Raymond To, Huong Minh & Walter, Terry Abstract We investigate the prevalence of the disposition effect (DE) amongst UK managed fund by using the Citywatch database of their daily holding positions in all equity stocks over the period September 2001 through to September In contrast to Odean s (1998) finding for clients of a discount brokerage house, we find that at once stock s capitalisation is controlled, UK managed funds tend to sell losers rather than winners. The most influential variable shaping funds propensity to sell a stock is its market capitalisation, a proxy for liquidity. Other significant variables positively correlated with the sell decision include market-to-book ratio and recent performance of the stock. UK funds tend to sell stocks that have had a recent reduction in price. We conclude UK managed funds do not exhibit the behavioural bias associated with the DE. JEL classification: G12; G23; G14 Keywords: Disposition effect, Managed funds, Size effect UWA Business School (M252), The University of Western Australia, 35 Stirling Highway, 6009, Nedlands WA. UNSW School of Banking and Finance, The University of New South Wales, 2052, NSW, and Capital Markets Cooperative Research Centre. Corresponding author: Ms Huong Minh To HuongMinh_To@yahoo.com We thank Phillip Brown, Terrance Odean, Tom Smith and participants of the 2004 Australasian Banking and Finance Conference for helpful comments. We are grateful to the data extraction assistance of Jennifer Cross. This paper is based on Huong Minh To s dissertation at the University of Western Australia. Financial support from the International Postgraduate Research Scholarship and International University Award is gratefully acknowledged. 1

2 I Introduction The disposition effect, i.e., investors tendency, even to their financial detriment, to sell stocks that have increased rather than decreased in value, challenges precepts of rationality underpinning neo-classical theories of financial markets. A potential neo-classical riposte to the impressive body of evidence on the disposition effect (DE) is that it reflects the behaviour of unsophisticated investors who are price followers rather than setters. Indeed, several studies indicate that the effect is substantially ameliorated, if not eliminated, amongst sophisticated investors 1. These considerations prompted Odean, in his landmark (1998) investigation of the DE amongst clients of a discount brokerage house, to observe that it would be useful to investigate the effect in settings where agency issues may play a greater influence in trading decisions. Our research is motivated by this concern. We investigate the prevalence of the DE amongst UK fund managers, who manage total assets worth about $2 trillion, 28% of it in UK equities 2. Our study is made possible by access to the Citywatch database of the daily holding positions in all equity stocks of all UK managed funds for the period from 21 September 2001 to 18 September For this period, we count in our data 2,581 different stocks, 4,264 different funds and over 78 million stock holding positions on the day that individual funds had a net increase or decrease in their holding of a given stock. In short, the data in our study allow us to directly address the remaining important question about the DE: its prevalence amongst sophisticated market participants whose trades have a substantial influence on market prices and who act as agents for investors. Our novel results are from logit regression analysis designed to test the hypothesis that evidence consistent with the DE amongst fund managers is function of coincidentally winning stocks having characteristics that promote their sale. Contrary to the DE evidence, we find that when fund managers decide which stocks to sell, they tend to select stocks of large firm, income stocks, and stocks that experienced a recent decrease in share price. After controlling for stock size, stock market-to-book ratio and stock s recent market-adjusted returns, the position of a stock compared to its reference point is no longer a significant factor affecting the selling decision. To test the robustness of our findings, we rerun 1 Studies documenting relevant evidence include Shapira and Venezia (2000), Locke and Manne (2000), and Brown, Chappel, Da Silva Rosa, and Walter (2002). 2 UK Investment Managers Association press release, 26 May URL last accessed 16 August

3 the regression analysis after separating samples of winning and losing stocks. The coefficients on the stock characteristics remain much the same. We conclude UK funds do not exhibit the behavioural bias associated with the DE. To facilitate comparisons with Odean (1998), we review evidence of the DE at the aggregate level, when gains and losses (realised and unrealised) are accumulated across time and across all funds under the assumption that each decision to sell or not is independent. We then review evidence of the DE at the fund level, that is, we assume the proportions of gains and losses realised in each fund is independent of that realised in other funds. The final tests depart from Odean s research design by, inter alia, assessing the association of the DE with frequency of trading by each fund and the size of stocks traded. These innovations are prompted by the possibility that evidence of the DE amongst fund managers is not a function of a behavioural bias but rather reflects that stocks that have increased in value over our sample period have characteristics that, quite rationally, differentially promote their sale by fund managers. Our findings include the following: (a) at the aggregate level, the disposition effect is apparent and it is robust to different measurement methods. This is consistent with the results of Odean (1998). (b) for low trading frequency funds who comprise the vast majority of funds, the DE is evident only in the last month of the UK financial year (March). The rest of the year, the low trading funds exhibit a reverse DE, i.e., selling a higher proportion of losers than winners. (c) High trading frequency funds show the DE in all months, although it intensifies in March. These results diverge dramatically to those documented by Odean (1998), who finds the DE disappears amongst retail investors in the last month of the financial year. He posits that the DE reversal amongst retail investors is motivated by their desire to crystallise losses for tax shielding purposes. Our evidence that the DE amongst fund managers is increased in the last month of the financial year is a clear indication that agency issues affect trading behaviour in a substantive way. In a further test, we find that when we sort observations into different groups of funds with different level of activity, the DE exhibits within each group. However, when we sort observations into different ranges with different levels of stock s market capitalisation and test for DE within each range, the DE reverses, i.e., the statistically significant manifestation of the DE evident when aggregated gains and losses are reviewed is replaced by a statistically significant tendency to sell losers in preference to winners. This result is consistent with the logit regression results that demonstrate UK funds have a systematic 3

4 preference for selling larger stocks, perhaps for liquidity reasons. In short, UK managed funds preference for selling larger stocks gives rise to the DE but it is not caused by a behavioural bias. The rest of the paper is organized as follows. An abbreviated summary of related research, intended to place this study in context rather than as a critique, is followed by a detailed description of the data made available to us, the steps we took in arriving at the final set of experimental data and the method we follow in calculating the respective proportions of gains and losses realized. Discussion of findings and conclusions follow in the succeeding sections. 2. Summary of relevant literature The DE is well documented. It has been found among individual stock investors in Odean (1998), Grinblatt and Keloharju (2001) and Shapira and Venezia (2001), professional stock traders in Lock and Mann (2000), futures traders in Heisler (1994), individual home owners in Genesove and Mayer (2000), and in employee stock option exercise behaviour (Heath, Huddart and Lang, 1999). In Australia, Brown, Chappel, Da Silva Rosa and Walter (2002) examine daily Australia Stock Exchange (ASX) stock registry data for investors in IPO and ASX index stocks between 1995 and 2000 and find that the DE is pervasive across investor classes with the exception of traders instigating larger investments who tend to be less affected by the behavioural bias driving the DE. Recent studies take the DE as given and focus on exploring the conditions under which it is more likely to manifest. The studies find that DE varies across investor types. For instance, Dhar and Zhu (2002) document that investor sophistication is related to the magnitude of the disposition effect. Recently, Barber et al. (2005a) in their empirical study on different investor groups composing the Taiwanese stock market found that individual investors, corporations and dealers prefer to sell winners rather than losers, while domestic mutual funds and foreign investors exhibit the reverse of the disposition effect. From those different in trading behaviour between different investor groups, Barber et al. (2005b) in their examination of the trading performance of different investor groups in the Taiwanese stock market reported systematic and economically large wealth transfers from individual investors to institutional investors. Notwithstanding the several studies linking investment sophistication with reduced susceptibility to the disposition effect, very few researches to date have investigated the incidence and strength of the disposition effect among fund managers. O Connell and Teo (2003) examine the relationship between past 4

5 performance and currency trading decisions of institutional investors and found no evidence of the disposition effects. Contrary, the authours report that the dominant characteristic is aggressive risk reduction in the wake of losses. Cici (2005) looks at the impact of the DE on the performance of a sample of 517 actively managed funds in the US and documents that 37 percent of the sample funds are affected by the DE and that the DE has an economically and statistically significant negative impact on fund performance. Different from Cici s study, our study relates the DE with a number of stock characteristics and the fund s level of activity to examine whether the DE is a result of behavioural bias or just a coincident result of fund mangers preference for selling stocks with some particular characteristics. Wermers (2003) observed the persistence in mutual fund returns over multi-year periods and link that persistence with the disposition effect. He argued that is because winning managers actively buy stocks on momentum, while losing fund managers also buy stocks on momentum but not as strongly as winning managers. Wermers (2003) found the underlying reasons are: (i) past winning funds experience high inflows from consumers while past losing funds experience outflows. As a result, losing funds don t have less funding to make additional purchases; (ii) past winning funds are more willing to sell off their existing position to finance new positions, while losing funds are less willing to do so. From that the author argued that losing funds appear reluctant to sell their losing stocks to finance the purchase of new momentum stocks, perhaps due to a disposition effect. This argument relating to the disposition effect, however, is relatively loose, since the author did not perform any direct test on the disposition effect, which is the comparison between the chance that a loss being sold compared with the chance that a gain being sold. One can argue that although losing funds are less willing to sell off their existing position, there is no difference regarding the probability that a gain or a loss in a losing fund portfolio being sold. Even if in fact losing funds exhibit the disposition effect, at the combination of both winning and losing funds level, the results may offset each other and it is possible that there is no disposition effect on the aggregate level. III Data and research method Data The Citywatch data used in our study comprises daily recording of holding positions of all UK managed funds for the period from 21 September 2001 to 18 September From this set of data, 78,044,174 observations are extracted they are stockholding positions on the days the fund has at least one increase or decrease in a stock s stockholding position. Among the 78,044,174 observations, there are 5

6 2,345 stock codes and 4,021 fund codes. Citywatch data fields used include: date, fund manager code, stock code, and number of shares held on the current date. There is no specific information on daily purchases or sales so we assume that any change in number of stocks owned by a fund manager from one day to the next is a result of a trade. Intraday multiple purchases and sales of the same stock are implicitly netted and treated as one transaction. Even so, some inaccuracy is unavoidable because dilution events 3, for example stock splits, stock bonuses, stock consolidation, are implicitly classified as purchases or sales. Given this caveat, there are 1,211,135 buys, 913,108 sells, and 75,919,931 holding positions. For each stock code, we extract stock price, market-to-book value, and number of stocks issued from Datastream and match with the Citywatch data set. Not all stock codes have the requisite information available in Datastream. There are 49,629,898 observations with available stock price data. The reason stock prices are unavailable for a proportion of stocks probably is that the stocks are unlisted. Unlisted stocks tend to be small and thus their exclusion is arguably desirable to ensure the results are not dominated by findings related an economically insignificant section of the market. Datastream fields used in this study are: date, stock code, adjusted stock price, number of stocks issued, and market-tobook value. There are 679,512 sales with stock price available. The mean value of sale transactions is 5,660,560 and the median value is 200,390. There are 864,499 purchases with stock price available. The mean value of purchase transactions is 6,092,848 and the median is 214,268. There are 48,085,887 holding positions. The mean value of the holding positions with available stock price is 9,699,119 and the median value is 410,865. Investigation of the disposition effect requires us to determine if an investment has made a gain or loss or neither. This first part of our study broadly follows Odean s (1998) approach: for any given investor, 3 To investigate the potential impact of dilution events on the empirical results, dilution factor which equals the number of stocks issued on day t divided by the number of stocks issued on day (t-1) is calculated for all stocks in the sample. The majority of the dilution factor values is very close to one, between 0.9 to 1.1. From Datastream dataset, there are 1,734 stockdate combinations which have dilution factor either greater than 1.1 or less than 0.9. Based on Citywatch data, most of the fund holdings on the days where dilution factor is close to one are unchanged, which indicates that there are no dilution events on those days. There are only 853 stock-date combinations which have dilution factor either greater than 1.1 or less than 0.9, which correspond to 17,128 observations (fund-stock-date combinations). Compared to the number of observations in the final dataset (36,989,344 observations), the number of observations affected by possible dilution events is, thus, non-substantial. 6

7 the proportion of all potential gains realized is compared against the proportion of all potential losses realized. Fund managers prone to the disposition effect exhibit a higher proportion of potential gains realized relative to potential losses realized. The research design is implemented as follows. Each day that a sale takes place, the selling price for each stock sold is compared with the reference point to determine whether the sale realised a gain or loss. In this study, the reference point is the volume weighted average purchase price (VWAPP). This approach is consistent with the approach in Brown, Chappel, Da Silva Rosa and Walter (2002). The use of the VWAPP as the reference point is based on the assumption is that fund managers update their reference point after each net purchase. From the initial dataset with 78,044,174 observations, all observations prior to or on 21 September 2001 are removed from the sample used to calculate Proportion of Gains Realized (PGR), Proportion of Losses Realised (PLR) and to run the regressions. That leaves 77,660,187 observations. The next step is to remove all those observations with no stock price available, which leaves 49,629,898 observations. Finally, only those observations on the days where the fund has at least one sale are kept. Also, all the observations on the day the fund sold out all the stocks are removed. In other words, only observations on the date that the fund has at least one sale and one holding position are kept. The final filtered dataset on which we undertake our analysis has 36,984,331 observations. Table 1 presents summary statistics for the sample of observations which underpins all the remaining analysis. The means of both firm size and market-to-book (MTB) ratio are higher than their medians, indicating that there are a small number of observations with very high firm size and MTB value. Similarly, the mean and median of the fund s activity suggest that there are a small number of very active funds. Table 2 presents the Pearson Correlation Coefficients between different variables in the data set. The signs of the coefficients indicate that large stocks and growth stocks are more likely to be in the gain zone during the studied period. Also, as expected, there is a negative relationship between the stocks market capitalisation and their MTB, or large stocks tend to be value stocks. More active funds tend to have stocks in the loss zone, smaller stocks and growth stocks. 7

8 Research method: Calculations of proportions of gains and losses realised VWAPP for stock i hold by fund x on a day t is calculated as follows: If the fund decreases or maintains their level of stockholding of stock i, the VWAPP of stock i on day t equals the VWAPP of stock i on day (t-1). If the fund increases their level of stockholding of stock i, the VWAPP of stock i hold by fund x on day t is recalculated as follows: Share Price (i, t) Number of Shares Bought (i, x, t) VWAPP (i, x, t -1) Number of Shares Held (i, x, t -1) VWAPP (i, x, t) = Number of Shares Held (i, x, t) + VWAPP is calculated based on the above formula for each fund-stock-date combination. Each day that a sale takes place, the selling price for each stock sold is compared with the VWAPP to determine whether the sale realised a gain or a loss. For other stocks in a portfolio held but not sold on the same day as a given stock is sold, the market price is compared with the reference point to determine whether a gain (paper gain) or a loss (paper loss) has been made. On days when no sales take place on a fund manager s account, no gains or losses, realised or on paper, are counted. These data thus allow the following ratios to be calculated, on each day that a fund is a net seller of stock: Proportion of Gains Realised = Realised Gains/(Realised Gains + Paper Gains) Proportion of Losses Realised = Realised Losses/(Realised Losses + Paper Losses) IV Results Table 3 reports PGR and PLR. We see that managed funds sell a higher proportion of their winners than of their losers when trades over the entire year are reviewed. PGR is 1.90% and PLR is 1.78%, the null hypothesis, PGR PLR, is rejected with a t-statistic of at 0.01 level of significance. The test of significance treats each sale for a gain, sale for a loss, paper gain on the day of a sale, and paper loss on the day of a sale as separate independent observations. Observations are aggregated across investors. The financial year end in the UK is most commonly the end of March. Odean (1998) reports a reversal of the disposition effect amongst the clients of his US discount broking house in the last month of the financial year as they (rationally) seek to realise their losses for tax purposes. Curiously, in light of 8

9 Odean s result, the middle column of Table 3 indicates the disposition effect is intensified amongst UK managed funds in March, the PGR being 2.62% and the PLR being 1.92% and the t-statistic of indicating beyond reasonable doubt that the difference is significant. For the remaining 11 months of the year, the difference between PGR and PLR is also statistically significant, but not as high as the March s result. Odean (1998, p. 1796) observes, in closing, that the trading data he analyses from a discount brokerage house avoids the need to consider agency issues that influence institutional investors. Arguably, our findings illustrate the pertinence of Odean s point. One may argue that there is possibly a high autocorrelation within the time-series daily PGRs and PLRs. We test the covariance between daily PGRs and PLRs, using the Generalised Method of Moments (GMM) covariance matrix approach. The estimated t-ratio is 1.88, suggesting there is no statistically significant autocorrelation between time-series PGR and PLRs 4. Next, we examine if stock characteristics rather than behavioural bias are the main factors affecting the selling decision. Among stock characteristics, liquidity is unlikely to be the only factor, although it is likely to be a major factor, influencing fund managers selection of stocks to sell. Two other factors likely to be influential are the market-to-book ratio and stocks recent performance. The market-tobook ratio is a likely candidate because of the evidence in Fama and French (1992) and elsewhere that return is positively associated with the value of the market-to-book ratio. Similarly, evidence supportive of the momentum effect suggests that managers will include the recent performance of a firm as a consideration when deciding whether to sell. We test these suppositions using logit regression. Our method and results are described next. Logit regressions of the probability to sell or hold a gain or a loss are performed. On each day a sale occurs, the dependent variable takes the value of one for the stock(s) being sold and zero for all other stocks remaining in that fund s portfolio. The logit regressions on the sell versus hold decision are estimated for the overall sample of transactions, and then separately for the sample of gains and the sample of losses. The analysis assumes that the fund managers action to sell a stock comprises two separate, consecutive decisions: (i) the decision to sell, followed by (ii) the selection of stocks to sell. Model 1 aims to test the disposition effect on the whole sample and takes the following form: 4 We are grateful to Tom Smith comments and suggestions regarding the GMM test. 9

10 P(sold=1) = β 0 + β 1 DV(Gain=1) + ε i (Model 1) with DV(Gain=1) equals to 1 for a gain and 0 otherwise. The results of Model 1 (see Table 4) shows that ignoring the impact of all other factors, UK managed funds tend to sell a position when the underlying stock is in the gain zone. This result is consistent with that presented in Table 3. Model 2 incorporates two stock characteristics: market capitalisation and market-to-book ratio: P(sold=1) = β 0 + β 1 DV(Gain=1) + β 2 ln(firm-size i ) + β 3 MTB + ε i (Model 2) With: DV(Gain=1): equals to 1 for a gain and 0 otherwise. Ln(Firm-Size): the logarithm of the market capitalisation of the firm. Market capitalisation is defined as the product of number of stocks issued and current stock price. MTB: the market-to-book ratio of the firm. The results reported in Table 4 show that once stock characteristics are taken into account, the positive relationship between the variable DV(Gain=1) or the position of an investment compared with its reference point and the selling decision no longer exists. The sign of the coefficient of DV(Gain=1) in Model 2 is negative, which indicates that the disposition effect is not manifest. UK managed funds exhibit the reverse of the DE, once stock characteristics enter the model as control variables. Model 2 shows that each stock s market capitalisation and its market-to-book value are significantly associated with the decision to sell. The coefficient of the Ln(Firm-Size) variable is , the coefficient of the MTB variable is These coefficients indicate that when considering which stocks in a portfolio to be sold, UK managed funds tend to select larger stocks and stocks with lower market-to-book ratio (or income stocks). In other words, the selling decision of UK managed funds is highly influenced by the characteristics of the stock. 10

11 Model 3 incorporates the Activity variable into the regression with Activity equals the total number of sales and purchases that the fund carried out during the studied period. The Activity variable is typically defined as the total number of trades that an investor executes within a certain defined time period, for example, one year. As the time series of the CityWatch data set used in this study is only nearly three years, we calculate the variable for the whole studied period. Thus, the value of the Activity variable only changes at the fund level. P(sold=1) = β 0 + β 1 DV(Gain=1) + β 2 ln(firm-size i ) + β 3 MTB + β 4 Activity + ε i (Model 3) The regression result of Model 3 is presented in Table 4. The positive coefficient of the Activity variable ( ) indicates that, as expected, funds with higher level of activity tend to sell more stocks compared with the number of holding positions. The coefficients of all the other variables, DV(Gain=1), Ln(Firm-Size), and MTB remain virtually unchanged between Model 2 and Model 3. Model 4 incorporates the Return variable into the regression with Return equals the market-adjusted stock return over the last 30 days immediately prior to the observation day. P(sold=1) = β 0 + β 1 DV(Gain=1) + β 2 ln(firm-size i ) + β 3 MTB + β 4 Activity + β 5 Return + ε i (Model 4) The regression result of Model 4 is presented in Table 4. The result of Model 4 indicates that UK managed funds selling decision is more influenced by the recent performance of the stock rather than the position of the stock compared with its reference point. UK managed funds tend to sell stocks which have recent reduction in stock price. The relatively stability of coefficients of the Ln(Firm-Size) and MTB variables in Models 2, 3 and 4 shows that the results on the relationship between firm characteristics and the selling decision is robust. In short, Table 4 shows that when fund managers make the selection decision of which stock(s) in the portfolio to sell (having made the selling decision), they tend to select stocks of large firm and income stocks rather than stocks that are considered as a gain as predicted by the disposition effect argument. Logit regression analysis run separately on winning stocks and on losing stocks 11

12 The logit regression results reported in Table 4 show that in overall UK managed funds do not exhibit the disposition effect. The selling versus holding decision is influenced by the stock characteristics rather than the position of the stock price compared with its reference point. To test the robustness of our findings on the relationship between the stock characteristics and the selling versus holding decision, we run different regressions separately on the sample of gains and the sample of losses. The sample of gains comprises all realised gains and paper gains. The sample of losses comprises all realised losses and paper losses. If stock characteristics, rather than the stock s position compared to its reference point, are important factors influencing the selling versus holding decision, their coefficients with the dependent variable should be consistent for the whole sample, sample of gains, and sample of losses. On the other hand, if the disposition effect in fact exists among UK managed funds, we expect the coefficient of the stock characteristic variables to vary when regressions are run on different data samples. Table 5 presents the regression results on the sample of gains. The coefficients of Models 5, 6 and 7 are very close to the value of the corresponding coefficients of Models 2, 3 and 4. Similarly to Table 4, Table 5 indicates that there is a strong positive relationship between the size of the firm and the selling decision. Also, the negative relationship between the stock s MTB ratio and the selling decision is statistically significant. Table 6 presents the regression results on the sample of losses. Again, the coefficients of Models 8, 9 and 10 are very close to the value of the corresponding coefficients of the models for the whole sample and for the sample of gains. Similarly to Tables 4 and Table 5, Table 6 indicates that there is a strong positive relationship between the size of the firm and the selling decision. In short, the regression results strongly indicate that regardless whether an investment is considered as a gain or loss, UK managed funds tend to sell larger stocks and hold onto smaller stocks. UK managed funds also prefer to sell income stocks in preference to growth stocks. This is consistent with common trading strategy of longer investment horizon for growth stocks compared with income stocks. Also, UK managed funds do not exhibit behavioural bias associated with the DE. The DE evidence when firm size and MTB are not controlled is actually the firm size and MTB effect. The seeming positive relationship between the dummy variable (gain=1) and the selling versus holding decision in Model 1 is because of the positive correlation between Ln(Firm Size) and the dummy variable (gain=1) (see Table 12

13 2). There is in fact no positive relationship between the dummy variable (gain=1) and the selling versus holding decision. It should be noted that the relationship between firm size and the selling versus holding decision in this study is different from the findings in the study of Ranguelova (2001). Ranguelova documents evidence that individual investors hold winners and sell losers in small stocks and hold losers and sell winners in large stocks. Ranguelova argues that individuals tend to chase trends in small stocks and value in large stocks. This study found that UK managed funds tend to consistently sell large stocks and hold small stocks, regardless they are in gain or loss zone. Additional Tests To test if the robustness of the above conclusion after controlling for the size of the funds, we divide the sample into four groups according to the size of the fund. Group 1 contains smallest funds and group 4 contains largest funds. Logit regression on the probability to sell a stock is re-run for each group separately. Table 7 presents the regression results. The coefficients of the Ln(Firm Size) variable are positive and statistically significant for all the four groups, indicating that the impact of stocks firm size on the selling decision is stable for all fund size. On the other hand, the coefficients of the dummy variable (gain=1) are statistically insignificant for group 1 and 2. Only the largest funds have the preference to sell losers. To recheck the above conclusions, we run logit regressions of the probability of sales versus holds on firm size and market-to-book ratio separately. Table 8 presents the result of the regression. Model 12 again shows that firm size has a positive relationship with the selling versus holding decisions. The Pseudo-R 2 of Model 12 (3.7%) is at a similar level compared with those of the previous models. This indicates that Ln(Firmsize) is an important variable. The value of the Ln(Firm Size) variable s coefficient is relatively close to its coefficient values in the previous models, indicating the relationship is robust. Also, when replacing Ln(Firm Size) by MTB variable in Model 13, the Pseudo-R 2 drops to only %. This indicates that although statistically significant, the impact of the MTB variable is 13

14 economically marginal. In short, Ln(Firm Size) is the most important variable influencing UK managed funds selling decision. The above results suggest a positive relationship between firm size and the selling decision at the fundstock-day observation level. Table 9 shows the regression results on the relationship between firm size and trading activity at the stock level. The result of Model 14 shows that large stock tends to have significantly higher turnover compared to smaller stocks. This is consistent with the results of the above regressions on the positive relationship between firm size and the selling decision. There are a number of possible reasons for the tendency of managed fund to sell (and purchase) large stocks more frequently than small stocks. First, large stocks are more liquid thus easier to sell. Second, fund managers may avoid selling small stock because a large sale in a small stock may mean they have to accept a selling price affected by price pressure. PGR and PLR analyses In the remaining section of this study, we analyse the PGR and PLR results in details. As mentioned above, Table 3 shows that at the aggregate level, PGR is greater than PLR for the whole year and for March, the month before the financial year end. The logit regression sections have indicated that this result is a by-product of the tendency to sell large stocks and hold on to smaller stocks, rather than a behavioural bias by itself. We further look that the PGR and PLR from different aspects to recheck this conclusion. We test the robustness of our results by investigating the DE at the fund level rather than at the transactional level, i.e., we assume the proportions of gains and losses realised in each fund are independent of those realised in other accounts. In this test, PGR and PLR are estimated for each fund and PGR PLR is calculated, also for each fund. A fund is included only if the denominators for both PGR and PLR are nonzero. There are 2,300 such funds. Table 10 presents PGR and PLR at the fund level. The results in Table 10 are consistent with Odean s findings. 14

15 For his sample of discount brokerage house accounts analogous to funds in our study - Odean finds that evidence of the disposition effect increases in strength relative to that observed at the transactional level: (t)he average account PGR is 0.57 [57%], the average account PLR is 0.36 [36%], the average of PGR-PLR is 0.21 [21%], and the hypothesis that the mean of PGR-PLR is less than or equal to zero is rejected at t-statistic of 19 (p. 1784). Consistently, we find that the funds average PGR is 27.15% and their average PLR is 21.56%, and the average of PGR-PLR is 5.59% The hypothesis that the mean of PGR-PLR is less than or equal to zero is rejected at t-statistic of Note that PGR and PLR in both Odean s and our study are higher when calculated at the accounts or funds level compared to when calculated at the transactional level. Odean (1998) explains the reason PGR and PLR are higher when calculated at the accounts level is that they are dependent on the average size of accounts. Given the way realised and paper gains or losses are counted, accounts with higher number of stocks and whose owners trade frequently will have smaller PGR and PLR measures. However, all accounts are weighted equally when calculating average PGR PLR. In his sample, smaller accounts whose owners trade infrequently predominate so the average PGR and PLR is higher. Given that our results for PGR and PLR at the funds level are qualitatively similar to those reported by Odean there is a prima facie assumption that the same applies to our sample: it is dominated by small funds characterised by relatively infrequent trading so average PGR and PLR are higher at the funds level. Nevertheless, as Odean observes, of primary interest is not the individual values of PGR and PLR but their values relative to each other (p. 1786). In Odean s sample the relative average values of PGR and PLR per account remain constant even when they are weighted by number of stocks or dollar value of stocks. Similarly, our results remain stable when we weight PGR and PLR by number of stocks or dollar value of stocks (see Table 10). Also, in our sample the value of average PGR relative to average PLR are steady when calculated either on the transaction, the stock volume, or dollar value bases. PGR is greater than PLR at the 1% level of significance on all three different measures. Evidence of the DE when gains and losses are weighted by number of stocks in Table 10 is consistent with more frequent traders driving the DE. This could be the case if frequency of trading is negatively correlated with information-based trading and such traders are more prone to behavioural biases. Differences in PGR PLR amongst groups of funds categorised on the basis of number of trades 15

16 undertaken over the sample period 5 are reported in Table 11. The results are striking. The 1,492 funds (i.e., 89% of the total) that undertake fewer than 2,500 trades over our sample period exhibit the DE only in March. In fact, the results show they appear to have a statistically significant preference to sell losing stocks in the rest of the year. In contrast, funds with many trades exhibit the DE all year round, although it is intensified in March. The relationship between the fund s trading frequency and the DE is further investigated in Tables 12 and 13. In Table 12, we sorted all observations into four different groups in accordance with the fund s level of trading activity. Each group has the same number of observations. Group 1 contains observations from funds with the lowest number of trades and Group 4 contains observations from funds with the highest number of trades. As presented in Table 11, PGR is statistically greater than PLR in all groups, and the difference between PGR and PLR consistently increases from Group 1 to Group 4. Please note that all observations of Groups 1, 2 and 3 and a significant proportion of observations in Group 4 belong to the 10% of funds that have more than 2,500 trades during the studied period. Thus, the result of Table 12 is consistent with the result of Table 11. Table 12 shows that among high trading frequency funds, the magnitude of the DE is also strongly correlated with the level of trading activity. Although Table 12 has an equal number of observations in each quintile, due to a small number of very active funds, most funds belong to quintile 1. In Table 13, we divide the 1,442 funds in our final dataset into five different groups by the fund s number of trades with each group has approximately an equal number of funds. Surprisingly, the majority of the funds (Groups 1 to 4) do not exhibit the DE, while the DE is strongly presented in Group 5. This indicates that at the fund level, the DE of the minority of funds with the highest level of trading activity is driving the result for the entire dataset. Another observation from Table 13 is that when we look at the ratio of sales over holding positions, this ratio is particularly high amongst Groups 1 and 2 (12.53% and 13.09% respectively) and low amongst Groups 4 and 5 (2.71% and 1.81% respectively). This indicates that funds with low level of trading activity also has a significantly smaller portfolio, and thus their managers might be able to follow their investments more closely and avoid any behavioural bias. Meanwhile, funds with high level of trading activity tend to have portfolios with much larger number of stocks. 5 We define a trade for each fund as a net change in its holding of a given firm over the course of a trading day. This of course is a downward biased estimate of transactions in that stock that might have been undertaken by the fund. However, our interest is in ranking funds by level of trading activity and there is no reason to believe our measure biases our rankings. 16

17 The results in Table 13 are consistent with managers of high trading frequency funds being more susceptible to the behavioural bias associated with the DE but there is another explanation that also fits the results. If, having made the decision to sell, managers select stocks on the basis of characteristics that are correlated with those stocks that have increased in value, then not controlling for those characteristics will give rise to evidence consistent with the DE. The most likely characteristic is liquidity. The relatively large parcels of shares traded by fund managers means they are likely to select more liquid stocks having made the decision to sell. If liquid stocks have experienced a greater increase in value over the sample period relative to less liquid stocks and fund managers generally sell (and purchase) more liquid stocks the disposition effect will manifest but for reasons unrelated to behavioural biases. We report tests of this explanation below. We use the size (i.e., market capitalisation) of the stocks in which funds have invested as a proxy for liquidity. In our first pass at controlling for the impact of firm size, we review evidence of the DE within each of four ranges of firm sizes (see Table 14 for span of each range). Each group has the same number of observations. To clarify, the analysis remains at the transaction level but average PGR and PLR are reported separately for each size range of stocks. This approach prevents the transactions for the largest, most liquid stocks dominating calculations of average PGR and PLR. Table 14 reports results from our review of PGR and PLR after we control approximately for firm liquidity. The number of firms in each of the four size ranges is reported in the second row of data. A salient point is that smaller firms predominate; firms larger than 133,292 million (the range with the largest firms) comprise just 8.45% of all firms. However, Table 13 indicates that the very largest firms account for just under half, 47.33% of all realised gains, 46.58% of all realised losses, and 46.99% of all realised gains and losses. This last pair of statistics point to why controlling for firm size (among other potential factors) is important in evaluation of the DE. If investors sell (and purchase) more of large firms for liquidity reasons then trading activity consistent with the DE will manifest when large firms increase in value over the experimental period. The evidence consistent with the DE will be enhanced when gains and losses are weighted by volume of shares traded or dollar value. The PGR and PLR statistics in Table 14 show that once firm liquidity is controlled even approximately, the DE effect reverses. Within all the four size ranges, funds are significantly more likely to sell their 17

18 losing stocks rather than their winning stocks. This strongly indicates that stock characteristics rather than the DE are the main determinant of the selling decisions. Finally, we re-divide the sample into five groups in accordance to the stock firm size. Each group contains the same number of stocks. The results presented in Table 15 reconfirm the results in Table 14. Once firm size is controlled, UK managed funds exhibit the reversal of the DE. One of the limitations of this study is that it does not take into account the fund s investment styles, particularly if the fund is active, passive or index. The information on the fund s investment style is not available in the Citywatch database. Since the sale of a stock in a passive index fund entirely depends on whether the weight of that stock in the index is reduced, there is no decision to be made by the fund manager. Because this study is about the selling decision of fund managers, ideally index fund managers should be excluded from this study. The distinction between passive and active funds can influence the results of this study if passive index funds account for a large proportion of the sample. Nevertheless, since the level of trading activity of passive and index funds is expected to be much lower than active funds, the influence of such passive trading transactions on the overall result of this study should be insignificant. V Conclusions This paper analyses the factors affecting the selling decision of UK managed funds. The paper finds strong evidence that the disposition effect does not exhibit among UK managed funds and the most important factor influencing the selling versus holding decision is the size of the stock s market capitalisation. When selecting stocks to sell, managed funds tend to choose large rather than small stocks. There are a number of implications associated with this finding. First, this result indicates that the psychological reason of the disposition effect (if it is the real cause) can be overcome. Fund managers with a higher level of sophistication compared to individual investors appear to not exhibit the disposition effect. Second, this result raises question on the behavioural explanation of the disposition effect. The literature tends to argue that it is difficult, if not impossible, to overcome psychological factors. If so, the disposition effect might not be psychologically driven, but could be the outcome of deliberate investor decisions based on the expectation that selling winning and retaining losing investments maximises return. 18

19 REFERENCES 1. Barber, B., Lee, Y., Liu, Y. and T. Odean (2005a). Is the aggregate investor reluctant to realize losses? Evidence from Taiwan. Working Paper. University of California and the National Chengchi University. 2. Barber, B., Lee, Y., Liu, Y. and T. Odean (2005a). Who losses from trade? Evidence from Taiwan. Working Paper. University of California and the National Chengchi University. 3. Brown, P., Chappel, N., Da Silva Rosa, R. and T. Walter (2002). The reach of the disposition effect: Large sample evidence across investor classes. Working Paper. University of Western Australia and University of New South Wales. 4. Cici, G. (2005). The impact of the disposition effect on the performance of mutual funds. Working Paper. Wharton Research Data Services. 5. Dhar, R. and N. Zhu (2002). Up close and personal: an individual level analysis of the disposition effect. Working Paper No Yale International Center for Finance. 6. Genesove, D. and C. Mayer (2000). Loss aversion and seller behaviour: Evidence from the housing market. Working Paper. Hebrew University of Jerusalem. 7. Grinblatt, M. and M. Keloharju (2001). What makes investors trade? Journal of Finance. 52(2) Fama, E. and K. French (1992). The cross-section of expected stock returns. Journal of Finance. 47(Number???), Heath, C., Huddart, S., and M. Lang (1999). Psychological factors and stock option exercise. Quarterly Journal of Economics Heisler, J. (1994). Loss aversion in a future market: an empirical test. Review of Futures Markets. 13(???) Lock, P. R., and S. C. Mann (2000). Do professional traders exhibit loss realization aversion. Working Paper. The George Washington University. 12. O Connell, P.G.J. and M. Teo (2003). Prospect theory and institutional investors. Working Paper. State Street Associates, LLC and Singapore Management University. 13. Odean, T. (1998). Are investors reluctant to realize their losses? Journal of Finance. 53(5) Ranguelova, E. (2001). Disposition effect and firm size: New evidence on individual investor trading activity. Working Paper. Harvard University. 15. Shapira, Z. and I. Venezia (2001). Patterns of behaviour of professionally managed and independent investors. Journal of Banking and Finance Wermers, R. (2003). Is money really smart? New evidence on the relation between mutual fund flows, manager behaviour, and performance persistence. Working Paper. University of Maryland. 19

20 Figure 1: Flow diagram of datasets Citywatch 78,044,174 obs (2,581 stocks) (4,264 funds) Variables: date, fund code, stock code, current stock holding Datastream Variables: date, stock code, adjusted stock price, market-to-book value, number of stocks issued Keep observations from 22/9/ ,653,265 obs Keep observations with attached stock price 49,629,898 obs Keep observations on the days the fund has at least one decreased stockholding position 36,989,344 obs Remove all observations on the days the fund sold out all stocks. 36,984,331 obs 20

21 Table 1: Descriptive Statistics Table 1 reports the descriptive statistics of stock market capitalisation and market-to-book ratio, and funds total number of trades included in the regression data set. Variable N Mean Median Standard Deviation Firm Size 38,292, ,720,000 21,779,667 1,052,931,509 Market-to-book ratio 36,829, Activity 38,292,235 7,893 7,

22 Table 2 Pearson Correlation Coefficients Table 2 reports the Pearson Correlation Coefficients between the variables and the Prob> r under Ho: Rho=0. DV(Sold=1) DV(Gain=1) Ln(Firm Size) MTB Activity DV(Sold=1) 1 DV(Gain=1) (<0.0001) Ln(Firm Size) (<0.0001) (<0.0001) MTB (<0.0001) (<0.0001) (<0.0001) Activity (<0.0001) (<0.0001) (<0.0001) (<0.0001) 1 22

23 Table 3 PGR and PLR at the aggregate level Comparison of the aggregate Proportion of Gains Realised (PGR) to the aggregate Proportion of Losses Realised (PLR), where PGR is the number of realised gains divided by the number of realised gains plus the number of paper (unrealised) gains, and PLR is the number of realised losses divided by the number of realised losses plus the number of paper (unrealised) losses. Realised gains, paper gains, realised losses and paper losses are aggregated over time (22 Sep 2001 to 18 September 2004) and across all UK managed funds in the data set. PGR and PLR are reported for the entire year, for March only, and for April through February. Entire Year March Apr.-Feb. Realised Gains 384,263 41, ,078 Paper Gains 19,815,150 1,528,200 18,286,950 Realised Losses 321,598 29, ,371 Paper Losses 17,771,224 1,494,130 16,277,094 Proportion of gains realised 1.90% 2.62% 1.84% Proportion of losses realised 1.78% 1.92% 1.76% PGR-PLR 0.12% 0.71% 0.08% t-statistic (To calculate the t-statistics in Table 3, the standard error for the differences in the proportions PGR and PLR is PGR( 1 PGR) PLR( PLR) + 1 Nrg + Npg Nrl + Npl where Nrg, Npg, Nrl and Npl are the number of realised gains, paper gains, realised losses and paper losses respectively. 23