The Behavior of individual investors 1

Outline Introduction Barber et al. (2008)  Data and Methods  Results  Reasons to Trade Barber et al. (2007)  Data and Methods  Results 2

Introduction A large body of empirical research indicates that real individual investors behave differently from investors in modern finance model (rational model). 1. Many individual investors trade actively, speculatively, and to their detriment. Surprising, many studies document that individual investors earn poor returns even before (transaction) costs. 2. As a group, individual investors make systematic, not random, buying and selling decisions. 3

Introduction  Disposition effect: Individual investors tend to sell winning investments while holding on to their losing investment. This effect is among the widely replicated observations regarding the behavior of individual investors.  Failure to diversify: Individual investors tend to hold stocks of companies close to where they live and invest heavily in the stock of their employer. These behaviors lead to an investment portfolio far from the market portfolio proscribed by the CAPM. 4

Introduction  Attention-based buying: Individual investors are influenced by the media. They tend to buy, rather than sell, stocks when those stocks are in the news. 5

Data and Methods- Barber et al. (2008) This study acquired the complete transaction history of all traders on the TSE from January 1, 1995, through December 31, The trade data include the date and time of the transaction, a stock identifier, order type (buy or sell), transaction price, number of shares, and the identity of the trader. The trader code allows us to categorize traders broadly as individuals, corporations, dealers, foreign investors, and mutual funds. The basic descriptive statistics on the market during the 1995–1999 period are presented in Table 1. 6

Data and Methods  Turnover in the TSE is remarkably high—averaging almost 300% annually during the sample period. In contrast, annual turnover on the New York Stock Exchange (NYSE) averaged 97% annually from 2000 through  Day trading is also prevalent in Taiwan. Day trading is defined as the purchase and sale of the same stock on the same day by an investor. Over the sample period, day trading accounted for 23% of the total dollar value of trading volume. 7

Data and Methods Table 2 reports the total value of buys and sells of stocks for each investor group by year. Individual investors account for roughly 90% of all trading volume and place trades that are roughly half the size of those made by institutions. Each of the remaining groups accounts for less than 5% of total trading volume.  Equities are an important asset class for Taiwanese. Table 3 illustrates the ratio of equity value to total assets (and to total assets excluding real estate). For all households owning equity, equities average 24% of total assets and 45% of non-real-estate assets. 8

Data and Methods Dollar Profits In the main analysis, the authors calculate a time series of daily trading profits earned by each investor group so as to precisely calculate the trading gains and losses between investor groups. The robustness of the results is further tested by analyzing abnormal returns. The calculations of dollar profits  Each day construct two portfolios for each investor group: one that mimics the net daily purchases and one that mimics the net daily sales. 9

Data and Methods  The purchase price is recorded as the difference between the total value of buys and the total value of sells divided by the net shares bought. (take net buy for example)  Shares are included in the portfolio for a fixed horizon; different horizons of 1, 10, 25, and 140 trading days are considered. Shares are marked to market daily.  The daily dollar profits for the buy portfolio are calculated as the total value of the buy portfolio at the close of trading on day t − 1 multiplied by the spread between the return on the buy portfolio and the market on day t. 10

Data and Methods  Ultimately, the statistical tests use a time series of daily dollar profits from January 1995 to December Thus, it is assumed that each day represents an independent observation of the total profits earned by a particular group. Return Calculations To test the robustness of the dollar profit calculations, the authors also calculate monthly abnormal returns on the buy portfolio, sell portfolio, and buy less sell portfolio for all investor partitions. 11

Data and Methods  Statistical tests are based on the monthly time series of the portfolio return and abnormal returns from a four- factor model (eq. (1)). 12

Results Table 4 presents the main results on the dollar profits (and losses) from trade for each investor group. 1. Individual investors incur losses that grow from mean daily losses of $NT 35.3 million after one day to $NT million after 140 trading days (column 1). At each horizon, the losses are highly significant with test statistics ranging from −4.68 to −  Stocks bought by individuals lose money at horizons of 1 and 10 days, but their losses on purchases are indistinguishable from zero at the longer horizons of 25 and 140 trading days (column 2). 13

Results  Stocks sold by individuals subsequently perform well at all horizons resulting in trading losses to individuals. Taiwanese investors do not face capital gains taxes, but do exhibit a strong disposition effect (Barber, Lee, Liu, and Odean, 2007). It is possible that the disposition effect contributes to the poor sales decisions of Taiwanese individual investors. 2. Institutions earn profits that are identical to the losses of individuals. Each of the institutional subcategories earns reliably positive overall trading profits with the exception of corporations at a horizon of 140 trading days. 14

Results To test the robustness of the results (from dollar profits), the authors also analyze the mean monthly abnormal returns on the buy, sell, and buy minus sell portfolios. Table 6 presents the monthly abnormal return measures (four-factor intercepts) for each investor group.  Consistent with prior evidence, the results provide strong evidence that institutions earn positive abnormal returns, while individuals earn negative abnormal returns. In general, the monthly abnormal returns decrease with the holding horizon. 15

Reasons to Trade There are several reasons why uninformed investors might trade: liquidity requirements, rebalancing needs, hedging demands, entertainment (or sensation seeking), and the mistaken belief that they are informed, that is, overconfidence. The authors propose that a combination of overconfidence and the desire to gamble account for much of the active trading and substantial losses of individual investors in Taiwan. To see whether some of the excessive trading in Taiwan is driven by gambling desire, model (7) is estimated for January 1995 through February

Reasons to Trade  The estimated coefficient on the lottery dummy variable (β 5 ) is −5.62 (t = −3.69), and the mean of monthly TSE turnover from 1995 through 2001 is 22.6%. Thus, controlling for other factors, the introduction of legal gambling in Taiwan reduced turnover on the TSE by about one-fourth.  The authors compare lottery losses to stock market trading losses. If the Taiwanese derived the same utility of gambling from the lottery that they had previously derived from additional trading, investors could do so at a lower cost by gambling from the lottery. 17

Reasons to Trade  When regression model (7) is augmented to include the dollar volume of options trading scaled by the market capitalization of Taiwan common stocks, the coefficient on options trading variable is negative, but not reliably so (−11.9, t = −0.84), while the coefficient on the lottery dummy remains reliably negative (−4.6, t=−2.41). 18

Data and Methods- Barber et al. (2007) This paper investigates whether investors are reluctant to realize losses. To test the null hypothesis that investors are equally likely to realize gains and losses, the authors break up an investor’s portfolio into stocks held for gains and stocks held for losses on each day. Then analyze the selling activity of the investor and calculate the proportion of his winners sold and the proportion of his losers sold.  By going through each investor’s trading records in chronological order, construct a portfolio of individual stocks for which the purchase date and price are known. 19

Data and Methods- Barber et al. (2007)  For stocks sold, the sales price for the stock is compared to its average purchase price to determine whether that stock was sold for a gain or a loss.  Each stock that was in that portfolio at the beginning of that day but was not sold is considered to be a paper (unrealized) gain or loss.  Compare the stock’s daily high and low price to the average purchase price of the stock and categorize paper positions as gains, losses, or indeterminate (if the average purchase price falls between the daily high and low price). 20

Data and Methods- Barber et al. (2007) For each trader calculate two ratios: Proportion of gains realized (PGR) Proportion of losses realized (PLR)  A large difference in PGR and PLR indicates that this investor preferred realizing gains rather than losses (relative to his opportunity to realize each). 21

Data and Methods- Barber et al. (2007) The establishment of statistical significance  First, calculate the difference between PGR and PLR for each investor. We calculate the mean difference across investors within a particular investor group (individuals, corporations, dealers, foreigners, or mutual funds). Statistical significance is based on the mean difference and the cross-sectional standard deviation of the difference. ( 橫斷面 )  Second, separately sum realized gains, realized losses, paper gains, and paper losses across all investors and across each investor group on each calendar day. Then 22

Data and Methods- Barber et al. (2007) calculate the difference between PGR and PLR on a particular day. The mean difference is calculated across days for investors within a particular group (individuals, corporations, dealers, foreigners, or mutual funds). Statistical significance is based on the mean difference over time and the time-series standard deviation of the difference. ( 時間序列 ) 23

Results- Barber et al. (2007) Cross-sectional results 1. Table 3, Panel A, presents the total value of paper gains, paper losses, realized gains, and realized losses for all investors and by investor type. Each field is summed across investors and over time. These values are used to calculate the PGR and PLR in Table 3, Panel B. 2. First, consider the results for all investors (in the last column of Table 3, Panel B). Gains are realized at a daily rate of 2.9%, while losses are realized at a daily rate of 1.4%. In aggregate, investors are roughly twice as likely to sell a winner rather than a loser. 24

Results- Barber et al. (2007) 3. To formally test whether investors are reluctant to realize losses, the authors separately calculate PGR and PLR for each investor and then average across investors. These results are presented in the last column of Table 3, Panel C. For the average investor, the proportion of gains realized is 9.4%, while the proportion of losses realized is only 2.3%. The difference in PGR and PLR (7.1%) is reliably positive (p < 0.01). 25

Results- Barber et al. (2007) 4. The results by investor type indicate individuals, corporations, and dealers prefer to sell winners rather than losers. These results are similar by aggregating across investors and over time (Panel B) or averaging across investors (Panel C). In contrast, foreign investors and domestic mutual funds do not prefer to sell winners rather than losers. When averaging across investors, the null hypothesis that PGR equals PLR for foreigners can not be rejected, while domestic mutual funds display a modest preference for selling losers rather than winners (p < 0.05). 26

Results- Barber et al. (2007) Time-series results As described previously, the authors sum paper gains, paper losses, realized gains, and realized losses across investors for a particular day. Then calculate a daily value for the PGR and PLR. Table 5 presents the results of the time-series analysis. Panel A contains the mean daily value of PGR; Panel B contains the mean daily value of PLR; Panel C contains the difference (PGR less PLR). 27

Results- Barber et al. (2007) 1. Consider first the results for all investors (in the last column of Table 5). PGR exceeds PLR in each year and is reliably positive in each individual year with the exception of 1997 (t = 1.63). Furthermore, in aggregate, investors realize gains at a greater rate than losses on 87% of days analyzed (PGR exceeds PLR on 1,214 days out of 1,395 total trading days). Again, the authors find strong support that the aggregate investor is reluctant to realize losses. 28

Results- Barber et al. (2007) 2. The time-series results by investor type are generally consistent with those reported in Table 3. Individuals, corporations, and dealers prefer to sell winners rather than losers. In contrast, with the exception of 1995 – the first year in the analysis, foreign investors and domestic mutual funds prefer to sell losers rather than winners. Market movements and the disposition effect This study also analyzes the relation between market movements and the propensity to sell winners and losers. The authors offer two reasons for observing a relation between broad market movements and PGR (or PLR). 29

Results- Barber et al. (2007) 1. First, it is likely that investors’ reference points change as prices change. If this is the case, PGR would be expected to decrease following periods of appreciation, since some perceived losses are incorrectly classified as gains. Analogously, following periods of depreciation, PLR would be expected to increase, since some perceived gains are incorrectly classified as losses. 2. Second, heterogeneity in the tendency to sell winners and losers across investors will lead to a relation between broad market movements and PGR (or PLR). This heterogeneity will cause PGR (PLR) to decrease following 30

Results- Barber et al. (2007) periods of appreciation and increase following periods of depreciation. 3. To analyze these effects, the authors estimate a simple time-series regression using weekly values of PGR and PLR. Weekly values are obtained by summing paper gains, paper losses, realized gains, and realized losses across the week. Then estimate the three time-series regressions shown in p.438.  The results are presented in Table 7. Consider first the results for the ratio (PGR/PLR) for long positions (panel A). There is strong evidence the propensity to sell winners, 31

Results- Barber et al. (2007) relative to losers, declines following strong market returns.  When PGR and PLR are separately analyzed, as anticipated, lagged returns are negatively related to PGR. This is consistent with both changing reference points and heterogeneity in the willingness to sell winners. However, PLR is found to be positively related to past return (with the exception of lag length eight).  To test the robustness of these results, the authors also estimate analogous time-series regressions for PGR and PLR based on short positions (Table 7, Panel B). 32

Results- Barber et al. (2007)  In summary, there is strong evidence that the propensity to sell winners declines following periods of appreciation (or depreciation for short positions). Both heterogeneity in the willingness to sell winners across investors and changing reference points would yield this result. Neither explains why the proportion of losses realized (PLR) increases following periods of appreciation (or depreciation for short positions). 33