# Just How Much Do Individual Investors Lose by Trading?

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9 Just How Much Do Individual Investors Lose by Trading? in profits observed at a one-day horizon, we use a Newey-West procedure to correct the estimated standard errors using an assumed lag length of six days Return calculations To test the robustness of our dollar profit calculations, we also calculate monthly abnormal returns on the buy portfolio, sell portfolio, and buy less sell portfolio for all investor partitions. Consider, for example, the portfolio that mimics the buys of individual investors. We first calculate the daily returns on this portfolio (again, assuming a holding period of 1, 10, 25, or 140 days). Daily returns are compounded within a month to yield a time series of sixty monthly returns for the individual investor buy portfolio. Statistical tests are based on the monthly time series of the portfolio return and abnormal returns from a four-factor model; results are qualitatively similar if we use market-adjusted returns or the intercept from a one-factor model with the market risk premium as the sole factor. For example, we calculate the abnormal return on the corporate investor buy portfolio as the intercept from the following four-factor model: ( R corp t R ft ) = α j + β j (R mt R ft ) + s j SMB t + h j HML t +w j WML t + ε jt, (1) where R ft is the monthly return on T-Bills, 9 R mt is the monthly return on a value-weighted Taiwan market index, SMB t is the return on a value-weighted portfolio of small stocks minus the return on a value-weighted portfolio of big stocks, HML t is the return on a value-weighted portfolio of high bookto-market stocks minus the return on a value-weighted portfolio of low bookto-market stocks, and WML t is the return on a value-weighted portfolio of stocks with high recent returns minus the return on a value-weighted portfolio of stocks with low recent returns. The construction of the size and book-tomarket portfolios is identical to that in Fama and French (1993). The WML return is constructed based on a six-month formation period and a six-month holding period. The regression yields parameter estimates of α j, β j, s j, h j, and w j for regression j. The error term in the regression is ε jt. 8 There is a small, but reliably positive autocorrelation of total profits at a one-day horizon (ranging from 6.3% to 14.2%). No autocorrelations beyond one day are reliably different from zero. To test the robustness of our profit results, we also calculate monthly returns on the buy and sell portfolios. Monthly portfolio returns for all investor partitions have no reliable serial dependence. 9 We use the series of one-month deposit rates of the First Commercial Bank as the risk-free rate. This interest rate series is taken from Financial Statistics Monthly, Taiwan District, ROC, and is compiled by the Central Bank of China. 617

11 Just How Much Do Individual Investors Lose by Trading? Figure 1 Cumulative (market-adjusted) abnormal returns (CARs) in event time for stocks bought less stocks sold by institutions and individuals Panel A: CARs are weighted by aggregate value of stocks bought and stocks sold. Panel B: CARs are weighted by net value of stocks bought and sold. 619

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