Are Proprietary Day Traders Too Slow To Realize their Losses?

1. Are Proprietary Day Traders Too Slow To Realize their Losses? Anthony Murphy Nuffield College, Oxford anthony.murphy@nuf.ox.ac.uk

2. Outline • Data for a U.S. proprietary stock-trading team suggest that traders hold on to their losing trades too long and sell their winning trades too soon • Evidence of “disposition effect” • In a three month period in early 2000, the fifteen traders earned more than $1.4m in gross trading profits • However they realized their winning trades at a much faster rate than their losing trades. • Leads to considerably lower profits

3. Proprietary Day Traders • Employees of large, direct access, US broking firm • Traded firm’s capital • Paid very low commissions (less than $2 per round trip on average) • Licensed, passed NASD series 9 exams • Remuneration - responsible for losses; shared 50% of net profits

4. Proprietary Day Traders • Mainly traded large cap NASDAQ stocks • No particular restrictions on going short apart from “up tick” rule • Closed out almost all positions at close of day (and often during the day as well) • Often benefited from the spread by posting limit orders on ECNs, especially Island ECN

5. Some Summary Statistics Based on 58,835 round trips (43½% on short positions) for 15 traders in period 8 March to 13 June 2000

6. Duration of Round Trips * Statistically significant at 1% level

7. Duration of Round Trips • Consistent large differences in durations of winning and losing trades controlling for: - Time of day - Trade size - Trader etc. • Differences in duration are statistically significant • Are they financially significant?

8. Impact on Gross Trading Profits Excludes 5,935 round trips with zero gross profit Statistically significant differences at 1% level denoted by *

9. Impact on Profitability (Cont’d) • Absolute price change rises with duration and duration of losing trades longer • Suppose absolute price change of losing trades reduced by 1c from 10c to 9c, then gross profitability maybe 12% higher • Suppose absolute price change of losing trades reduced by 1c and winning trades increased by 1c, then gross profitability maybe 37% higher

10. Feasible To Alter Durations? • Need to examine price trends before and after closing trades • Check if, on average, prices continue to rise when selling and continue to fall when buying • Answer is yes for winning trades and possibly for losing trades (since market orders generally used to close these trades) • Traders not “informed” • However, they are quick to exploit existing price trends

11. Are Holding Times Justified? • Look at price changes before and after closing (round trip) trades • Closing trade at time t. • Look at prices between t-45 to t+45 • Winning long positions – average prices continually rising from 45 sec before to 45 sec after closing trade • Winning short positions – prices continually falling…. • Losing long positions – prices continually falling…. • Losing short positions – prices continually rising….

12. Average Price Changes Before and After Closing Trade – Top 20 Stocks Pt±s - Pt Based on mid-points of Nasdaq inside quotes and 50358 round trips – 17321 winning long, 10218 losing long, 13925 winning short and 8894 losing short

13. Ongoing Research – Decline in Prop. Trader Profitability • Explaining the decline in prop. trader profitability from 2000 to 2003 • At least three factors need to be untangled (a) Decline in market (b) Decline in spreads (c) Greater competition

14. Falling Market • Decline in market - Rising/falling tide type argument. - However, traders positions are very short term - Can go long or short - Traders mainly profit from intra day volatility and supplying liquidity

15. Decline in Spreads &Greater Competition • Decline in spread from 6¼ to½ cent - Timing correct • Greater competition - Competition for traders (quality) and from hedge funds etc. (quantity) - Harder to execute limit orders which are well placed w.r.t. inside spread

16. Prospect Theory and the Disposition Effect • Modelling revealed behaviour / preferences of YAB, a highly profitable trader • Direct test of prospect theory (Kahneman & Tversky, 1979), a key concept in behavioural finance. • Also main explanation for disposition effect • Don’t have to worry about representative agent, time horizon of agent, mean reversion etc. • Model future price changes using ordered probit model and size at the inside spread inter alia

17. Prospect Theory and the Value Function • According to Prospect Theory, agents maximise vale function which is • Defined in terms of gains and losses • Concave over gains and convex over losses • Steeper for losses than gains

18. Calibrating the Value Function • Typical value function v(πt) shown on r.h.s. • Calibrate model using observed choices of YAB • Look at Etv(πt+15) and Etv(πt+60) • Value function v(πt) = πtγ or -δ|πt|γ depending on whether net profit πtis positive or negative • Results plausible.

19. Some References • Garvey, R. and Murphy, A. (2004). “Are Professional Traders Too Slow to Realize their Losses”, Financial Analyst’s Journal, 60(4), 35-43. • Garvey, R. and Murphy, A. (2004). “Commissions Matter: The Trading Behavior of Institutional and Individual Active Traders”, Journal of Behavioral Finance, forthcoming. • Garvey, R. and Murphy, A. (2004). “Entry, Exit and Trading Profits: A Look at the Trading Strategies of a Proprietary Trading Team”, Journal of Empirical Finance, forthcoming. • Harris, J. and Schultz (1998). “The Trading Profits of SOES Bandits”, Journal of Financial Economics, 50, 39-62. • Jordan, D. and Diltz, D. (2003). “The Profitability of Day Traders”, Financial Analyst’s Journal, 59(6), 85-94. • Kahneman, D. and Tversky, T. (1979). “Prospect Theory: An Analysis of Decisions under Risk”, Econometrica, 47(2), 263–292. • Odean, T. (1998). “Are Investors Reluctant to Realize Their Losses?”, Journal of Finance, 53(5), 1775–1798. • Shefrin, H. and Statman, M. (1985). “The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence”, Journal of Finance, 40(3), 777–790.