Trading Securities Using Trailing Stops
STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH
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A common trading maximum is to cut your losses and let your profits run. To implement this policy, traders often use what is called a trailing stop. Suppose a trader buys a security for 100 in hopes that it will appreciate in price. At the time of purchase he enters in the market a stop order to sell at 95, say. The stop order becomes a market order, if the security trades at 95. In placing this stop order, the trader is limiting his loss to approximately 5. As the security trades, the stop order is moved to 5 below the maximum price attained by the security. Since the maximum price is never less than 100, the stop order can never be less than 95. The trade will be stopped out whenever the price of the security suffers a 5 draw down from its peak price. Being stopped out is essentially guaranteed. This procedure has been called trading the line. In the paper we discuss the distribution and moments of the gain to the trader in following this strategy as well as the duration of the trade. Both discrete time random walks and continuous time Brownian motion and geometric Brownian motion price processes are treated. The discrete time model is closely related to the GIG1 queue. Also of interest is the optimal value of the distance to the stop, 5 in the above example. This model can, of course, be inverted to handle short selling....Brownian motion, Financial securities, Geometric Brownian motion, GIG1 queue, Random walk, Reflecting Brownian, Regenerative processes.
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