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I have the following exit strategy under consideration.

Suppose I have n shares of stocks that I want to sell. When the price reaches n/(n-1) of the original price, I sell 1 share. When the price reaches n/(n-2) of the original price, I sell another share ...

Basically when the stock price increases, I keep on selling the shares one by one to keep the dollar amount of the stock constant.

This seems to balance the profit and risk, especially when I am not sure how much gain I can have in the stock. But I don't have a quantitative assessment of this strategy.

Has this strategy been studied already so that I can know when this strategy is a good one and when it is not a good one? If so, could anybody show me the analysis of the pros and cons of this strategy?

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There can be no rational trading entry or exit strategy based on your pnl, i.e. a function of past and current prices. The only way to make a "strategy" is to predict, one way or another, future prices. Without predictions, the most rational action is to have zero exposure. An exception is when a trader extracts a utility from the thrill of gambling. Another situation when exiting a position based on recent pnl is rational is to avoid a margin call on a levered position.

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  • $\begingroup$ What does pnl mean? $\endgroup$
    – user15482691
    Sep 16, 2021 at 23:09
  • $\begingroup$ profit and loss $\endgroup$
    – Michael Isichenko
    Sep 16, 2021 at 23:53
  • $\begingroup$ How do you prove this mathematically? Is it the Martingale Stopping Theorem of Doob? $\endgroup$
    – nbbo2
    Sep 17, 2021 at 16:56
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    $\begingroup$ This question is more about common sense than math. A rigorous approach to defining a 'rational' allocation $P_i(t)$ (positions or exposures to available strategies or securities) would require introducing a utility functional $U[\{P_i(t)\}]$. This step involves human preferences even though it looks like math. My preferences would include larger future profits and lower risk, which is a version of mean-variance utility. YMMV. $\endgroup$
    – Michael Isichenko
    Sep 17, 2021 at 17:44
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    $\begingroup$ "n a trader extracts a utility from the thrill of gambling" - decades ago, one could lose a little money in Las Vegas and get comped the hotel room, food, and a couple of shows - much better than just a thrill. Alas, those days are long gone. $\endgroup$
    – Dimitri Vulis
    Sep 17, 2021 at 18:10

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