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If I set the trailing stop loss as 5% based on Last. Is the stop price updated every time Last is published? e.g. If the current Last is $100, then current stop price is $95; when the next Last comes, say $101, and then the next stop price is $95.95 (101 * .95). Is this correct?

For a sell order, if the most recent Last is below .95 of the previous Last, order executes. What if the latest Last falls just 2% of previous Last and the stock keeps falling and Last declines 2% per Last, would the order execute?

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    A trailing stop loss is usually based on the latest high price traded not the last price traded. A trailing stop can move up but can never move down. – Victor Jul 12 '17 at 0:47
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The price doesn't have to drop 5% in one go to activate your order. The trailing aspect simply means your sell trigger price will increase if the current value increases (it will never decrease).

Example 1: start with a valuation of $100 and a trailing 5% loss trigger

  • Price increases to $105 (+5%). Trigger price is increased to $99.75.
  • Price drops to $104 (-1%). Trigger price remains at $99.75.
  • Price drops to $102 (-2%). Trigger price remains at $99.75.
  • Price drops to $100 (-2%). Trigger price remains at $99.75.
  • Price drops to $98 (-2%). Market order executes.

Example 2: start with a valuation of $100 and a trailing 5% loss trigger

  • Price drops to $98 (-2%). Trigger price remains at $95.
  • Price drops to $96 (-2%). Trigger price remains at $95.
  • Price increases to $102 (+6%). Trigger price is increased to $96.90.
  • Price drops to $96 (-6%). Market order executes.

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