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Drawdown Leads to Triple Penance

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One of our favourite quantitative finance academic/practitioners is Marcos Lopes de Prado who has co-authored a number of excellent papers with David Bailey. The paper I will focus on today is the one they call the Stop-Outs under Serial Correlation and the “Triple Penance Rule”.
 
The concepts of maximum quantile-loss (??????) and quantile-time under water (????) are closely related. This is formalized in the following theorem (or “triple penance rule”): 
 
Under standard portfolio theory assumptions, a strategy’s maximum quantile-loss ?????? for a significance level ? occurs after ??? observations. Then, the strategy is expected to remain under water for an additional 3??? after the maximum quantile-loss, with a confidence (1 ? ?). If we define ??????? = ???? ? 1, then the “triple penance rule” tells us that, assuming ??? independent ??? identically distributed as Normal (which is the standard portfolio theory assumption), ??????? = 3, regardless of the Sharpe ratio of the strategy
 
In other words, it takes three time longer to recover from the maximum quantile-loss than the time it took to produce it and this rule doesn’t change if you are more skilful than another trader.
 
  
 
You will notice on your PsyQuation chart dashboard the option of viewing a DD (drawdown) chart. We conveniently do the math of the triple penance rule for you with an Expected Recovery Time.
The key point I wish to leave you with is that drawdown is part of trading life. However, from experience what I notice is that traders struggle to accept the fact that they are in drawdown. It becomes a repressed emotion that needs to be eliminated from ones trading record at once. The obvious way to eliminate a drawdown is by making profits. The more profit a trader makes the quicker the drawdown goes away. 
 
But there is a catch, for some beautiful mathematical and perhaps symbolic reason there is an asymmetry to the probable recovery from drawdown and  yes, it takes longer to recover than it does to falter – don’t fight it.
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