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Sorry this might sound a silly question, but -humbly- I don't understand why models assume that returns range from [-∞,+∞] instead of [-stoplimit, +takeprofit].

A common objection to most models is "it works with normal return distributions, but real return distributions have fat tails"

But why worry about fat tail distributions and potentially infinitely negative returns, if we can just use stoploss / takeprofit barriers to constrain returns within some arbitrary range?

I appreciate that stoploss barriers are not guaranteed in turbulent times, but then one could use a tighter barrier for an extra-safety margin ...

thanks for your thoughts!

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    $\begingroup$ Imagine Harvard University, with a 40 billion USD endowment fund, trying to implement a "stop loss" as soon as S&P 500 hits a critical level ;) $\endgroup$ – noob2 May 23 at 8:59
  • $\begingroup$ πŸ˜‚ ok ok but the Harvard University does not trade with its fund (I hope πŸ˜…) they are just long on the SP500 - for that we don't need quants in the first place $\endgroup$ – elemolotiv May 23 at 9:36
  • $\begingroup$ I don't see how a SL can help against fat tails: if tails are fat, the probability of hitting your SL is far larger than that implied by a Normal distribution. So, for repeated bets, you will have a lot of frequent small losses because of SL being hit. $\endgroup$ – Lisa Ann May 23 at 13:56
  • $\begingroup$ thanks @LisaAnn - to my understanding, having frequent small losses is better than having 1 single major loss. If your returns are constrained between [-10%, +10%] you know that you will NEVER be surprised by a single loss bigger than your capital. If your returns vary between [-∞, +∞] you have a nonzero probability that a single trade wipes out your capital, even more for fat tails distributions. It seems to me a fundamental difference. Is that correct? $\endgroup$ – elemolotiv May 23 at 14:22
  • $\begingroup$ @LisaAnn That's not quite true, it depends entirely on where his stop-loss is. If he's got a conservatively placed stop loss it will be smaller than that of the Normal Distribution. Especially if you increase the kurtosis by a lot, fatter tails means more mass closer to the center $\endgroup$ – Oscar May 23 at 14:53
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Because we are modelling the underlying price process, not the value process of your stop-loss portfolio...

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  • $\begingroup$ Exactly. Implementing a stoploss is an example of a trading strategy. Of course, with any strategy there are many questions regarding implementation. $\endgroup$ – RWP - Down by the Bay May 26 at 15:13
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Not sure if this question deserves to be further piled onto, but alas...

Large, institutional portfolios nearly always hold relatively illiquid and OTC traded instruments. There is no stop-loss order on a corporate bond or term loan, as an example. This is unrealistic even in equities. Let's say you hold 5% of the shares out on a small cap, do you just have a resting SL to sell all the shares at once? The transaction cost on that would be enormous along with the low likelihood of the manager even being able to fill the entire order.

Another example: you trade a dealer book. Your firm uses VaR to manage risk and you breach the 1 day threshold. Do you stop making markets for your customers and unwind all of your inventory at the current level? What would be the business implication of doing that?

Final point for thought: what is your objective? Would it be consistent with your objective to unwind a position due to a temporary shock even if the investment still fits your criteria? Market timing is generally a bad strategy, so selling low to buy lower is unlikely to be met with success.

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  • $\begingroup$ Very well reasoned. $\endgroup$ – Kermittfrog May 23 at 17:25
  • $\begingroup$ thank you @Kch ! now I understand my question originated from the narrow perspective of someone who does intraday trading ... so I do not consider the factors you mentioned, although I recognise they are major factors for institutional fund managers $\endgroup$ – elemolotiv May 23 at 18:36
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all metrics like VaR (how much you can lose on a given day) are based on a confidence interval in the distribution.

but the most important part of risk management is tail risk /extreme loss, which can actually cause the business to go bust, and metrics like expected shortfall (if you end up in the tail, how ugly can things really get) are much more relevant there

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  • $\begingroup$ thanks! but my provocation is that you don't end up in the ugly tails if you simply use a stoploss barrier in your trades πŸ™‚(with some extra margin if you need) $\endgroup$ – elemolotiv May 23 at 11:24
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    $\begingroup$ I see, the thing is, risk managers compute exposure at the counterparty and portfolio levels, for many reasons including margin agreements, portfolio correlation and diversification effects, etc. whilst having a stop loss here or there at the trade level isn't accounting/helping with larger credit risks effects. of course in the extreme case we consider 1 portfolio with 1 counterparty and 1 asset, then the interpretation is very different $\endgroup$ – John May 23 at 11:35
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This is a real life empirical example: my ex-colleague now runs a trend following strategy (with some leverage time-to-time) and did not lose money during the recent market crash all thanks to his stop loss triggers combined to the strategy.

Stop losses are helpful and some big asset managers (I believe Aussies are in this category) do consider this a very powerful risk management tool. But it all depends how you use them.

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  • $\begingroup$ thanks @AK88 it still surprises me though that stop losses are considered an implementation detail, by all the comments I received (which probably signals that's the right way πŸ™‚). To me it seems that the theory changes quite a bit, if in your model you consider ${return \space on \space price}=\frac {trade \space price \space delta} {initial \space price}$ versus ${return \space on \space stop} = \frac {trade \space price \space delta}{stop \space loss \space span}$ $\endgroup$ – elemolotiv May 26 at 14:48
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If you do only one trade, you don't need to think of the fat tail of your account's balance distribution because the one trade is protected by the stop-loss. But if you do the multiple trades and you lose all the time, you will encounter the fat tail. And that's the point your ordinary Sharpe ratio doesn't work anymore.

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  • $\begingroup$ @elemolotiv: Could you explain what is meant by "return on stop = trade price delta/stop loss span" . I ask because I am working on an intraday strategy and haven't implemented a stop loss but, if you think it's valuable, maybe I should start investigating that. thanks. $\endgroup$ – mark leeds May 26 at 16:15

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