I think this is all over the place. In risk, while discussing the strengths of the different types of Var, it’s mentioned that it’s not appropriate to use Analytical Var for securities with option-like behavior (not normal). I think the same point is even made in Behavioral Finance somewhere.
I think the closes thing to a list is the ways in which managers can game the Sharpe Ratio (and all of them are ways to game standard deviation). I don’t remember where this is (I’d look in equities or maybe risk). It goes something like:
- lengthening the measurement interval
- smoothing of returns (like appraisals for illiquid assets)
- eliminating extreme returns (like swapping the best and worst returns against the index)
- writing out-of-the-money options or any kind of catastrophe event
Opinion: The first two are somewhat easier to spot, so we must compare apples to apples. The elimination of extreme returns may be OK if its a regular part of the process and that’s what the client wants (after all they really are getting less volatility).
I think the most important one to always have in the back of the mind is the tail risk/catastrophe event stuff. Those are often legit strategies (writing options may look like easy money). The mean will be improved, and the standard deviation may be improved as well. As long as the calls are kept out-of-the-money, the manager generates steady profits. If something happens and they all get in the money (puts in a crash) the fund may be wrecked.
The famous LTCM fund broke in a way akin to that. They did extremely levered arbitrage and were almost always right. Amazing Sharpe, until they blew up.