I guess the point here is that there is usually an explicit downside risk constraint in most basic portfolio optimization problems; not to mention there are usually leverage constraints, among many other things, which of course aren't captured by just vanilla EV.
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So what hedge funds really do here is:
1) estimate linear EV. This is always the first and most important thing to do.
2) estimate correlated volatility with your portfolio
3) if (1)/(2) is small then just do it
4) if it's short-term just do it
But honestly usually just (1).
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There are exceptions, obviously! Times when the downside risk is significant.
But then you separately think about downside risk for it.
To use something other than linear EV (or similarly sharpe adjusting for correlation with portfolio) would get you laughed out of the room.
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True for spot portfolios, but definitely not true for leveraged derivatives
I don’t know any serious options or swaps trader who doesn’t discount linear EV by time decay or other processes that add in concavity by the nature of the instrument + microstructure
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The instruments are naturally overexposed to gamma/shifts in gamma, so you discount and use sublinear reweighting / constraints
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what do you mean by "time decay"? If you're trading options then it's the linear EV of the option you care about (which is not the linear EV of the stock, of course); "time decay" is built into calculating the linear EV of the option.
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And swaps *are* just linear instruments, so what I said holds, you just care about the linear EV of underlying (marked to how long you're planning to hold, plus interest rates you'll have to pay, etc.)
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Right, but interest rate volatility factors into your expectation operator and potentially does as a constraint
Worst-case volatility corrections != average case, and for some markets you do one and not the other
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why does interest rate *vol* matter, and not just EV of interest rate?
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Because it effects the discounted expectation E[e^(-\int_0^t r(s) ds Price(t)]
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are you talking about market prevailing rates or the rates of the thing you're trading a swap on?
The latter, although the former impact how you aggressively discount depending on the leverage needed / liquidation conditions
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for very few trades do nonlinear terms in the interest rate matter; those are going to be third-order effects
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