I believe that you (and the Twitter thread) are saying something meaningful, but I’m having trouble parsing it.
I had thought of the difference between variance and volatility as just that one is the square of the other. So saying that the VIX is “variance in vol units, but not volatility” doesn’t mean anything to me.
I think these are the critical tweets:
VIX is an index that measures the market implied level of 1-month variance on the S&P 500, or the square root thereof (to put it back in units we are used to).
This is not the same as volatility. A variance swap’s payoff is proportional to volatility squared. If you are short a variance swap at 10%, and then realized volatility turns out to be 40%, you lose your notional vega exposure times 16 (= 40^2 / 10^2 ).
To compensate for this, an equity index variance swap level is usually 2-3 points above the corresponding at the money implied volatility. So don’t look at VIX versus realized vol and make statements about risk premium without recognizing this extreme tail risk.
I was with him at “a variance swap’s payoff is proportional to volatility squared”. That matches my understanding of volatility as the square root of variance. But then I don’t get the next point about realized volatility needing to be “compensated for”.
Roughly speaking, it’s about “when” you take square roots and what that means for the product you are trading. Here is a handy guide on a zoo of vol/var swap/forward/future products.
The key thing is less about what “volatility” and “variance” have been. (Realized volatility is the square-root of realised variance). We’re talking about the expectation for the next month’s volatility or variance.
The “mathematician” way to think about this (although I think this is a little unhelpful) is E(√X)≤√E(X). If “X” is (future) realised variance (as yet unknown), then the former is “volatility” and the latter is “square root of variance” (what I call “variance in vol units”). Therefore “expected volatility” is lower than “square root expected variance”. The difference is what needs compensating
The more practical way to think about this, is that variance is being dominated much more by the tails (or volatility of volatility). When you trade a variance, you need a premium over volatility to compensate you for these tails (even if they don’t realise very often).
Another way to think about this, is there is “convexity” in variance (when measured in units of volatility). If you are long and volatility goes up, you much more (because it’s squared), but if it goes down, you aren’t making as much less.
I believe that you (and the Twitter thread) are saying something meaningful, but I’m having trouble parsing it.
I had thought of the difference between variance and volatility as just that one is the square of the other. So saying that the VIX is “variance in vol units, but not volatility” doesn’t mean anything to me.
I think these are the critical tweets:
I was with him at “a variance swap’s payoff is proportional to volatility squared”. That matches my understanding of volatility as the square root of variance. But then I don’t get the next point about realized volatility needing to be “compensated for”.
Anybody care to explain?
Roughly speaking, it’s about “when” you take square roots and what that means for the product you are trading. Here is a handy guide on a zoo of vol/var swap/forward/future products.
The key thing is less about what “volatility” and “variance” have been. (Realized volatility is the square-root of realised variance). We’re talking about the expectation for the next month’s volatility or variance.
The “mathematician” way to think about this (although I think this is a little unhelpful) is E(√X)≤√E(X). If “X” is (future) realised variance (as yet unknown), then the former is “volatility” and the latter is “square root of variance” (what I call “variance in vol units”). Therefore “expected volatility” is lower than “square root expected variance”. The difference is what needs compensating
The more practical way to think about this, is that variance is being dominated much more by the tails (or volatility of volatility). When you trade a variance, you need a premium over volatility to compensate you for these tails (even if they don’t realise very often).
Another way to think about this, is there is “convexity” in variance (when measured in units of volatility). If you are long and volatility goes up, you much more (because it’s squared), but if it goes down, you aren’t making as much less.