Levy, Post, and van Vliet wrote an article in 2003 entitled Risk Aversion and Skewnes preference: A Comment. They were responding to the claim that selective application of ‘risk loving’ preferences could explain ad hoc anomalies, the current favourite academic explanation for all those anomalies (in finance, that’s most of the data).
However, if people are globally risk averse, so that ‘risk’ generally explains expected returns on things like the supposed equity risk premium, then to be consistent with a preference towards really high positive tail returns (eg, lottery tickets), you have risk premiums of trivial absolute amounts to this tail risk, around one-tenth the equity risk premium. You can get the signs to go the right way, but then you can’t get the relative magnitudes right.
Good economists never let theory constrain them, rather, theory is mainly used to play parochial status games and browbeat outsiders as to the very rigorous foundations of their opinions. I doubt a single financial economist who likes the skew rationale for anomalies cares about this inconsistency as it is rarely cited; ‘complete’ models always applied piecemeal.
It’s still useful to believe true things, it’s easy to explain them than untrue theories: unforeseen facts will also be consistent with true theories, making life a lot easier, and filled with comforting corroboration as opposed to ever more complex rationalizations. Case in point, the sultry sounding Carol Alexander and Dimitris Korovilas just wrote a delightful paper addressing the currently popular tactic of buying volatility (I love when English women say whilst).
The idea is like when a child makes a sundae given every option: they just add everything they like together. In this case, investors think that if they take everything that ‘worked’ and just add it to the mix, it dominates a single thing in their they like. So as volatility went way up in 2008 when the market crashed (like always), why not own equities and volatility? Win/win!
While the VXX as a volatility proxy is a disaster because its annualized return is 23% lower than that on the VIX index it targets due to contango, the problem with buying the VIX is much more fundamental because it just doesn’t make sense to buy the VIX to hedge an equity position. Say Alexander and Korvilas:
we ask whether it has ever been optimal to add a long VIX futures position to a long position on the SPY within the Markowitz framework. Then we ask: given that an investor is long SPY, how large does the expected return on VIX futures need to be in order to justify adding a long position on VIX to the SPY portfolio?
VIX futures expected returns always need to be positive (and often quite large) to justify volatility diversification for a long equity investor.
So, don’t ‘hedge’ your equity position with the VXX or going long the VIX futures, just lower your equity position. If you are long the VXX, fine, but you should expect the return on that to be positive because it’s a crappy pure hedge.
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