Thursday, December 11, 2014

Requisite Assumptions for the Persistence of the Low Volatility Anomaly

My new paper was motivated by Frazzini and Pedersen's model of the low volatility anomaly. Though I think they are profoundly wrong, I think the paper was done well in good faith. Wrong mainly because it still implies people think there's a positive Security Market Line, even though at best it's flat, and wrong also because high vol assets like puts lose just as much money as calls (ie, the alpha is not linear in beta so much as correlated with volatility).  As to it being well done in spite of that, note that unlike Buffa, Vayanos and Woolley (2014), it's not so convoluted it could basically never be estimated, rather it has a concise and simple implication. Working through F&P's result, I think they actually made a math error; not something like a wrong sign, but rather, assumed an invertible matrix in one place, which is then applied to a world where such a matrix is non-invertible. If that doesn't make sense but sounds interesting, take a look at my paper, where I think I have the simplest relative utility model out there (eg, compared to DeMarzo et al, 2005, or Roussanov, 2010). I could have a big mistake in there, so comments welcome.

Alas, I needed three assumptions to get the low volatility result to hold while still matching some other big datapoints. That is, I don't want a result that implies the equity risk premium is zero, or that rational investors are all shorting high vol stocks, because that's clearly counterfactual, and I also want to explain why high beta/vol assets have a negative alpha in equilibrium. Those assumptions are
  1. some delusionally optimistic investors
  2. systematic risk across beta (eg, high beta stocks can't be hedged with Spiders to create arbitrage)
  3. relative utility (though, not completely, otherwise the equity risk premium is zero)
I put in some data related to items 1 and 2, because I didn't see a lot of references for these points even though they are pretty plausible and I don't think too controversial. Item 3 is quite controversial, so I motivate that a little by pointing to a lot of other data, especially non-economic data.

It's here, Requisite Assumptions for the Persistence of the Low Volatility Anomaly.

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