Embedded Leverage And Returns

by: Eric Falkenstein

Frazzini and Petersen, the duo behind AQR's Betting Against Beta theory behind the low vol anomaly, have a new paper out on embedded leverage. Their theory is basically that investors are constrained in their allocation to equities, so overload on those equities with the highest betas in order to get more equity exposure. The paper looks at both levered ETFs, and options (from 1996-2010). Here's a graph showing the embedded leverage (aka omega) in options, and monthly returns.

Monthly Returns (y-axis) and Option Omega (x-axis)

Click to enlarge

This adds more data to the fact that options are not just bad investments, but worse the more out-of-the-money they go. These are horrible long investments (large negative returns to out-of-the-money options).

I don't really see how this comports with their theory, however, because if investors want more access to the equity factor, they are getting extremely negative returns. Thus, it really isn't a rational theory of constrained optimization, but delusional speculation. Further, investors are acting the same to puts and calls, and constraints on access to short positions doesn't seem to make sense in their model unless they have heterogeneous (and persistently wrong) beliefs. So, the idea that rational, constrained, investors explains this effect doesn't make any sense. Perhaps they can explain.