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Leverage Aversion and Portfolio Optimality

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There’s a strange article, Leverage Aversion and Portfolio Optimality,  by Bruce Jacobs and Ken Levy in the FAJ. It’s not clear what their paper is trying to explain. That is, a theory should either predict something new, integrate two seemingly separate results, or explain a paradox to standard theory. This paper seems to merely show that if people explicitly take into account leverage, then portfolio holdings will be different. They don’t even reference Asness, Frazzini and Pedersen (2011), the most recent piece on this subject.

But their piece is strange in several ways. First, they implicitly have people maximizing ‘relative returns’, what they call ‘active return’ (with the leverage constraint added on).  On one hand, this is great, because is consistent with my thesis in The Missing Risk Premium, that this is what most people actually are maximizing.  Yet, they propose this as if it is de rigueur. This highlights that 1) this utility function is so intuitive people generally don’t even think about justifying it on more general grounds and 2) they blithely ignore the many contradictory implications of this assumption applied generally (eg, a zero risk premium).  Yet, if the utility function is relevant it can’t exist parochially in one asset class without a massive arbitrage opportunities.  I know a foolish consistency is the hobgoblin of small minds, but this parochial-general distinction as applied to equilibrium returns is not foolish.

 Secondly, their model seems to imply that with 200 and 300% enhancement funds available via leveraged ETFs (Ultras, UltraPro), does this then imply the expected return on these sectors is now lower because people can buy a 200% allocation to these sectors without direct leverage (ie, you ‘only’ lose 100% with an ETF)? Do stocks with options have lower expected returns because of these outlets (options are levered positions that, when long, ‘only’ lose you 100%)?

Lastly, they imply that everyone should be leveraged somewhat.  Now, on one hand this is obvious because if they are maximizing relative return, and they presume some alpha, there’s some non-negative allocation regardless of how risk-averse one is. This was proven back in the 1960s via the symmetric problem of how much of an allocation one should apply to a risk portfolio when you have absolute utility. If your theory says ‘everyone’ and the data say much less than half, the theory’s wrong. It’s a much bigger disagreement than the theory saying 80% and data saying 40%.

2012-09-21 16:44:32



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