Sunday, December 02, 2012

Embedded Leverage and Returns

Frazzini and Pedersen, 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 leveage (aka omega) in options, and monthly returns.

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

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 aka AntiFragile 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.


Anonymous said...

Ahem, Pedersen

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Anonymous said...

So does selling options have a good return?

Anonymous said...

Does the model proposed in this working paper accurately describe the mechanism that causes high beta to be overpriced?

Anonymous said...

OK, here you go Eric:

First of all, the mere existence of leveraged ETFs (at high fees!) and options is evidence that some people demand embedded leverage. These products were designed precisely for that reason.

Second, investing in a twice-leveraged ETF that gives less than twice the excess return than a regular ETF means that outright leverage would be better, but it could still be optimal for a leverage-constrained investor to buy it. Similarly, the negative alphas for delta-hedged options means that one can do better by using outright leverage and dynamic trading, but, if investors are leverage constrained and buy unhedged options, that could potentially make sense. (We focus on alphas of hedged options because this has the most statistical power in analyzing the pricing.)

Third, regarding puts, you must not forget put-call parity: if calls get expensive, so do puts. Further, puts provide embedded leverage on the short side so there is an independent reason for these to be expensive.

In summary, we have a theory that can help explain the cross-section of equities, treasuries, and credit markets, the time series, the beta compression during crises, and investors’ actual portfolios (“Betting Against Beta”), the returns across asset classes and the efficacy of risk parity (“Leverage Aversion and Risk Parity”), the existence and pricing of securities with embedded leverage (the paper you asked about), and the performance of Warren Buffett (“Buffett's Alpha”). Not bad for a simple theory. Of course, your behavioral effects can play a role too and the two views can complement each other.

Lasse H. Pedersen

Eric Falkenstein said...

Well, I like that your theory explains lower returns on embedded securities like 2x ETFs, and lower returns on high beta stocks. I especially like the fact the BAB portfolio is significantly correlated with ted spread. What I find anomalous are the existence of 'embedded leverage' assets with not merely negative alpha, but with 'lower than average' returns. Levering up to get more of the 3-5% equity premium is not rational if their return is below the risk-free rate as it is for many of these categories (often negative in absolute returns).

Your theory seems to explain an insufficiently positive sloping SML, but not a negative sloping one.

If this effect were constrained to puts, it would make sense, but it's not.