PowerShares rolled out a pair of ETNs offering inverse exposure to Japanese government bonds, the 3x Japanese Government Bond Futures ETN (JGBT), and the 3x Inverse Japanese Government Bond Futures ETN (JGBD). Government bonds are typically considered low risk, but to generate sufficient demand, it appears you need to lever them so they have high enough risk to warrant interest. I suspect that in 10 years, everything will have a 2x and 3x derivative that's tradable on liquid exchanges.

Now, one reason for the demand is that accounts like 401ks discourage leverage, so the leverage is implicit in the ETF, and not explicit. This is a big problem with leverage limits because leverage can always be gamed in this way, and there is no simple solution.

But I suspect the main reason is more fundamental: people like volatility, and so demand increases with higher volatility. Now, in most formulations, risky asset demand is determined something like this.

First, maximize the weight on the risky asset, where w is a proportion of the investor's portfolio allocated to the risky asset:

By definition, the risky asset has a Gaussian distribution, and the risk-free asset is some constant.

Taking the derivative with respect to w and setting equal to zero gives us the familiar risky asset demand.

This says it is linearly related to the expected return, and inversely related to its variance. Increasing leverage increases the return (numerator) by X, and the variance (denominator) by X

Yet, in practice that's not what happens. I'm not sure what's going on, but I think part of it is a quantum effect, where investors are not interested in something until it can generate a sufficient threshold return. That is, most investors basically have 'null' for their Japanese bond exposure. A significant number of investors would put down $1000 if they had a chance to make $200, but many fewer are interested in putting down $1000 to make $100. Sure, they could always lever positions themselves but that's another level of complication, creating all sorts of operational risk such as issues about taxation and margin calls.

Now, one reason for the demand is that accounts like 401ks discourage leverage, so the leverage is implicit in the ETF, and not explicit. This is a big problem with leverage limits because leverage can always be gamed in this way, and there is no simple solution.

But I suspect the main reason is more fundamental: people like volatility, and so demand increases with higher volatility. Now, in most formulations, risky asset demand is determined something like this.

First, maximize the weight on the risky asset, where w is a proportion of the investor's portfolio allocated to the risky asset:

By definition, the risky asset has a Gaussian distribution, and the risk-free asset is some constant.

Taking the derivative with respect to w and setting equal to zero gives us the familiar risky asset demand.

This says it is linearly related to the expected return, and inversely related to its variance. Increasing leverage increases the return (numerator) by X, and the variance (denominator) by X

^{2}, so the ratio changes by 1/x. Optimal demand, in this theory, goes down*parri passu*with the leverage; leverage should not affect actual $ demand because it washes out.Yet, in practice that's not what happens. I'm not sure what's going on, but I think part of it is a quantum effect, where investors are not interested in something until it can generate a sufficient threshold return. That is, most investors basically have 'null' for their Japanese bond exposure. A significant number of investors would put down $1000 if they had a chance to make $200, but many fewer are interested in putting down $1000 to make $100. Sure, they could always lever positions themselves but that's another level of complication, creating all sorts of operational risk such as issues about taxation and margin calls.

## 6 comments:

I think the threshold effect in potential returns you propose may have potential. With the thousands upon thousands of financial products investors need to sift through in order to build their portfolio, it makes sense that they would "filter" them based on something like that.

On the other hand leveraged funds do provide a useful service: we don't live in an MM world (I can't borrow at the same rates they do), and my leverage is prohibited by regulations anyway. Leveraged funds are a good way around both issues.

Short both.

From my experience there is a large (larger than you'd think) sub-set of scalpers that love these products because they present a more robust P&L opportunity intra-day. They have no interest in trading something that has a 1% daily range but all the interest in trading something that has a 3% daily range even if it's just a levered version of the exact same thing. Those scalpers, by definition, are also the least sensitive to the leverage costs used to generate that larger range because their holding period is minutes or hours, not days or weeks. They also account for a disproportionate amount of volume given that same turn-over issue.

If your model is to purely trade technicals on an intra-day basis, these levered products are actually fundamentally better securities to trade.

We advise institutional investors and I think about this a lot. A lot of interesting ideas become less interesting if the expected return is far enough below your nominal return targets. In reality it's likely not just pension funds that have nominal return targets. People probably set these subconciously, almost surely in suboptimal ways (i.e. via behavioral biases).

Leverage aversion is a real phenomenon. Investors that are happy to pay exorbitant fees to hedge funds for levered beta, are often unwilling to consider futures based leverage at the portfolio level.

This is Lasse Pedersen at AQR, NYU, and CBS. This post makes an interesting observation. The existence (and fees!) of leveraged ETFs provide an insight into the drivers of the beta effect: Namely, some investors are averse to using outright leverage and hence demand securities with “Embedded Leverage”. This is indeed the title of a recent paper that I wrote with one of my colleagues at AQR Capital Management, Andrea Frazzini. We show how leveraged ETFs and options are designed to embed leverage and that embedded leverage lowers returns, very much in the spirit of your discussion. The underlying theory of leverage constraints can both explain leveraged ETFs as well as many of the other empirical findings related to the beta effect (as discussed in our companion papers), though other things may contribute as well, of course.

Check it out:

http://pages.stern.nyu.edu/~lpederse/papers/EmbeddedLeverage.pdf

Lasse,

Interesting, thanks for the link, I haven't read that.

Cheng and Madhavan (2009) basically find that the leverage effect is really a correlation, and the main driver of leveraged underperformance are 'transaction costs' from these leveraged funds. At least, that's my inference of their work.

Eric

Post a Comment