In an article on the Carry Trade, Menkhoff, Sarno, Scheling, and Schrimpf say they explain the positive returns to strategy via a 'risk premium'. This is how it is supposed to be, any identifiable return premium should be explainable in terms of risk alone.

So, here's a little throw-away line about prior work on volatility:

we investigate the empirical 2 performance of another risk factor: innovations in global FX volatility. This factor is a proxy for changes in market volatility suggested by the ICAPM theory, and is the analogue of the aggregate volatility risk factor used by Ang, Hodrick, Xing, and Zhang (2006) for pricing the cross section of stock returns. We show that global FX volatility is indeed a pervasive risk factor in the cross-section of FX excess returns.

OK, what they are saying is "There is no puzzle. It's all explainable in the standard framework. We use the risk factor 'innovations in volatility', which has been shown a relevant pricing factor back in 2006". The problem is that the paper referenced showed that high volatility innovation is correlated with lower returns. Further, higher volatility ex-innovation is correlated with lower returns. Indeed, the 'volatility innovations' ruse is clearly an attempt to torture the data to tell it what the authors wanted. Here, the risk premium actually makes sense (if you believe their results, and I'm skeptical they are robust as the carry trade did well in years like 2001-2002, and poorly in 1997-2000; there isn't as much data as you might think; eyeball below and see if it looks like returns are positively correlated with 'good times'). If volatility innovation is a priced risk factor, it doesn't make sense in general because in other markets volatility and things correlated with it are inversely related to returns.

So, financial economists appear to have shown again that some asset pricing pattern can totally be explained via some correlation with some new metric of risk that is strangely parochial to that specific asset class (that's not how it should work). They all know that returns are totally explained via risk premiums, as defined as covariances with proxies of their marginal utility. So, when convoluted tendentious drivel like this shows up again and again, it is considered serious research. I say, it's only interesting to academics if you believe the risk-premium theory (99%+ economists).

This search for the evanescent risk premium that appears as an ephemeral ghost, yet is omnipresent and very important, is one of the myths of our age. I've got better things to do.

## 14 comments:

"The problem is that the paper referenced showed that high volatility innovation is correlated with lower returns."

That's not what the paper shows. The paper shows that stocks that have a high beta to volatility innovations have lower average returns. That is stocks that do well when there is jump in VIX are stocks that have low average returns, presumably because they do well when (like taser) things are crashing.

ok, I'm confused... when they say the 'price of volatility risk' is negative (page 282 of Ang et al 2006), is this because unlike the market premium, higher values are 'bad'?

Yes. Thinking of a negative premium got me confused as well. The best way to think about it is in terms of tradable risk factors. The risk premium will be equal to the average return on the tradable asset. So the market risk premium will be return on the market index. If you think of ways of trading volatility like variance swaps, atm straddles, delta hedged options,these all have significant negative average returns.

The idea is that to the extent you have assets that do well when volatility is high they should have low returns because of their hedging value (kind of like paying for insurance premium).

To confuse matters more, in the paper they are also talking about returns to stocks sorted on volatility and find the puzzling relationship between high volatility and low returns. They find that stocks that have high volatility also have high volatility beta, that is they have high returns when market volatility is high. But volatility beta explains only a portion of the low returns so the puzzle is still there.

Dear Eric, you should actually read the papers before criticizing them.

What matters is, as Dan correctly says, the beta with volatility and results for stocks, corporate bonds, swaps,FX markets (and other asset classes) are perfectly consistent here and show that volatility has a negative market price of risk. So, vol risk is not "some new metric" that is "strangely parochial to that specific asset class".

Also, this finding not some ridiculous data torturing exercise with a questionable motivtaion but a central prediction from the ICAPM.

Hi, Dan is correct but what are you actually talking about in your blog post here?

Higher values of volatility are of course "bad", what else could they be? And how do you come to the conclusion that results make sense for one asset class and not the other when results for both asset classes are the same?

I also do not understand why you think the results are not robust over time? Did you check this or just accuse the authors of being stupid? I think the papers show that it the pattern is pretty stable over different subperiods.

Maybe you could explain your reasoning in some more detail.

Hi, Dan is correct but what are you actually talking about in your blog post here?

Higher values of volatility are of course "bad", what else could they be? And how do you come to the conclusion that results make sense for one asset class and not the other when results for both asset classes are the same?

I also do not understand why you think the results are not robust over time? Did you check this or just accuse the authors of being stupid? I think the papers show that it the pattern is pretty stable over different subperiods.

Maybe you could explain your reasoning in some more detail.

Going 'long' volatility hedges against crashes, and thus should be 'insurance'. Fine. Buying straddles is a money loser, so that premium is negative.

But while they seem to estimated that the beta of an asset against the VIX index returns is positively correlated with future returns, I don't see it, and unlike the raw volatility/returns finding, it doesn't show up much in the literature. That result is forgotten. True facts tend to come up again and again, because facts are real, and so different people see them. Untrue assertions show up in particular datasets with particular formulations (adjustments for conditional means, etc).

I find that high beta assets tend to have higher betas against the VIX changes. Do you see anyone suggesting people buy 'volatile' assets because these have lower betas against unexpected volatility? It's an implausible argument. Why do people care about increases in volatility, but not straightforward measures of wealth? Because you have to torture the data to get the 'right' result.

Eric, you just don't get it... High volatility betas mean low returns -- not high returns.

You obviously have no idea what you're talking about in this whole post and the comments. So, it's not surprising that you "don't see" the result in the data.

And it is ridiculous to write that "the literature has forgotten" the result. The Ang paper is from 2006 and already has about 500 cites.

You really shouldn't talk about stuff you do not understand. Some weeks ago, I actually thought about buying your book by I guess it won't be worth it.

I think Mr Falkenstein just doesn't understand the difference between cross-sectional results (that's what the Ang paper is about) and time-series results.

At least, that's the impression you get when someone tries to dispute cross-sectional results with time-series plots of a single return series.

To be clear to my excitable commenters: the cross-sectional result is that high volatility is correlated with lower returns. This is the result that is referenced, corroborated, and found interesting.

negative risk premium on stocks with high correlation with volatility innovations is a very weak (ie, non-robust) result. No one else corroborates it, and it's referenced only by academics trying to rationalize their obscurantism.

The cross-sectional is, in fact, not very robust as well.

The other stuff is extremely robust for other assets than stocks.

But it is really a waste of time in this blog. You are not better than the academics you are critizising. You simply know that it cannot be risk and that's what you find then.

You keep using that word [science]. I do not think it means what you think it means.

What's the series you plot as

Carry Trade Returns? It's not from the cited paper. Possibly AUDJPY? Thanks.Yeah, somewhat strange. Plotting one dubious time-series to show that a cross-sectional result cannot be true or robust?

Come on... that doesn't make any sense.

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