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.