We began this series of posts recapping the finding that a currency carry trade investment has historically produced high return relative to the low risk. This finding is not consistent with models in finance that focus on the correlation between an investment’s return and the return on some benchmark stock portfolio. Using these models, and looking at the historical distribution of returns, the carry trade looks like a good bet, even accounting for bad outcomes. Posts #2 and #3 in the series reported on one route of the research effort to explain the puzzle, which attributes the abnormal return to the “peso problem”. But other researchers have been pursuing different routes. To wrap up this series, we’ll quickly mention some of this work.

First, a paper by Lustig and Verdelhan finds that the returns on the currency carry trade are tied to US investors’ consumption risk, the underlying variable that (in theory) ought to determine asset prices. “*Low* interest rate currencies expose US investors to *less *nondurable and durable consumption risk than *high* interest rate currencies.” Hence the higher return required to invest in currencies with a higher interest rate.

This result is interesting, but it has one serious caveat. The consumption-based model the authors use to make sense of the carry trade returns relies on parameters describing investors’ risk aversion that are wholly unrealistic. This caveat applies equally to the broader finance literature trying to make sense of historical asset returns, where it is known as the *equity premium puzzle*. So, this line of research provides cold comfort by placing the carry trade puzzle into embarrassing context.

Second, a paper by Lustig, Roussanov and Verdelhan identifies a risk factor in exchange rates that accounts for the variation in excess returns across high and low interest rate currencies. This risk factor is related to global equity market volatility. Investing in the currency carry trade means loading up on this global risk factor, and investors require a return for doing that. Here we are talking again about a multiple factor model, a version of the factor models for stocks such as the Fama-French and Carhart models, suited to exchange rates and interest rates. These results, too, leave the larger issue unresolved. After all, it remains to be said whether such global risk factor actually explains the returns to the carry trade in the sense of puncturing the illusion of a free lunch.

Third, reality is a lot more complex, and different risk models co-exist to explain the peculiar dynamics of interest rates and exchange rates. The prevailing paradigm is that returns are generated by a single, stationary process. But the evidence shows that the process driving interest rates depends upon the level of rates. For example, a paper by Aït-Sahalia finds that standard models of interest rates which assume a linear trend don’t fit the data: “Around its mean, where the drift is essentially zero, the spot interest rate behaves like a random walk,” while “the drift then mean-reverts strongly when far away from the mean.” The implication? The risk-return relation is shaped by the environment…and vice-versa. At times, exchange rates and interest rates are explained by a particular model, and at other times they are explained by a different model. Clearly, there are plenty of variations on this theme that might be relevant.

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