Tarek Hassan and Rui Mano have an interesting NBER conference paper (h/t Econbrowser (Menzie Chinn) that comes pretty close to saying that there is really no forward premium puzzle at all. Their paper itself tends to obscure the message using phrases like cross-currency, between-time-and-currency, and cross-time components of uncovered interest parity violations. So what follows is my take on their paper.

Uncovered interest parity says that ignoring risk aversion, currencies with high interest rates should be expected to depreciate so as to neutralise the interest differential. If not risk neutral investors from the rest of the world would move all their money into the high yielding currency and earn higher returns. Similarly, currencies with low interest rates should be expected to appreciate to compensate the interest differential so that risk neutral investors do not stampede out of the currency.

Violation of uncovered interest parity therefore have a potentially simple explanation in terms of risk premia. The problem is that the empirical relationship between interest differentials and currency appreciation is in the opposite direction to that predicted by uncovered interest parity. In a pooled time-series cross-sectional regression, currencies with high interest rates appreciate instead of depreciating. A whole investment strategy called the carry trade has been built on this observation. A risk based explanation of this phenomenon would seem to require implausible time varying risk premia. For example, if we interpret the pooled in terms of a single exchange rate (say dollar-euro), the risk premium would have to keep changing sign depending on whether the dollar interest rate was higher or lower than the euro interest rate.

This is where Hassan and Mano come in with a decomposition of the pooled regression result. They argue that in a pooled sample, the result could be driven by currency fixed effects. For example, over their sample period, the New Zealand interest rate was consistently higher than the Japanese rate and an investor who was consistently short the yen and long the New Zealand dollar would have made money. The crucial point here is that a risk based explanation of this outcome would not require time varying risk premia – over the whole sample, the risk premium would be in one direction. What Hassan and Mano do not say is that a large risk premium would be highly plausible in this context. Japan is a net creditor nation and Japanese investors would require a higher expected return on the New Zealand dollar to take the currency risk of investing outside their country. At the same time, New Zealand is a net debtor country and borrowers there would pay a higher interest rate to borrow in their own currency than take the currency risk of borrowing in Japanese yen. It would be left to hedge funds and other players with substantial risk appetite to try and arbitrage this interest differential and earn the large risk premium on offer. Since the aggregate capital of these investors is quite small, the return differential is not fully arbitraged away.

Hasan and Mano show that empirically only the currency fixed effect is statistically significant. The time varying component of the uncovered interest parity violation within a fixed currency pair is not statistically significant. Nor is there a statistically significant time fixed effect related to the time varying interest differential between the US dollar and a basket of other currencies. To my mind, if there is no time varying risk premium to be explained, the forward premium puzzle disappears.

The paper goes on to show that the carry trade as an investment strategy is primarily about currency fixed effects. Hasan and Mano consider “a version of the carry trade in which we never update our portfolio. We weight currencies once, based on our expectation of the currencies’ future mean level of interest rates, and never change the portfolio thereafter.” This “static carry trade” strategy accounts for 70% of the profits of the dynamic carry trade that rebalances the portfolio each period to go long the highest yielding currencies at that time and go short the highest yielding currencies at that time. More importantly, in the carry trade portfolio, the higher yielding currencies do depreciate against the low yielding currencies. It is just that the depreciation is less than the interest differential and so the strategy makes money. So uncovered interest parity gets the sign right and only the magnitude of the effect is lower because of risk premium. There is a large literature showing that the carry trade loses money at times of global financial stress when investors can least afford to lose money and therefore a large risk premium is intuitively plausible.