# Carry Trade and Tail Risk

FUJIWARA Ippei
Senior Fellow, RIETI

It is recognized that the currency of a country with high interest rates tends to appreciate. This sounds like an indisputable theory. However, if this is correct, those borrowing funds in low interest rate countries such as Japan and investing in high interest rate countries such as Australia and New Zealand can achieve high profitability, benefiting not only from interest rate spreads but also from capital gains in the form of depreciation in the Japanese yen. This is what is referred to as carry trade. In particular, the yen carry trade has become such a globally reputed model of financial transactions in recent years that "Mrs. Watanabe," the fabled Japanese housewife investor supposed to engage in such transactions aggressively, has come to be recognized by traders around the world.

Although the yen carry trade may not be as voluminous as it was some time ago, we continue to hear people claiming that the aggressive monetary easing of the U.S. Federal Reserve is the primary factor behind the downward movement of the yen-dollar exchange rate (or the yen's appreciation). In this regard, it seems that potential profits from the yen carry trade remain substantially large. However, from the viewpoint of financial arbitrage, carry trade must not always be profitable. If it is profitable on average, then there should be certain risk taken in compensation.

## Uncovered interest arbitrage

One of the most prominent theories used to explain foreign exchange rate fluctuations is that of the uncovered interest rate parity condition, which is based on a simple thought that the expected returns on deposits of any two currencies are equal when measured in the same currency. Specifically, where i is the Japanese interest rate, i* is the Australian interest rate, and S is the Australian dollar's rate against the Japanese yen, the following equation should hold:

The left side of the equation represents the return on investment in Japan and is equal to the right side, which represents the return in Australia denominated in yen. According to this equation, the expected return on carry trade (denominated in yen) must be zero, calculated as the right side minus the left side.

## Tail risk

However, many existing studies have found that actual returns on carry trade, as seen from an ex post facto viewpoint, have been positive. The fact that actual returns have been positive in average terms indicates the presence of some sort of risk in carry trade. In other words, any return on carry trade must be compensation for risk. Then, what sort of risk is it?

When the growth rates of the exchange rate between a high interest rate currency and a low interest rate currency, such as that between the Australian dollar and the Japanese yen, are plotted in a histogram, they are not distributed symmetrically across the center position of zero and are skewed to the left, toward the depreciation of the high interest rate currency. In particular, it is known that high interest rate currencies, albeit at an extremely low probability, depreciate dramatically in a very short period of time. The risk of such sudden and sharp depreciation, which is referred to as "tail risk" or "disaster risk," has been drawing much attention recently as the cost of positive returns from financial transactions.

Investors may be able to receive positive returns on carry trade in average terms. However, they are embracing the risk of a sharp depreciation in the high interest rate currency at the same time. In other words, carry trade poses the potential risk that investors could face a significant depreciation when they are in need of cash. After all, there is no free lunch in financial transactions.

August 14, 2012

August 14, 2012

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