# basis risk in currency management: question from Schweser

An analyst is managing a portfolio denominated in a foreign currency. In her analysis, she estimates that the hedge ratio of the portfolio is equal to one, and she implements the appropriate hedge. She also forecasts that there will be a negative correlation between the interest rate in her country and the interest rate associated with the foreign currency. This relationship of the interest rates: A) will reduce but not eliminate the basis risk of the hedged position. B) will eliminate the basis risk of the hedged position. C) is unrelated to basis risk. D) will introduce basis risk to the hedged position. Your answer: The correct answer was D) will introduce basis risk to the hedged position. Basis is the difference between the spot and futures exchange rates at a point in time. The magnitude of the basis depends upon the spot rate and the interest rate differential between the two economies. Interest rate parity describes the relationship between spot and futures exchange rates and local interest rates. Hence, if the interest rates move in the opposite direction, then the basis will change. ********************************************************* Why the fact that int rates movve in different direction means basis will change. They could have this relationship initially, and then the relationship between spot price and forward price wouldn’t change. Shouldn’t Schwesr in this question say that there would be a change in the correlation between the interest rate in her country and the foreign interest rate since she implements the hedge? Am I wrong?

very good question. for a fully hedged foreign investment, the return is roughly equal to domestic risk-free rate plus foreign risk premium. with above mentioned hedge, the investor would receive the foreign premium in one piece. no basis risk is of concern. but, the problem is the domestic risk-free rate. this rate is correlated to the foreign currency the investor currently owns. given the fact that imposed hedge didn’t cover this risk, therefore, there is basis risk to the hedged position.

At any given time, ratio of future to spot ratio is proportional to the ratio of risk free interest rate in domestic to foreign market (Interest rate parity). Given that the interest rates in domestic & foreign markets move in opposite direction (negative correlation), it is highly likely that over a period of time, the % change in spot rate doesn’t equal % change in future rate. This essentially implies that such a hedge would result in translation risk not being offset by gain from the futures transaction —> means that this will introduce basis risk. Having said that, it is possible to introduce basis risk even if the correlation between the two interest rates are positive, but the level of risk will be lower as the ratio of future/spot rate will be relatively constant when both interest rate moves in same direction. - BN

Basis risk for currency futures depends on the interest rate differential rd-rf. If rd and rf are negatively correlated: rd - rf widens if rf decreases (as rd will increase then) rd - rf shrinks if rf increases (as rd will decrease then) As a result basis risk can increase or decrease in this hedge.