Question

Do you agree with the following statements? Please provide reasons to support your answer.

“Covered interest parity is forced by arbitrage, which is not the case for uncovered interest rate parity. If the forward rate is equal to the expected future spot rate, we say that the forward rate is an unbiased predictor of the future spot rate: F = E(S1). In this special case, given that covered interest parity holds, uncovered interest parity would also hold (and vice versa). In other words, if uncovered interest rate parity (and covered interest parity) holds, the forward rate is unbiased predictor of future spot rate”

Answer 1

Covered interest rate parity is an arbitrage relation that states that forward exchange rates are a function of current spot rates and interest rates in each currency. Essentially it says that you can’t profit by borrowing in one currency and investing in another over a period because the forward rate you would lock in would exactly offset the changes in value due to the different interest rates. It is an arbitrage reltiaon because you know all factors at the present time, you know the current spot rat, you know the interest rates for each currency and you can lock in a price with the current forward rate.

Uncovered interest rate parity has nothing to do with forward rates, it is forecasting EXPECTED FUTURE SPOT RATES. It states that the expected future spot rate is a function of the current spot rate and the interest rates of each currency. It is not an arbitrage relation because you cannot lock in the future spot rate at the present time.

You’ll notice that they are pretty much the same thing, and if the forward rate is an unbiased predictor of the future spot rate then they are the same thing. The critical difference is that covered parity uses forward rates you can lock in TODAY and uncovered forecasts the spot rate that will occur at time T.

There are two related puzzles in the empirical foreign exchange literature. The first is the finding that there is a marked difference in the conclusion about the forward rate unbiasedness hypothesis depending on whether the hypothesis is tested using the forward rate or forward premium equation. The second—the forward premium puzzle— is the fact that the forward premium incorrectly predicts the direction of the subsequent change in the spot rate, which implies a massive rejection of UIP. This paper resolves both puzzles. The first puzzle is resolved by showing that estimates of the slope parameter from the forward rate and forward premium equations are not comparable under the alternative hypothesis. Since there are several reasons why unbiasedness will not hold exactly, there is no reason to be concerned that the estimates from these equations are different— indeed, they are not comparable. Simple Monte Carlo experiments show that the estimates from these equations will be very different even for tiny violations of the null hypothesis. The noncomparability of these parameters also means that, contrary to the suggestion in the literature that it is better to test unbiasedness using the forward premium rather than the forward rate specification, it is impossible to test unbiasedness using the forward premium specification. This conclusion stems from the fact that it is impossible 24 to obtain an estimate of the parameter under the alternative hypothesis that is comparable to the parameter under the null. The resolution of the forward premium puzzle stems from the observation that the stochastic perfect foresight assumption used to derive the forward premium test of UIP is greatly at odds with the near random walk behavior of exchange rates. The near-randomwalk behavior of exchange rates implies a weak relationship between changes in the spot rate and the forward premium, which is consistent with estimates of the forward rate equation found in the literature. CIP, however, implies that there is a strong positive correlation between the forward premium and the difference between domestic and foreign interest rates. Hence, the sign of the estimate of the slope coefficient from the forward premium equation depends on the sign of the correlation between the change in the spot rate and the difference between domestic and foreign interest rates, being positive when this correlation is positive and negative when the correlation is negative. This resolution is supported by the fact that time variation in the correlation between the change in the spot rate and the difference between domestic and foreign interest rates explains much of the time variation in the estimates of the slope coefficient. This is true for a variety of exchange rates and over several different sample periods. The sign of this correlation is determined by economic fundamentals. The correlation is positive when the behavior of the domestic/foreign interest rate differential is due to relative changes in real rates and negative when it is due to changes in expectations for inflation. The forward premium puzzle—the preponderance of negative estimates of the slope coefficient—is because, for most exchange rates and for most sample periods, the 25 difference between domestic and foreign interest rates reflects concerns about inflation rather than the behavior of real rates. Of course, the above explanation need not account for all of the anomalous results obtained using (15). Other factors may also play a role. As noted in Sections 3 and 4, minor violations of the unbiasedness condition can generate negative estimates of the slope coefficient as well. Moreover, because exchange rates are not pure-random-walk processes, there may be some marginal predictability in the spot exchange rate beyond its current value (e.g., Clarida, Sarno, Taylor, and Valente, 2003). Nevertheless, the results presented here suggest that the near-random-walk behavior of the spot rate, CIP, and economic fundamentals that generate correlation between the domestic/foreign interest differential and the change in the spot rates are important—if not the most important— reasons for the empirical failure of UIP and, consequently, critical for resolving the forward premium puzzle.