The relationship between exchange rates, interest rates • In this lecture we will learn how exchange rates accommodate equilibrium in ﬁnancial markets. For this purpose we examine the relationship between interest rates and exchange rates. Interest rates are the return to holding interest-bearing ﬁnancial assets. In the previous lecture we have pointed out that as being a ﬁnancial asset exchange rates tend to adjust more quickly to new information that goods prices. Like exchange rates, interest rates are also the prices of ﬁnancial assets and hence adjust quickly to new information. • The proﬁt-seeking arbitrage activity will bring about an interest parity relationship between interest rates of two countries and exchange rate between these countries. • A U.S. investor deciding between investing say in New York and in Tokyo must consider several things: – the interest rate in the U.S., i$ , (interest rate in aU.S¿ dollar denominated bond, or rate of return in a U.S. dollar denominated US stock etc), interest rate in Japan (iY ; – the spot exchange rate, S; and – the future exchange rate for maturity date, forward rate, F . • If the investor did not lock in a future exchange rate now, the unknown future spot exchange rate would make the investment risky. The investor can eliminate the uncertainty over the future dollar value of the investment by covering the investment with a forward exchange contract. • If the investor covers the investment with a forward contract the arbitrage between two investment opportunities results in a covered interest parity (CIP) condition: (1 + i$ ) = (1 + iY ) 1 F S (1)
which may be rewritten as (1 + i$ ) F = (1 + iY ) S (2)
• The interest rate parity equation can be approximated for small interest rates by: i$ − iY = F −S S (3)
• This later equation says that interest diﬀerential between a US denominated investment instrument and a Yen denominated investment instrument is equal to the forward premium or discount on the Yen. • Example: i$ = 5%, iY = 3%. Suppose S = 0.0068 dollars per Yen. What should be the 90-day forward rate? 0.05 − 0.03 = F − 0.0068 0.0068
F = 0.0068 + 0.02 ∗ 0.0068 = 0.00694 Thus we expect that a 90-day forward rate of $0.00694 to give a 90-day forward premium equal to the 0.02 interest diﬀerential. • If the forward exchange rates were not consistent with the respective interest rates, then arbitrageurs could proﬁt by immediately changing currency in the spot market, investing it and locking in the proﬁtable forward exchange rate. These actions in the market would increase the spot rate and lower the forward rate, bringing the forward premium into line with the interest diﬀerential. • Suppose the actual 90-day forward rate is not 0.00694 dollars per yen but 0.0071 dollars per yen. Then proﬁt-seeking arbitrageurs could buy Yen spot, then invest and sell the Yen forward for dollars, since the forward price of Yen is higher than that implied by the covered interest parity relation. These actions will tend to increase spot rate and lower the forward rate, thereby bringing the forward premium back in line with the interest diﬀerential. 2
• The interest rate parity condition (CIP) can be used to compute eﬀective return on a foreign investment. Re-write (3) as: i$ = i Y + F −S S (4)
This latter equation says that the return on a US dollar denominated asset (US dollar interest rate) is given by the Japanese interest rate plus the forward premium or discount on Yen. If CIP holds then equation (4) will hold as well. • What happens when an investor does not use the forward market? Then we can not expect eﬀective return on US dollar denominated asset be given by (4) as the investor in question will not be able to get the premium on Yen (or lose the discount). In this case, we say investor has an uncovered investment. The eﬀective return then will be determined by the Japanese interest rate plus the change in the spot exchange rate between today and say 90 days from...
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