Question

the current usd/euro exchange rate is 1.4000 dollar per euro. the six month forward exchange rate is 1.3950. the six month usd interest rate is 1% per annum continuously compounded. estimate the six month euro interest rate. 13. a stock is expected to pay a dividend of $1 per share in two months and in five months. the stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. an investor has just taken a short position in a six-month forward contract on the stock. a) what is the forward price now? what is the initial value of the forward contract? b) three months later, the price of the stock is $48 and the risk-free rate of interest is still 8% per annum. what is the forward price? what is the value of the short position in the forward contract? 7

Answer 1

The estimation of the six-month euro interest rate involves using the Interest Rate Parity theory, which relates interest rate differentials to the discrepancy between the spot and forward exchange rates. For the stock in question, the forward price and value of the forward contract are calculated using the cost-of-carry model and adjusted for dividends and interest rates. The demand and supply shifts in USD due to interest rate changes demonstrate the interrelationship between exchange rates and international economics.

Step-by-step explanation:

To estimate the six-month euro interest rate given a spot exchange rate of 1.4000 USD per euro, a six-month forward exchange rate of 1.3950, and a six-month continuously compounded USD interest rate of 1%, the Interest Rate Parity (IRP) theory can be applied. According to IRP, the difference in interest rates between two countries is equal to the difference between the forward exchange rate and the spot exchange rate, adjusted for the time to maturity of the contract. The expected euro interest rate can be derived from the given rates and is necessary to ensure no arbitrage opportunities exist.

Concerning the stock with a projected dividend, to determine the forward price and initial value of a forward contract, the cost-of-carry model, which includes the current stock price, the present value of dividends, and the risk-free rate, is used. For the short position taken in a six-month forward contract, the value at inception and after three months can be calculated using the change in the forward price due to movement in the stock price and interest rates, which remain at 8% per annum with continuous compounding.

In the case of the foreign exchange market for U.S. dollars reacting to higher interest rates, the resulting shift in demand and supply causes an appreciation of the exchange rate. This dynamic illustrates how changes in interest rates can affect currency strength and international trade by making a currency more or less attractive to hold as an investment.