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Six-month T-bills have a nominal rate of 7 percent, while default-free Japanese bonds that mature in 6 months have a nominal rate of 5.5 percent. In the spot exchange market, 1 yen equals \(\$ 0.009\). If interest rate parity holds, what is the 6 -month forward exchange rate?

Short Answer

Expert verified
The 6-month forward exchange rate is approximately $0.00908 per yen.

Step by step solution

01

Understand the Problem

We need to find the 6-month forward exchange rate given the nominal interest rates of U.S. T-bills and Japanese bonds, and the current spot exchange rate, using the principle of interest rate parity.
02

Apply Interest Rate Parity Formula

Interest rate parity states that the forward exchange rate should reflect the interest rate differential between two countries. The formula is:\[ F = S \times \frac{1 + r_{domestic}}{1 + r_{foreign}} \]where \( F \) is the forward exchange rate, \( S \) is the spot exchange rate, \( r_{domestic} \) is the domestic interest rate, and \( r_{foreign} \) is the foreign interest rate.
03

Identify the Variables

From the problem, we know:\( r_{domestic} = 0.07/2 = 0.035 \) (annual rate divided by 2 for 6 months)\( r_{foreign} = 0.055/2 = 0.0275 \) (annual rate divided by 2 for 6 months)\( S = 0.009 \) yen/USD.
04

Plug Variables into Formula

Insert the identified variables into the interest rate parity formula:\[ F = 0.009 \times \frac{1 + 0.035}{1 + 0.0275} \]
05

Calculate the Forward Rate

Perform the calculation:\[ F = 0.009 \times \frac{1.035}{1.0275} \approx 0.00908 \]
06

Interpret the Result

The calculated forward rate \( F \approx 0.00908 \) means that, according to interest rate parity, one yen is expected to equal approximately $0.00908 in 6 months.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Forward Exchange Rate
The forward exchange rate is a concept in international finance that helps predict the expected future value of a currency compared to another. It is essential for businesses and investors involved in international trade and finance. The forward exchange rate provides a contractual agreement today to exchange a specific amount of currency at a set rate on a future date.
This mechanism allows for better planning and budgeting, as it helps to mitigate the risk of fluctuating currency values. For example, if you know that you will need a set amount of Japanese yen in six months, you can arrange a forward exchange contract.
  • This stabilizes the cost of future payments and receipts.
  • It protects against potential adverse movements in exchange rates.
  • It ensures that you can plan operations without surprise currency expenses.
Understanding how to calculate it, using interest rate parity, ensures you compare an apple to an apple by adjusting for interest rate differences between countries.
Nominal Interest Rate
Nominal interest rates are the stated interest rates on financial products, like bonds and loans, without adjusting for inflation or other factors. They represent the rate of return earned or paid over a period, like a year.
Understanding nominal rates is crucial because they affect various elements of finance and economics.
When comparing bonds from different countries, like our example with U.S. T-bills and Japanese bonds, nominal rates give us a raw comparison.
  • They show the base earning or paying rate without adjustments.
  • They help to make baseline assessments of interest rate parity conditions.
  • They serve as fundamental figures for economic decision-making.
However, when it comes to real-world investments, it's important to consider that these rates do not reflect purchasing power changes due to inflation or other economic factors.
Spot Exchange Market
The spot exchange market, also known as the cash market, is where currencies are traded for immediate delivery. In this market, transactions are settled on the spot, which typically means within two business days.
The key feature of the spot exchange market is its immediacy. Traders, businesses, and investors use it for rapid currency conversions.
  • It determines the current exchange rates or spot rates.
  • It provides liquidity for global currency needs.
  • It reflects market sentiment and economic conditions instantly.
In our exercise, the spot rate gives the base on which any future rate is calculated. Notably, it's this fixed point that gets adjusted by predicting relative economic changes, like differing national interest rates, to form the forward rate under interest rate parity assumptions.

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Most popular questions from this chapter

A television set costs \(\$ 500\) in the United States. The same set costs 725 euros. If purchasing power parity holds, what is the spot exchange rate between the euro and the dollar?

If British pounds sell for \(\$ 1.50\) (U.S.) per pound, what should dollars sell for in pounds per dollar?

Suppose the exchange rate between the U.S. dollar and the Swedish krona was \(10 \mathrm{krona}=\$ 1.00\), and the exchange rate between the dollar and the British pound was \(£ 1=\$ 1.50 .\) What was the exchange rate between Swedish kronas and pounds?

After all foreign and U.S. taxes, a U.S. corporation expects to receive 3 pounds of dividends per share from a British subsidiary this year. The exchange rate at the end of the year is expected to be \(\$ 1.60\) per pound, and the pound is expected to depreciate 5 percent against the dollar each year for an indefinite period. The dividend (in pounds) is expected to grow at 10 percent a year indefinitely. The parent U.S. corporation owns 10 million shares of the subsidiary. What is the present value in dollars of its equity ownership of the subsidiary? Assume a cost of equity capital of 15 percent for the subsidiary.

Chamberlain Canadian Imports has agreed to purchase 15,000 cases of Canadian beer for 4 million Canadian dollars at today's spot rate. The firm's financial manager, James Churchill, has noted the following current spot and forward rates: $$\begin{array}{lcc} & \text { U.S. Dollar/Canadian Dollar } & \text { Canadian Dollar/U.S. Dollar } \\ \hline \text { Spot } & 0.6930 & 1.4430 \\ \text { 30-day forward } & 0.6935 & 1.4420 \\ \text { 90-day forward } & 0.6944 & 1.4401 \\ \text { 180-day forward } & 0.6957 & 1.4374 \end{array}$$ On the same day, Churchill agrees to purchase 15,000 more cases of beer in 3 months at the same price of 4 million Canadian dollars. a. What is the price of the beer, in U.S. dollars, if it is purchased at today's spot rate? b. What is the cost, in U.S. dollars, of the second 15,000 cases if payment is made in 90 days and the spot rate at that time equals today's 90 -day forward rate? c. If the exchange rate for the Canadian dollar is 1.20 to \(\$ 1\) in 90 days, how much will Churchill have to pay for the beer (in U.S. dollars)?

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