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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, one 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 0.009128 USD/JPY.

Step by step solution

01

Understand Interest Rate Parity

Interest Rate Parity (IRP) is a fundamental principle in exchange rates that suggests the difference in nominal interest rates between two countries is equal to the expected change in exchange rates between these countries' currencies. This concept can be used to find the forward exchange rate.
02

Define the Given Information

You are given the following data: \( r_{us} = 0.07 \) (6-month US nominal rate), \( r_{jp} = 0.055 \) (6-month Japanese nominal rate), and the current spot exchange rate \( S = 0.009 \) USD/JPY.
03

Set Up the Interest Rate Parity Formula

The IRP formula is given by:\[ \frac{1 + r_{us}}{1 + r_{jp}} = \frac{F}{S} \]Where \( F \) is the forward rate we need to find.
04

Substitute the Values into the IRP Formula

Replace \( r_{us} \), \( r_{jp} \), and \( S \) in the IRP formula:\[ \frac{1 + 0.07}{1 + 0.055} = \frac{F}{0.009} \]
05

Solve for the Forward Rate \( F \)

Calculate the expression on the left side:\[ \frac{1.07}{1.055} \approx 1.01422 \]Then solve for \( F \): \[ F = 1.01422 \times 0.009 \approx 0.00912798 \]
06

Final Answer

The 6-month forward exchange rate is approximately \( 0.009128 \) USD/JPY.

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Key Concepts

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

Forward Exchange Rate
A forward exchange rate is essentially an agreed-upon rate at which a currency pair will be exchanged on a future date. This is different from the spot exchange rate, which is the rate at which currencies are exchanged directly in the present. It's like making a deal today to exchange currencies later at a pre-determined rate.
  • Forward exchange rates are used to hedge against currency fluctuations. This is useful for companies engaged in international trade who may want to avoid the risk of currency value changes in the future.
  • They are calculated using the interest rate parity, which considers the interest rate differences between two countries.
In the context of our exercise, knowing the forward exchange rate allows us to anticipate how much one would need to pay in dollars for yen in six months. Thus, it provides a safety net against unforeseen changes in the currency markets. By using the Interest Rate Parity formula, we can calculate this rate fairly easily given nominal interest rates and the current spot rate.
Nominal Interest Rate
The nominal interest rate of a country is the annual percentage increase in the value of a loan or investment without considering inflation. It's a basic indicator of the return or cost of financing in a financial market. This figure can differ between regions or countries depending on various economic factors.
  • Nominal interest rates are crucial for international finance as they directly affect the exchange rate calculations through Interest Rate Parity.
  • A higher nominal interest rate in a country means that its investors are rewarded more, which can affect currency flows as investors seek the best returns.
In our problem scenario, we have 6-month nominal rates of 7% for the US and 5.5% for Japan. These rates reflect the yearly returns investors expect, influencing calculations for the forward rate using the Interest Rate Parity equation. A larger difference in these rates often means a more substantial expected change in the currency exchange.
Currency Exchange
Currency exchange is the process of exchanging one form of currency for another and is a vital component of international trade and finance. The rate at which currencies are exchanged is known as the exchange rate. In daily life, this is how you convert money from one currency to another when traveling or doing business with overseas partners.
  • Spot exchange rates are the current rates for immediate currency exchanges.
  • Forward rates are used for transactions set to occur at a later time, helping manage future financial risks.
  • Currency exchange rates are influenced by various factors, including interest rates, inflation, political stability, and economic performance.
In the provided exercise, we are given a spot exchange rate of 0.009 USD/JPY, which means for every yen, you get $0.009. Understanding how currency exchange works and the factors involved can provide insights into international economics and help manage financial expectations effectively.

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Most popular questions from this chapter

In the spot market 7.8 Mexican pesos can be exchanged for 1 U.S. dollar. A compact disc costs \(\$ 15\) in the United States. If purchasing power parity (PPP) holds, what should be the price of the same disc in Mexico?

The problems included in this section are set up in such a way that they could be used as multiple-choice exam problems. If British pounds sell for \(\$ 1.50\) (U.S.) per pound, what should dollars sell for in pounds per dollar?

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.

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?

Assume that interest rate parity holds and that 90 -day risk-free securities yield 5 percent in the United States and 5.3 percent in Britain. In the spot market 1 pound equals 1.65 dollars. a. Is the 90 -day forward rate trading at a premium or discount relative to the spot rate? b. What is the 90 -day forward rate?

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