Question

The spot rate between the Japanese yen and the U.S. dollar is ¥107.87/$, while the one-year forward rate is ¥108.42/$. The one-year risk-free rate in the U.S. is 2.79 percent. If interest rate parity exists, what is the one-year risk-free rate in Japan

Answer 1

The one-year risk-free rate in Japan, based on the given exchange rates and the interest rate parity formula, is approximately 2.99 percent.

Step-by-step explanation:

In order to calculate the one-year risk-free rate in Japan, we can use the interest rate parity formula, which states that the forward exchange rate should equal the spot exchange rate multiplied by the ratio of one plus the foreign interest rate to one plus the domestic interest rate.

So, if we plug in the given values, we have:

¥108.42/$ = ¥107.87/$ * (1 + Rj) / (1 + Ru)

Where Rj is the Japanese risk-free rate and Ru is the U.S. risk-free rate.

Since the one-year risk-free rate in the U.S. is 2.79 percent, we can rearrange the equation to solve for the Japanese risk-free rate:

Rj = (¥108.42/$ / ¥107.87/$) * (1 + Ru) - 1

Calculating this, we find:

Rj ≈ (1.0050856) * (1 + 0.0279) - 1 ≈ 0.0299

Therefore, the one-year risk-free rate in Japan is approximately 2.99 percent.