Final answer:
The yield on 180-day risk-free securities in the United States is approximately 7.11%, calculated using the spot and forward exchange rates between the Japanese yen and the U.S. dollar, along with the Japanese securities yield.
Step-by-step explanation:
To calculate the yield on 180-day risk-free securities in the United States assuming interest rate parity holds, we need to consider the given spot and forward exchange rates, as well as the yield on Japanese securities. Let's go through the calculation step by step:
- Spot exchange rate: 1 Japanese yen = $0.01.
- Forward exchange rate (180-day): 1 Japanese yen = $0.0106.
- 180-day yield in Japan: 1.1%.
The formula to calculate interest rate parity is:
(1 + i_US) = (Forward Rate / Spot Rate) * (1 + i_Japan)
Where i_US is the interest rate in the US and i_Japan is the interest rate in Japan. Plugging in the numbers:
(1 + i_US) = ($0.0106 / $0.01) * (1 + 0.011)
(1 + i_US) = 1.06 * 1.011
(1 + i_US) = 1.07106
Now, solving for i_US:
i_US = 1.07106 - 1
i_US = 0.07106 or 7.11%
The yield on 180-day risk-free securities in the United States is approximately 7.11% when rounded to two decimal places.