In: Finance
Investment in 90-day, 180-day, 360-day treasury bills denominated in Euro provide annualised yields of 6%, 6.5% and 7% respectively. where those of identical maturities in the USA in US dollars offer 4%, 4.25% and 4.50% respectively.
If the current exchange rate is Euro 1.2 / dollar, what should be the value of euro in terms of US dollar after 90 days, 180 days and 360 days ?
Risk Free Rates in Euro:
90 Days = 6%
180 Days = 6.5%
360 Days = 7%
Risk Free Rates in Dollar:
90 Days = 4%
180 Days = 4.25%
360 Days = 4.5%
Spot Exchange Rate = Euro 1.2 / Dollar
As per Interest Rate Parity / Covered Interest Arbitrage theory:
Expected Future Price of Euro / Dollar =
We have assumed 360 days in a year for ease of calculation. If taken 365 or other, it might differ slightly.
With this formula,
Expected future price in 90 days = 1.2 * (1 + 6%)(90 / 360) / (1 + 4%)(90/360)
Expected future price in 90 days = Euro 1.2057 / Dollar
Expected future price in 180 days = 1.2 * (1 + 6.5%)(180 / 360) / (1 + 4.25%)(180/360)
Expected future price in 180 days = Euro 1.2129 / Dollar
Expected future price in 360 days = 1.2 * (1 + 7%)(360 / 360) / (1 + 4.5%)(360/360)
Expected future price in 360 days = Euro 1.2287 / Dollar