An FI has purchased (borrowed) a one-year $10 million Eurodollar deposit at an annual interest rate of 6 percent.It has invested these proceeds in one-year Euro (€) bonds at an annual rate of 6.5 percent after converting them at the current spot rate of €1.75/$.Both interest and principal are paid at the end of the year. Assume that instead of investing in Euro bonds at a fixed rate of 6.5 percent, it invests them in variable rates of LIBOR + 1.5 percent, reset every six months.The current LIBOR rate is 5 percent.What is the annual spread earned by the bank if LIBOR at the end of six months is 5.5 percent? Assume both interest and principal will be reinvested in six months.Assume the exchange rate remains at €1.75/$ at the end of the year.

Question

Quizplus · Accepted Answer

The bank borrows at 6% and initially invests at LIBOR + 1.5%, which is 5% + 1.5% = 6.5% for the first six months. For the next six months, the LIBOR rate is 5.5%, so the investment rate becomes 5.5% + 1.5% = 7%. The average rate over the year is (6.5% + 7%) / 2 = 6.75%. The spread earned by the bank is the investment rate minus the borrowing rate, which is 6.75% - 6% = 0.75%. However, since interest is compounded semi-annually, we need to adjust our calculation. The effective annual rate (EAR) for the investment can be calculated using the formula for semi-annual compounding: $(1 + \frac{r}{2})^2 - 1$, where $r$ is the annual nominal rate. Substituting the given rates: $(1 + \frac{0.0675}{2})^2 - 1 = (1 + 0.03375)^2 - 1 = 1.06890625 - 1 = 0.06890625$ or 6.89%. The spread is then 6.89% - 6% = 0.89%. Given the options, the closest to the calculated spread is 0.86%, acknowledging a slight approximation in the final step.

An FI Has Purchased (Borrowed) a One-Year $10 Million Eurodollar