Assume that a bank can borrow or lend money at the same interest rate in the LIBOR market. The 91-day rate is 5% per year, and the 182-day rate is 5.2%. Assume the LIBOR rates are continuously compounded. The Eurodollar futures price for a contract maturing in 91 days is quoted as 96.
Equilibrium for Forward Rate Agreements:
LHS = eR2 T2 = e ^ 0.052 * 6/12 = 1.02634
182 days LIBOR is 5.2% (R2) * 6/12 (T2) which is continuously compounded
RHS = eR T x e r t = e ^ 0.05* 3/12 x e ^ 0.04*3/12
= 1.0258 x 1.0101 = 1.03616
R = LIBOR 91 days rate T is 91 days
r = 100 -96 = 4 (Eurodollar futures trading at 4% discount)
t = 91 days
RHS > LHS
Arbitrage occurs if Investor borrows for 6 months at 5.2% and invests for 3 months at 5%. Buys Eurodollar 91 day futures.
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