Question

13.A bank can borrow or lend at LIBOR. The 6-month rate is 5% and the 9-month rate is 5.5%. The Eurodollar futures contract expiring in 6 months is trading at 94. What arbitrage opportunities are open to the bank

Answer 1

The arbitrage opportunities are as Buy Eurodollar futures, Borrow Money for 9 months and Invest Money for 6 months.

Step-by-step explanation:

The future rate of Eurodollar at the end of contract expiring in six months is

`Rate=(100-94)/(100)* 100=6\%`

This is biannual compounding with actual on 360 days.

Now converting this into the continuous compounding as

`Rate=6\%* (365)/(360)\\Rate=6.083\%`

The formula for continuous compounding is as

`R_c=mln(1+(Rm)/(m))\\R_c=2ln(1+(0.06083)/(2))\\R_c=0.0592=5.92\%`

Now from the formula

`R_F=(R_2T_2-R_1T_1)/(T_2-T_1)\\R_F=(5.5\%* 9-5\%*6)/(9-6)\\R_F=(5.5\%* 9-5\%*6)/(3)\\R_F=6.5\%`

As the forward rate is more than both the 6 month and 9 month rate thus

The arbitrage opportunities are as Buy Eurodollar futures, Borrow Money for 9 months and Invest Money for 6 months.