Question

Consider a forward contract to purchase a coupon-bearing bond whose current price is $900. Suppose the forward contract matures in 9 months. Assume the coupon payment of $40 is expected after 4 months. Assume that the 4-month and 9-month risk-free continuously compounded interest rate are 3% and 4% per annum, respectively. Suppose the forward price is $910. Is there an arbitrage opportunity? If so, how do you take advantage of the arbitrage opportunity?

Answer 1

Solution:
Current price	$900
Term	9 Months
Coupon payments after 4 months	$40
4 month risk free rate	3%
9 month risk free rate	4%
Forward price	$910
Arbitrage would borrow $900 to purchase the bond a short a forward contract
Present value of first coupon we will calculate the discounted value @ 3% for 4 months
40e^-0.03*4/12
40e^-0.03*0.3333333
40*0.990049844
39.60199376
$39.60
Using the EXP Function in excel we will calaculate value of e
EXP(-0.03*0.333333)
0.990049844
The balance $860.40 ($900-$39.60) is borrowed at 4% annually for 9 Months, so
860.40e^0.04*9/12
860.40e^0.04*0.75
860.40*1.030454534
886.6030811
$886.60
Using the EXP Function in excel we will calaculate value of e
EXP(0.04*0.75)
1.030454534
The arbitrage will make Profit of = Forward price - PV of borrowed amount
$910-$886.60
23.4
The Arbitrage will make $23.40