Consider a long forward contract to purchase a coupon-bearing bond whose current price is $910. We will suppose that the forward contract matures in 9 months. We will also suppose that a coupon payment of $45 is expected after 4 months. We assume that the 4-month and 9-month risk-free interest rates (continuously compounded) are, respectively, 3% and 4% per annum. Explain how an arbitrageur can make profits from this scenario.

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Solution:     Current price $910   Term 9 Months   Coupon payments after 4 months $45   4 month risk free rate 3%   9 month risk free rate 4%   Forward price $910   Arbitrage would borrow $910 to purchase the bond a short a forward contract   Present value of first coupon we will calculate the discounted value @ 3% for 4 months 45e^-0.03*4/12     45e^-0.03*0.3333333     45*0.990049844     44.552242     $44.552242     Using the EXP Function in excel we will calaculate value of e   EXP(-0.03*0.333333)     0.990049844   The balance $865.447758 ($910-$44.552242) is borrowed at 4% annually for 9 Months, so 865.447758e^0.04*9/12     865.447758e^0.04*0.75     865.447758*1.030454534     891.8045     $891.8045     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-$891.8045     18.1955           The Arbitrage will make $18.1955 ...