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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Step 1Forward contract as the name suggests is not related to the present scenario. It means the buying and selling of the stocks, currencies, and commodities at a specified price but this will be at a future date. It occurs on a cash and delivery basis.These contracts can be made customized because these types of contracts are not traded on the centralized exchange market and therefore these are regarded as over counter instruments. Though it lacks clearing from the centralized exchange market, the default risk involved in it is high. Step 2Arbitrage is related to the buying and selling of the same commodity in the same market. It means buying one commodity at a certain price and simultaneously selling that commodity in the same market at a higher price than that of the purchase price. This is done to avoid any unfair difference in the prices. Arbitrage deals with stocks, commodities, and currencies.Current price: $910Term: 4 monthsCoupon payments after 4 months: $454-month risk-free rate: 3%9-month risk-free rate: 4%Forward price (assumed to be $920)Arbitrage would borrow $910 to purchase the bond a short a forward contract. Present value of the first coupon we will calculate the discounted value at the rate of 3% for 4-months=45*e-0.03*4/12=45*e-0.03*0.333333=45*0.990049844=44.552243=$44.55Where e means the equivalent rateUsing the EXP function in excel we will calculate the value of eEXP(-0.03*0.333333)=0.990049844The balance of ($910-$44.55)=$865.45 is borrowed at 4% annually for 9months, so=865.45*e0.04*9/12=865.45*e0.04*0.75=865.45*1.030454=891.806414=$891.80Where e means the equivalent rateUsing the EXP function in excel we will calculate the value of eEXP(0.04*0.75)=1.030454534The arbitrage will make a profit of the forward price - the present value of the borrowed amountForward price (assumed) =$920, present value of borrowed amount = $891.80=$920-$891.80=$28.20And also in absence of the assumption of the forward price, the current price will be taken for the calculation of arbitrage profit. So in that case, the arbitrage profit will be:=$910-$891.80=$18.20     ...