 Before understanding the hedge positions in interest rate future contracts, it is good to understand the mechanics of pricing treasury bonds and treasury bonds forward contracts. Let discuss the pricing of a treasury bond as a hedge tool. The power value of this bond is $1,000 with annual coupon rate of 8%. So the semi-annual interest payment on this bond is equal to $40 each. The bond has maturity terms of 20 years. Now how to price this particular treasury bond? There is a tool that is the discounting. We can use the discounting of each bond's periodic payment and the payment of its face value at its terminal life at the certain discount rate. And that discount rate in our example is termed as the spot rate. This spot rate is denoted as capital R in this particular case. So we see that each spot rate or the R is expressed in semi-annual term. So each spot rate is equal to 3.92%. Now this is a one-period spot rate to discount a one-period cash inflow on the bond. Now we have 40 periods on this bond, accordingly 40 payments on this bond. So we will be using 40 spot rates to discount 40 payments in order to determine the price of the bond as of today. Now let's come to the pricing of a forward contract using this treasury bond as a forward. We see on the screen two types of cash flow, one is in purple and the other is in green. The purple cash flow is denoting the cash flows on the treasury bond. It starts from March 1 and ends on March 1 of the 40th period. So there are 40 cash flows on this treasury bonds. The other cash flows are related to the treasury bonds forward contracts and its cash flow is starting from some later period and that is September 1. Accordingly it is going some one period further that is for the first period. Now imagine a forward contract on this treasury bond. You see that on March 1, person is agreeing to buying a new 20 years 8% treasury bond in 6 months. That is the payment will be done on September 1. The payment under this forward contract or FC is on the March 1 and not is on September 1 and here that not on the March 1 at zero time period. The cash flows on the treasury bond begin exactly 6 months earlier than do cash flows on the forward contract. This means that cash flows on the treasury bonds are starting at time zero whereas cash flows on the forward contracts are starting at period one. Now let's see on the cash flows on this treasury bond. You see that cash buying of treasury bond is on March 1 and that is time zero. The first coupon payment on this treasury bond is going to happen on September 1 and that is the date one. So there would be as many as 40 payments and a payment on face value of the bond and these two payments will be on the date 40. So far as the cash flows on the forward contracts are concerned the price of the forward contract on this treasury bond is happening on September 1 and that is the date one whereas there is a receipt of a new treasury bond on the same day and that is the September 1. The first payment received from the treasury bond on March 1 of the following year and this is in fact date two. The last coupon payment occurs at date 41 on this forward contract and this will be happening along with the payment on the face value of $1,000 of the treasury bond. So with these payments how this forward contract on the treasury bond can be priced? We have a tool and that is net present value. So we can use net present value analysis in order to price this forward contract on the treasury bond. So we have a model in equation form where we are discounting each coupon payment using a certain spot rate. We see that the first cash flow occurs on the date two and that is in fact the March 1 of the following year or the year two. So this payment will be discounted by R2 or the spot rate two. The last cash flow that is the 41st cash flow which is the sum of the 40th coupon payment and the face value of the bond. It is occurring at date 41 so this amount will be discounted using the spot rate 41. The left side of the equation represents the cost of the forward contract as of date zero. So this cash flow at date zero will be discounted using this spot rate one because this is the first cash flow occur at the forward contract. Now if these spot rates are known by the investor in the market place then we can easily price this forward contract using the process of discounting and with the help of determining the net present value of all these cash flows the forward contract can be priced to a certain value. But what will happen if there is any change in the spot rates over the terms of 40 periods of semi-envolved. In case of rise in the interest rate the treasury bond will have a lesser net present value the value of the forward contract will go down conversely if there is any fall in the interest rates in the days to come then the treasury bond will have higher net present value and as a result the present value or the value of this forward contract on the treasury bond will go higher.