If a fixed income portfolio manager wishes to change the duration of the portfolio, they can do that using Bond Futures as an alternative to buying and selling bonds within their portfolio. So our bond Futures can be used to manage interest rate risk within a bond portfolio. as with any derivatives if the value of the underlying asset increases a long position is going to benefit from that for our bond Futures. The underlying asset is a bond. So a long Bond Futures position, we'll make a gain if interest rates fall because bond prices will go up and we have a long Bond Futures position. If we have a short Bond Futures position, we will get a gain if interest rates rise because of interest rates go up on prices will come down. In terms of how many contracts we need to trade. It is first worth being aware that you can only trade whole contracts. So the outcome of this formula needs to be rounded to the nearest whole number. The formula says that we need to take our Target duration what we hope to achieve as to the duration of the portfolio of bonds. Plus this Bond Futures addition to the portfolio sometimes referred to as a derivative overlay. So we take our Target duration and subtract from that what we have at the moment within our portfolio.

as our portfolio duration This will give us the amount that we want to change the duration by. We then need to divide this by the duration of a Futures Contract features contracts are made up for bonds and the value of the bond Futures Contract will change as interest rates changed so we can calculate the duration of the Futures Contract which says as interest rates change. How much does the value of the Futures Contract change? So that's the value of one Futures contracts duration. But we then need to scale this calculation to the relative sizes of the Futures Contract and the bond portfolio. So we need to take that and multiply it by the market value of the portfolio. It's not the par value. We're looking at the market value and we need to divide this by the value of one Futures Contract the typical size for a bond features contract is to have a par value of a hundred thousand dollars to calculate the value of one Futures Contract. We need to take the Futures price quoted price at the features contract expressed as the price per one dollar of nominal value and multiply that by the hundred thousand dollar size of a typical bond Futures Contract. This will give us the market value of one Bond Futures Contract. In terms of the direction of trade if the target duration is bigger than the portfolio duration. We are looking to increase duration, which means we need to have a long position. So if we get a positive outcome to this formula, that means we need to buy bonds or have a long position in those Bond Futures contracts. If we want to reduce our duration. Our Target duration will be less than our current portfolio duration. And therefore that will give us a negative outcome to this formula telling us that we need to enter into a short position in these features contracts all we need to sell those features contracts.