In this workout, we're looking at using derivatives to manage interest rate risk within a portfolio. The portfolio we're looking at is for a fixed income portfolio manager who expects interest rates to rise and therefore wishes to protect their portfolio against interest rate Rises, but does not want to remove exposure in case they get it wrong and interest rates for So we're looking to reduce our exposure to interest rates rising and therefore and erosion in the value of the portfolio, but not taking away that exposure entirely.

A portfolio that we're looking at has a market value of 200 million dollars and they current portfolio modified duration of 7.1. The portfolio manager wishes to reduce that duration down to 3.5 to reduce their exposure to interest rate movements.

The US treasury bond Futures Contract that we have available as a price at the moment of 127.2 dollars per hundred dollars of par value. Or in other words that's can be viewed as 127.2% of the par value. The bond future has a duration of 9.5 and each one Futures Contract has a par value of a hundred thousand dollars. So we're asked to reduce the duration of the portfolio and to do that. We're going to need to sell our futures contracts or have a short position in those contracts.

the number of contracts that we're going to need to trade we're going to first of all need to take our Target duration of 3.5 subtract from that the existing portfolio duration So this is the amount of duration that we want to change and we divide this by the duration of the Futures contracts that we're going to be using to make that adjustment. We then need to multiply this by the market value of our portfolio.

Now that is going to be in millions of dollars. So I need to multiply this by. 1 million to get it to be an absolute value and then divide this by. the value of one Futures Contract Which is going to be the price in percentage terms are the 127.2. So what I divide that by a hundred turn it into percentage terms and then multiply that by the size of one contract.

This will give us negative 59.6.

We can only trade whole contracts. So as a result, we're going to need to sell. A rounded version of this so we might use a round function.

To change this from 59.6. So 0 decimal places to be 60. So the negative sign here indicates that we need to be selling or have a short position in these 60 contracts.