In this workout, we are looking to enter into a 10s30s US treasuries flattener with a spread DV01 of $50,000 using the bonds below. The information we have for the 10 year and 30 year bonds is the time to maturity, the coupon rates, and the bond prices. And in this case, we are assuming the clean price is the same as the dirty price. The first thing we are asked to do is to calculate the entry level of the flattener. The assumed settlement date, I'm going to use today's date, so equals today.

And it doesn't matter if the date you're using is different because what matters is that the maturity date is going to be 10 years from the assumed settlement date and then 30 years for the 30 year bond. To work out the assumed maturity date, we'll use the edate function and we need to put in the start date, which is the settlement date. I'm just going to lock onto that so I can copy this formula to the right. And then we need the number of months. So for the 10 year bond, that will be the 10 years times 12, and if we copy that to the right for the 30 year bond, we get a maturity date. That's 30 years after today's settlement date. Next, we need to work out the yield on the two bonds. And to do that, we are going to use the yield function We need the settlement date, and I'm going to lock onto that so I can copy to the right for the 30 year bond. Then we need the maturity date. After that, we need the coupon rate followed by the bonds price, so I'm just going to multiply that by 100. Then we've got the redemption amount, which is 100, followed by the frequency, which is semi-annual as these are US treasuries. And then the day count convention, which is actual actual. And that gives us a yield of 4.6044% for the 10 year bond. And if we copy that to the right 4.7232% for the 30 year. We can now work out the entry level of the flattener, and that is the difference in yield between the two bonds, which is 0.1189%, or in basis points we multiply by 10,000 to give us 11.89 basis points.

The next part of this workout asks us to calculate the notional amounts required to enter the position. We are also asked whether we are buying or selling the respective bonds, and we can assume that the bond notional can be traded in any amount. We were told at the start of the workout that the spread DV01 is $50,000.

Now we need to think about whether we need to be long or short. The 10 year and 30 year bonds.

Remember that a flattener benefits from an expected decrease in the yield differential between the two maturities. This decrease in differential could happen in various ways. For example, the 10 year yield could rise while the 30 year yield stays flat or falls, or the 30 year yield could fall while the 10 year yield stays flat or rises. Thinking about what happens to bond prices. Under these scenarios, we want to be short the tenure as prices fall when yields rise, and long the 30 year as prices rise when yields fall.

Now onto working out the required notional. To do that, we need to start by calculating the modified duration of both bonds. We are going to use the M duration function and start by inputting the settlement date, which we have in row 13. I'm going to lock onto that so I can copy my formula to the right, followed by the maturity date.

Then the coupon, the yield, which we just calculated, the frequency, which we said is semi-annual, and the basis, which is actual actual. That gives us a modified duration of 8.1 for the 10 year And 16.31 for the 30 year. Now we need the modified duration to help us calculate the DV01 per million notional. Before we do that, let's just remind ourselves of what modified duration means and what DV01 is. Modified duration indicates the percentage change in a bonds price for a 100 basis points change in yield and DV01 tells us the dollar profit and loss impact of a one basis point change in yield.

What we want here is the DV01 per million dollar notional.

There are different ways at arriving at the answer, but I'm going to work out the change in the bonds price for a 100 basis point change in yield. So that's going to be 8.1% times the bonds price, but then I want that for a one basis point change in yield because we are looking at the DV01, so I'm going to divide by 100, and then I wanted per million notional, so I'm going to multiply by 1 million.

And that gives us 771.36. If we copy this to the right for the 30 year bond, we get 1,507.89. Finally, we need to work out the required notional to achieve a $50,000 P&L impact for a one basis point change in yield. So I'm going to take the $50,000, I'm going to lock onto that because I wanna copy to the right, divide that by the 771.36, we just calculated and multiply by a million. And that gives us $64,820,611 worth of 10 year notional.

And for the 30 year, that's $33,158,993. It stands to reason that we require less of the 30 year bond because it has a higher duration, meaning that the price of the bond will change more for a change in yield compared to the 10 year bond.