In this workout, we are told that a trader has sold 50 million US dollars notional of a nine year US Treasury Note.

The DV01 of this position is 36977.5 US dollars.

The trader is looking to hedge the interest rate risk by buying the current 10 year benchmark bond, which has exactly 10 years to maturity, pays a coupon of 4% and trades at a price of 97.68%.

The question we need to answer is, how much notional does the trader have to transact to achieve DV01 neutrality? There are no other positions below we have the settlement date as today's date, the maturity date, 10 years after that, the coupon of 4% and the price of 97.68%.

To calculate the DV01, we need modified duration.

And to calculate modified duration, we need the yield to maturity.

So let's start by calculating that.

We can use the yield function to do this.

Following the prompts at the top of the screen, we need to start by inputting the settlement date that is then followed by the maturity date.

Next, we have the coupon rate, followed by the bond's price.

I'm going to multiply that by 100 to get it from a percentage into dollar terms.

Next, we need to put the redemption value, which is 100.

Next, we need to put in the frequency of the coupon payments, which is semi-annual for US government bonds.

So that's two. And finally, the day count convention, which is actual, actual, so one that gives us a yield to maturity of 4.29%.

We can now use this to calculate modified duration for this bond.

To calculate modified duration, we take the macauley duration divided by one plus the yield.

In this case, we haven't calculated the macauley duration.

We could do that, but instead we could use the modified duration function, which is M duration.

Following the guidance, we start with the settlement date followed by the maturity date.

Then we need to put the coupon, the yield, which is what we just calculated, frequency, which we said is two, and day Count convention, which is one, and that gives us a modified duration of 8.1.

This brings us to the DV01 calculation.

One of the inputs we need is the notional value.

However, that is what we are trying to solve.

So we are going to leave the notional value in C 17 blank for now, and then use goal seek to solve for it.

To calculate DV01, we take the negative of the modified duration.

Remember, that's because of the inverse relationship between bond prices and yields.

We multiply that by one basis point.

We then multiply by the price of a bond, and finally we multiply by the total notional, which for now we have as blank.

So as expected, when we press enter, we are going to get an answer of zero.

Now we can use the goal seek function to solve for the notional value.

Goal seek is under the data ribbon.

So if you're using your keyboard shortcuts, that's alt A under what if analysis W and goal seek is G.

We need to start by saying which sell value do we want to set to a certain value? And we want to set the DV01.

So sell C 15 to be negative 3 6 9 7 7 0.5 to offset the existing DV01 one in the portfolio.

What value do we wanna change in order to make this happen? And we want to change our notional amount, so C 17.

And when we press enter, we can see that the total notional we need is $46,500,396.30.

And that would mean that on our portfolio, the DV01 is the existing 3 6 9 7 7 0.5 on the short position that the trader has plus the DV01 on the long position the trade is gonna take, and that gives us zero DV01.

So a fully hedged portfolio.