In this workout, we are going to calculate the Macauley duration, the modified duration, and the DV01 of a 50 million notional long position in a 10 year bond with an annual coupon of 3% at a yield to maturity level of 4.28%.

So we have the settlement date as today's date.

The maturity date is exactly 10 years after that, the coupon of 3%, the yield to maturity of 4.28% and the position size of 50 million.

Let's start by calculating the McCauley duration.

Remember that McCauley duration is the time taken on average for a bond holder to receive all the cash flows of the bond.

The long way of calculating it is to calculate the present value of each cash flow, multiply it by the number of years until that cash flow is received.

Then add these all up and divide by the bond price.

The good news is that there's a function in Excel that essentially does this for us, and that is the duration function.

So let's use that. The duration function starts with asking for the settlement date, so that's the first term we need to go pick up settlement date.

Next, we need to put in the maturity, which we've got being 10 years later.

After that, we need to put the coupon in.

Then we need the yield, which we've got 4.28%.

Then we need to put in the frequency, and we can see on the right that we've got one for annual, two for semi-annual, four for quarterly, et cetera.

And we are told that this is an annual bond, so we are gonna put one, and then we have gotta put the day count convention.

In this case, we're going to assume actual, actual.

So we are going to put the number one as indicated close bracket, and we get a duration of 8.7 for this bond.

That means that on average, a bond holder has to wait 8.7 years to receive all the cash flows of the bond.

The higher this number, the more sensitive the bond's price is to a change in interest rates.

Now let's calculate the modified duration.

Modified duration is simply the McCauley duration divided by one plus the yield, and that gives us 8.35.

Our answer of 8.35 means that for every 1% change in the yield to maturity, the bond's price will change by 8.35% of its current price.

Remember that when we use this number, we are going to make it a negative given the inverse relationship between the yield and the price of a bond.

Finally, we need to calculate the DV01, which is going to tell us the actual profit and loss impact of a one basis point change in yield.

One of the inputs into the DV01 is the bond's price, so let's calculate that first.

Using the price function in Excel, as the bond has exactly 10 years to maturity, we can assume the clean price equals the dirty price.

So using the price function, if we follow the prompts at the top of the screen, we can see the first thing that we need to input is the settlement date.

That is then followed by the maturity date.

Then we need the rate, which is the coupon that is then followed by the yield.

After that, we need the redemption value of a bond, and we put that in as 100.

We've then gotta indicate the frequency of the coupon payments, which is annual.

So we put the number one, and then finally the day count convention, and we are using actual, actual, which is one, I'm gonna divide the answer by 100 so that we get the price in percentage form.

Now we can calculate the DV01 by taking the negative of the modified duration because remember, there's an inverse relationship between yields and prices.

We're gonna multiply that by one basis point, which is 0.01%.

We then multiply by the price of the bond, and then finally we multiply by the total notional, and that gives us a DV01 of negative 37464.2.

This means that if yields were to increase by 0.01%, a long position of $50 million, face value would lose approximately $37,464 in market value.

So this is your P and L impact.