when we're managing Bond portfolios looking at modify duration that tells us the approximate change in the price for a 1% to change in yields might not be granular enough because yields don't often change by a whole percent very often in a short time period so we might want to look at a more granular implication of interest rates changing and that's what this measure the dv01 tells us.

The dvr1 tells us the change in the value of the portfolio for a one basis point change in interest rates dvo. 1 stands for the dollar value of a one basis point change in interest rates.

And we can interpret it as the dollar value change of a portfolio.

If there is a change of one basis point in interest rates.

a hundred basis points equates to 1% So the dvl1 is much more granular than the modified duration calculation.

However, since modified duration assumes that the relationship between interest rates and prices is linear.

To scale down from modify duration down to a one basis point change in interest rates is relatively straightforward.

All we need to do to get to our dvo one. We take the price of the bond.

Expressed as the price per $1 of par value. We then multiply that by the modified duration and multiply that also by the future value of the portfolio which in other words means the par value of the bonds that we hold.

This will give us just the numerator of this formula will give us the approximate change in the bond portfolio for a one percent change in yields.

Well, if we divide this all by a hundred we'll get the approximate change in the value of the portfolio for a one basis point to change in units.

Dvo one takes into account both the sensitivity of a Bond's price to change an interest rates through the modified duration and also the size of the position that we hold through that future value or par value of those bonds.

Let's have a look at an example of how we calculate devi01.

In this example, we've got a bond with five years to maturity. We've got an annual coupon of 2% and a yield to maturity of 0.35% taking this Bond. We can calculate the modified duration as 4.8 which we can interpret as a 4.8% change in the price of a bond for 1% change in yields.

We can also calculate the bonds current price of 108.36% Now, this is the percent value or we can interpret this as the price effectively per $100 of par values. So 108.16 as the price of $100 of par value on this Bond.

This is though expressed as a percentage. So it's a hundred and eight percent of the par value 108.16% of the Parvin.

Okay, so if we assume that we've got a portfolio of a hundred million dollars of par value or future value. We would then be able to calculate the dvo one by taking the price in percentage terms 108.16% of the par value.

Multiply this by the modified duration and percentage terms.

And then also multiply it by the size of the portfolio in terms of our nominal value.

That all together will give us the approximate change in the portfolio value for a 1% change in yields. If we divide this all by a hundred we will then get the dvo one the change in the value of the portfolio for a one basis point to change in yields, which comes out here to be 51,000. 914.25.

So if there's a one basis point to change in yields, this will be the change in the value of this hundred million dollar nominal value portfolio of the 51,914.25.