Dollar duration & bond price prediction

1. Dollar duration & bond price prediction

We are now going to look at dollar duration and bond price prediction.

2. Dollar duration

Duration tells us the percentage change in a bond's price for a one percent change in yields. Dollar duration tells us the dollar change in a bond's price for a one percent change in yields, i.e. the amount of money we make or lose on a single bond if interest rates move by one percent. It is calculated by multiplying the duration by the bond price and then by zero-point-zero-one to convert the duration from a percentage to a decimal.

3. DV01

DV01 is the most common way of measuring interest rate risk. It is the dollar change in a bond's price for a zero-point-zero-one percent change in yields. In the finance world, zero-point-zero-one percent (or one percent of one percent) is referred to as "one basis point", and DV01 is short for "the dollar value of one basis point." DV01 is the same as dollar duration, except we multiply by one basis point instead of one percent.

4. Dollar duration example

Take a bond with a price of ninety two dollars and twenty eight cents and a duration of seven-point-nine-eight percent. We calculate its dollar duration by multiplying the bond price by its duration and then by one percent. To find the DV01 of the bond, we repeat the same process, but multiplying by one basis point instead of one percent.

5. Creating a duration neutral portfolio

Often in the real world, we want to eliminate the interest rate exposure of a portfolio, called "hedging." To do this, we calculate the DV01 of our portfolio, then take an instrument we will hedge our portfolio with, such as a bond, and calculate the DV01 of this bond. Finally, we find the quantity of the bond such that it has an equal DV01 to our portfolio. By selling that amount of the bond, we hedge the interest rate exposure of our portfolio as the losses on our portfolio will be offset by the gains on our bond position and vice versa.

6. Hedging DV01 example

Say your portfolio has a DV01 of ten thousand dollars. You can hedge this interest rate exposure by selling ten thousand dollars worth of DV01 of a bond. Take our bond from earlier with a DV01 of just over seven cents. By dividing the DV01 of our portfolio by the DV01 of the bond, we see that we need around one hundred and thirty six thousand units of the bond to hedge our portfolio.

7. Hedging DV01 example

Multiplying the quantity of bonds by their price, we see this costs around twelve and a half million dollars.

8. Bond price prediction

Another use of dollar duration is in predicting bond price changes for moves in interest rates. We estimate the price change of a bond by multiplying the dollar duration by minus one hundred (since prices decrease when yields increase) and by the size of the move in yields. This can be used to estimate how a bond's price or the value of a portfolio will change for a move in interest rates.

9. Price prediction example

Take a ten year bond with a four percent coupon, five percent yield, price of ninety two dollars and twenty eight cents, and a dollar duration of seven dollars and thirty six cents. If interest rates drop by three percent, our estimate for the price change is minus one hundred times the dollar duration times the change in yields, giving an estimate of twenty two dollars. By repricing the bond properly, we see the actual change was just under twenty six dollars.

10. Let's practice!

Now let's practice applying the concept of dollar duration.

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