1. Duration
We now discuss bond duration.
2. What is duration?
Duration is the estimated price change for a 100 basis point change in yield. So the prices of two bonds with the same duration are expected to move in the same way.
Why is this useful? For example, suppose you issued a bond with a duration of 10. We know bonds are liabilities. So if yields go down, the bond's value increases and the value of your liability also increases.
To protect yourself from the increasing liability, you can make sure your assets also have a duration of 10. This way, the value of that asset increases by the same amount as your liability when yields go down.
This practice is called 'Duration Gap' management.
3. Calculating duration
So how do we calculate duration?
The full duration calculation is quite complicated and beyond the scope of this course. If you're curious, I recommend looking at the Fixed Income chapter of my book to see how to implement this calculation.
For now, we can use an alternative formula often used in practice called "Approximate Duration".
In this formula, the numerator is the bond price when the yield goes down minus its price when the yield goes up. The denominator is twice the current price multiplied by the change in yield.
4. Estimating price change
Duration allow us to estimate the change in the bond's price given a change in yield. In particular, we can now calculate both the percentage change and dollar change in price.
The Percentage Change formula has a negative sign in front to reflect the inverse relationship between yield and price. Then you multiply that by the Duration and the change in yield.
Similarly, the Dollar Change is simply the Estimated Percentage Change multiplied by the bond's current price.
5. How do you use these formulas?
To use the duration formula, consider a bond with a par value of $100, 5% coupon, 10 years to maturity, and an initial yield of 4%. The price of the bond is the first input needed. Additionally, we need the bond price when the yields go up with 1 percent, and the bond price when yields go down with 1 percent as inputs.
6. How do you use these formulas?
The duration formula gives us that if yields increase 1%, the duration equals 7.89
Using the Percentage Change formula, we find that a 1% INCREASE in yield would lead to a 7.89% DECREASE in price.
The Dollar Change is then equal to the percentage change of NEGATIVE 7.89% multiplied by the current price of the bond of $108.11. This results in a price decrease of $8.53.
7. Duration in a chart
This chart shows how duration operates. The black line on the chart is the price of the bond at different yield levels. This bond has a 10% coupon with 20 years to maturity. The red line is the estimated price based on duration, which we calculate using the current yield of 10% and the current price of $100. The green dot.
As we can see, duration is a good estimate of the price when the yield change is small. But, the larger the yield change, the worse the estimate using duration is going to be.
Fortunately, we can augment this estimate to make it better. We do this by adding the Convexity Measure, which we will do in the next video.
8. Let's practice!
For now, let's practice what you learned about duration.