While we commonly refer to interest rate sensitivity as duration, there are actually several different measures used by market participants.
However, before exploring the various ratios you may encounter in practice, let's first develop an intuitive understanding of the key drivers behind interest rate sensitivity.
In the chart in front of you, you can see the price yield relationship for two zero coupon bonds, one with a time to maturity of two years and the other with a time to maturity of 10 years.
The reason we are using zero coupon bonds here is that we are looking to isolate the effect of time to maturity at a yield level of 0%, which was a real yield environment in many parts of the world. During the 2010s, both bonds would trade at a price of 100% par.
This is intuitive because when the coupon of a bond equals its yield, the bond should trade at par.
As yields rise, the price of both bonds falls.
However, the key observation here is that the prices of these two bonds fall at different rates.
The 10 year bonds price declines much more sharply than that of the two year bond.
Why does this happen? Zero coupon bonds essentially represent a single cash flow in the future.
The two year zero coupon bond represents a cashflow of 100% in two years.
While the 10 year zero coupon bond represents a cashflow of 100% in 10 years, the price of each bond is just the present value PV of these future cash flows, which means the price of the two year bond is calculated as 100% divided by one plus the two year yield raised to the power of two, and the price of the 10 year bond is calculated as 100% divided by one plus the 10 year yield raised to the power of 10.
So when yields for the bonds change by the same amount, the effect on the two year bond is to the power of two, whereas the effect on the 10 year bond is to the power of 10.
Naturally, this leads to a much larger impact on the 10 year bond.
The bottom line is the longer the bonds time to maturity, the higher its sensitivity to interest rate changes.
In other words, the longer the maturity, the more rapidly the bonds price will decline with an increase in yields, and conversely, the more rapidly it'll rise, with a decrease in yields.
