Fixed coupon bonds differ not only in terms of time to maturity, but also in terms of their coupon levels.

Let's now isolate the coupon effect to understand how it impacts interest rate sensitivity.

In the chart, you can see the price yield relationship of two bonds that both have the same time to maturity 10 years, but different coupon levels.

We're comparing a 10 year zero coupon bond and a 10 year bond with a 4% coupon.

Since the coupons differ, the bond prices also differ significantly.

For example, at a 0% yield level, the zero coupon bond trades at par 100%, while the 4% coupon bond trades at 140%.

Because of this difference in price levels, it is challenging to directly compare the absolute price changes.

To address this, we have calculated the percentage change in bond price for a 0.25% change in yield for both bonds as shown in the chart, as you can see, the zero coupon bond consistently experiences a larger price drop for all observed yield changes compared to the 4% coupon bond.

For example, when yields increase from 0% to 0.25%, the price of the zero coupon bond drops by around 2.5% of its current price.

While the 4% coupon bond drops by just over 2%, the conclusion is straightforward.

The higher the coupon on a bond, the lower the interest rate sensitivity.

Conversely, the lower the coupon, the higher the sensitivity.

But why is this the case? Let's start with an intuitive explanation.

As the holder of a fixed coupon bond where the coupon is not zero, you'll receive a portion of your return through regular coupon payments.

If we assume that investors reinvest these coupon payments, this reinvestment opportunity explains why a bond with a higher coupon tends to fall less in price when yields rise than an otherwise identical bond with a lower coupon.

In both cases, the investor misses out on higher yields for the amount already invested, but in the case of a high coupon bond, a significant portion of the investment is returned earlier, allowing it to be reinvested at higher rates.

This helps soften the impact of rising yields.

In contrast, if you hold a zero coupon bond, there are no interim cash flows for you to reinvest, so you cannot benefit from increasing reinvestment rates.

This example highlights that reinvestment risk should not always be viewed as negative.

It introduces uncertainty, but as we've seen, it can also have advantages.

Now, let's take a more numerical approach to understanding the link between coupon and sensitivity.

One way to interpret a 10 year 4% coupon bond is to think of it as a basket of zero coupon bonds.

If the coupon payments are annual, this basket consists of a one year zero coupon bond with a notional of 4%, a two year zero coupon bond with a notional of 4% and so on up to a 10 year zero coupon bond with a notional of 104%.

The interest rate sensitivity of this basket of bonds reflects the sensitivity of its components.

This brings us back to our earlier observation.

The longer the time to maturity of a bond, the higher the sensitivity.

Taking this one step further, the higher the coupon of a bond, the greater the portion of the bond's payments that are received earlier.

This means that more of the bond behaves like a shorter duration bond, which leads to lower overall sensitivity.