Let's have a look at interest rate sensitivity of floating rate notes.

To begin with, let's think about the question on screen.

Which of the bonds shown here would you expect to have the lowest interest rate sensitivity? The choices are A, a five year zero coupon bond, B, a 10 year bond with a four and a half percent coupon paid semi-annually, and C, a 30 year floating rate note, FRN linked to sofa.

If we had only shown you the first two options, the five year zero coupon bond and the 10 year four and a half percent coupon bond, you may have said the five year bond has lower interest rate sensitivity.

That's because although bond A is a zero coupon bond, which tends to have a higher duration, bond B has twice the maturity, and your intuition might tell you that this longer maturity outweighs the effect of receiving coupon payments.

However, including a 30 year bond into the mix makes the decision become more complex.

Based on the maturity argument alone, you might expect bond C to have even higher duration than the first two.

After all, it's a 30 year bond compared to a 10 year and a five year bond.

But wait, it's also a floating rate note.

So what actually drives the duration of an FRN? To answer the question about interest rate sensitivity of floating rate notes, let's first remind ourselves of their main characteristics.

RNs are bonds where it's not the coupon that is fixed at issuance, but rather the coupon formula. This means the coupons that investors receive are linked to future movements in the underlying reference rate.

For example, SOFA or your IBOR, how often the coupon is reset depends on the term of the reference rate.

For example, if the reference rate is a three month IBOR, the coupon will be reset every three months.

If the reference rate is an overnight rate like sofa, the coupon will be reset daily.

For simplicity. Let's set aside credit spreads and margins for now.

Let's think of a two year FRN that pays a coupon based on three month year IBOR with no additional spread.

This two year FRN is economically equivalent to a sequence of eight fictitious short term fixed coupon at issuance.

The FRN is effectively a three month fixed coupon bond because the coupon is set to the current three month EURIBOR rate, meaning it's issued at par.

If this were a sequence of short term fixed coupon bonds, after three months, the investor would receive par plus the coupon payment.

Then a new fictitious three month bond could be issued based on the updated your EURIBOR rate.

Since this rate is again the prevailing market rate, the bond is again issued at par with the coupon.

Now reflecting the new your EURIBOR level, this process repeats every three months for the duration of the imaginary scenario.

Because of the frequent resetting of the coupon, the interest rate sensitivity, or duration of a floating rate note is usually very low, as it only extends to the next reset date.

So the duration of an FRN is typically equal to the time until the next coupon reset rather than the entire term to maturity.

Let's visualize this concept using the example on screen.

When the bond is issued the first three month, EURIBOR is fixed at 3%.

This is the coupon for the first three month fixed coupon bond.

Since the coupon equals the yield of this bond, it is issued at par.

Three months later, the investor receives par back plus interest for the period, which, if we ignore day count conventions, is simply 0.75% a quarter of 3%.

In this imaginary scenario.

At that three month point, not only is the first three month bond repaid, but a new three month bond is issued.

By now, your EURIBOR has increased to 3.5%, so the new bonds coupon is set at 3.5%, which equals the yield.

As a result, the bond is gain issued at par and repaid three months later at par, plus the interest.

Now, let's generalize this.

Every three month bond in this imaginary sequence is issued with the prevailing market coupon.

So each bond will be issued at par and repaid at par plus coupon.

The proceeds can then be used to buy the next three month bond and so on.

The key takeaway is this, the maximum duration the investor faces on a two year bond linked to three month EURIBOR is indeed just three months.

If we apply this to a 30 year floating rate note linked to sofa, we see that even though the time to maturity is 30 years, the interest rate sensitivity is very low.

This is because the coupons will always be fixed for only one day at a time, as sofa is a daily rate.

So in theory, regular floating rate notes should always trade relatively close to par because they have minimal interest rate sensitivity.

However, changes in the issuer's credit risk can lead to significant deviations from par.