**Understanding Arsenal’s Floating Rate Note**

*Gerald*: All I want to do is get you in a straight bloody line! What do I have to do?

*Horse*: Well it’s the Arsenal offside trap isn’t it?

*Gerald*: You what?

*Horse*: The Arsenal offside trap! Lomper here is Tony Adams, right? Any bugger looks like scoring we all step forward in a line and waive our arms around like a fairy!

**The ‘Full Monty” (1997)**

Let’s start with a thought exercise. Suppose that you had to choose between two bonds with similar maturities, issued by the same entity (Arsenal Football Club in this case). Bond 1 is trading at a price of 84.50 while bond 2 is trading at a price of 113.50. Which one would you pick?

Perhaps an initial reaction might be that bond 1 is undervalued relative to bond 2? So, you may decide that some form of ‘relative value’ trade is appropriate i.e. go long bond 1 and short bond 2 on the basis that the two bond prices may eventually converge to some notion of ‘fair value’.

There is one crucial fact that I have omitted; bond 1 is a floating rate note (FRN) and bond 2 is a ‘vanilla’ fixed rate bond. This is a question that is posed as part of the ICMA’s level III ‘securitisation’ course and it is instructive to see how many people struggle to understand why the prices of the bonds are so different. Although all the participants are comfortable with the principles of fixed coupon bond valuation, their answers to the question do suggest a more general misunderstanding of FRN valuation conventions.

For a traditional fixed coupon bond, standard net present value (NPV) techniques can be used to determine the ‘fair value’ of the instrument. A common approach would be to present value all the cash flows using an appropriate yield to maturity. Although there is no single consensus, it would be reasonable to say that such a yield could be broken down into a variety of components:

- A risk-free element,
- A spread that reflects the credit risk for a given credit rating,
- An additional spread that reflects the specific credit risk of the bond being analysed,
- Perhaps some adjustment that might reflect the relative illiquidity of the bond.

So, in theory the value of a fixed rate bond could move because of a change in any one of these factors.

Now consider the FRN. The Arsenal example paid an investor 3-month GBP LIBOR plus a spread of 55 basis points (0.55%), which would have been reflective of the borrower’s credit risk relative to the interbank sector at the time of issue. This spread is referred to as the ‘quoted margin’. One way of understanding an FRN is to think of it as a rolling 3-month bank deposit that pays a floating rate plus a spread.

Having described the main feature of an FRN let us consider how the cash flows could be valued using conventional NPV techniques. The first step to be addressed is how to assign a value to all the unknown future LIBOR cash flows beyond the current period. The fact that the market approaches this in different ways is perhaps one of the reasons why there is so much confusion surrounding FRNs. Some of the popular techniques used will:

- ignore all future LIBOR values. This is because on the first day of each future coupon period the floating rate will set at the prevailing market price and so the FRN will trade at par.
- assume that the current LIBOR value will remain unchanged for the life of the transaction.
- use a set of observable 3-month forward LIBORs, since they are breakevens (they are NOT ‘the market’s best guess of where LIBOR is going to trade in the future’!).
- use the prevailing interest rate swap rate of a maturity equal to that of the FRN under analysis.

The second step is to consider how the cashflows should be discounted. Like fixed coupon bonds FRNs will also trade on a ‘yield basis’ and again this can be decomposed into two main elements:

- Financial theory tells us that cash flows should be discounted using an interest rate of the same degree of credit risk as the instrument under analysis. Since the FRN is paying an interbank rate then a LIBOR-related value would be appropriate. This would suggest that the trader could use either a short-term LIBOR value or an interest rate swap rate.
- However, like the conventional fixed coupon bond it is important to reflect how the specific credit risk of the issuer has evolved over time. In FRN speak this component is referred to as the ‘discount margin’. Indeed, the discount margin for the Arsenal FRN in question had increased to 195 basis points (1.95%) because of a credit downgrade. It was this deterioration in the credit risk that resulted in the deeply discounted price of 84.50.

So, what are the key points?

Floating rate notes are relatively insensitive to changes in the general level of interest rates. Based on our two examples, the dollar value of a one basis point change in yield (DV01) per 1 million nominal value was GBP 391 for the fixed coupon bond while for the FRN it was the princely sum of GBP 2. Recall that one of the approaches to valuation was to ignore all future LIBOR values as on a repricing date the investor receives the current value of LIBOR and so from a market risk perspective they are ‘on market’. As a result, the bond should trade at par, all other things being equal i.e. assuming no change in the credit risk. Over the course of the coupon period the investor’s coupon will inevitably deviate from the prevailing LIBOR level but since the period is relatively short, the impact on the bond’s value is very small.

FRNs are essentially credit instruments. If the perception of the issuer’s willingness or ability to pay deteriorates then this is reflected in an increase in the discount margin, which, all other things being equal will have a bigger impact on price than an equivalent move in interest rates.