**LIBOR and Derivatives – how close are they?**

**By Jasvin Josen**

*This article appeared in The Edge on Dec 3, 2012*

We are quite familiar with the recent LIBOR (London
Interbank Offered Rate) scandal in the financial markets. The obvious effect of
the manipulation of the LIBOR is to mortgage loans and corporate loans. However,
there was a bigger concern that LIBOR was integrated into approximately USD350
trillion worth of derivative contracts globally.

LIBOR affects derivatives in more that one way.
Firstly, interest rate derivatives use LIBOR to determine their payoffs at
certain dates. Secondly, all derivative positions are priced using LIBOR, where
LIBOR is used as the discounting rate.

**Interest rate Derivatives**

Interest rate derivatives have payoffs depending on
interest rate levels. For example if an investor buys the CME Eurodollar
Future, his profit from this derivative will depend on what level the 3-month USD
LIBOR is.

Other common interest rate derivatives are interest
rate forwards (also known as forward rate agreements or FRAs), interest rate
swaps, interest rate options and structured rate products. In this 2-part
article series, I demonstrate how LIBOR can affect interest rate swaps,
interest rate options and structured rate products.

**(i) Interest rate swaps**

Let us say that
Company BIG issued a $100m 5% fixed coupon bond to its investors when interest
rates in the market were generally high. After a few years, the general
interest rates have dropped. To benefit from the lower interest rates, BIG enters
into an interest rate swap with its investment bank with the following terms:

Fixed rate payer: Investment
Bank

Fixed rate: 5 percent p.a.

Fixed rate: 5 percent p.a.

Floating rate payer: Company
BIG

Floating rate: 6-month
Libor, paid semi-annually

Notional amount: $
100 million

Maturity: 5
years

The swap is shown in
Chart 1

**Chart 1: Interest rate swap**

The investment bank
agrees to pay 5.0% of $100 million on an annual basis for the next five years.
So, it will pay 5% of $100 million, or $5 million, once a year.

Company BIG agrees to
pay the 6-month Libor on $100 million on a semi annual basis to the Investment
Bank for the next five years. That is, the bank will pay the 6-month Libor
rate, divided by two and multiplied by the notional amount, two times per year.
For example, if the 6-month Libor is 4.2% on a reset date, BIG will be
obligated to pay 4.2%/2 = 2.4% of the notional amount, or $2,400,000. (To keep
it simple, day count conventions are excluded).

The idea is that BIG gets
the fixed rate of 5% from the bank and passes it on to its bondholders
annually. Then at every 6-month intervals BIG will make floating interest
payments to the bank. In this way, on a net basis, BIG is paying floating interest
payment on this $100m bond liability and gets to take advantage of the falling
interest rates in future.

The reader may now
wonder about the investment bank. Surely it will make losses as interest rates
come down in the market. Well, the bank works it out like this. At the initial
of the swap, the banker looks at the forward interest rate curve, to estimate
the future 6-month LIBOR it could receive from BIG. Now, there are many ways in
which the bank can structure the swap.

In the first scenario,
let us say that BIG is determined to receive a rate of exactly 5% payment from
the swap every year. The bank will analyse the future cash flows where it makes
a 5% fixed payment and receives floating interest payments in the five
years. In a low interest rate forward
environment, the net cash flows could very well prove negative for the bank.
The bank will have to charge an upfront fee to BIG, as compensation for taking
on the interest rate risk.

In the second
scenario, let us say that BIG is not too keen in paying any upfront fees. The
bank analyses its future cash flows again but this time, plays around with the
fixed rate until the present value of the net cash flows is almost zero. In a
low interest rate forward environment, the fixed rate is likely to be lower
than the original 5%. Under this arrangement, BIG will probably only receive,
perhaps a fixed rate of 4% and can only partially benefit from the low interest
rates in future.

__So how does LIBOR affect this swap?__

Well, at an obvious level, every six months re-set
dates, both parties will look at the LIBOR rate that morning to determine the
rate that BIG will pay the investment bank for a six- month period. Readers may
recall the Barclays case, where the corporate deals side of the bank allegedly
asked their money market traders to set the LIBOR rate at a certain date to be not
higher (or lower) than a certain rate, for its own benefit. Applying this case
to our example, let us assume that BIG’s investment bank also contributes to
the setting of LIBOR every morning. BIG’s investment bank, being a floating
rate receiver in the swap deal, could be tempted to submit a higher LIBOR rate,
hoping that a higher LIBOR setting that morning will result in the bank receiving
a higher floating rate payment from BIG. Every basis point matters – for this
deal, one basis point will results in an additional $10,000 (0.01% *
$100million). And the bank has thousand of such deals every day.

At a less obvious level, is the pricing of the swap in
both counterparties’ books. The bank and BIG will have to record the fair value
of the swap in their books. The fair value of the swap is simply the present
value of the total cash flows (or payoffs) in the future. For example, let us
say that BIG is into the 2

^{nd}year of the swap. The fair value of the swap will the be the future fixed $5 million received from the bank at end of Year 2,3,4, and 5, netted with the future semi-annual floating payments to be paid out to the bank in Year 2 to 5. To obtain the present value of these payments, they have to be discounted by a risk-free interest rate. Market players globally have been comfortable with using the LIBOR rate as the discount rate.
If LIBOR is artificially higher than it really should
be, BIG may have valued its net cash flows lower than it should and could be
showing a lower asset or liability in its books.

**Conclusion**

There are millions of interest rate swaps globally,
with counterparties wanting to hedge against interest rates such as industries,
financial institutions, pension funds, mutual funds, insurance companies, etc. Other
than the plain vanilla interest rate swap in the above example, many other
popular variations of the interest rate swap like collars, caps, floors, range
accruals, etc will be affected by LIBOR in the same way.

In the next article, I will illustrate how LIBOR
affects the payoffs and pricing of an options and structured rate products.

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