[FM] LIBOR & Interest Rate Swap

From fm exam sample #186

On a given day, the discount rate is 3.65%, the prime rate is 3.55%, the LIBOR is 3.30%, the federal funds rate is 3.25%, and the federal funds target rate is 3.20%

On the same day, Bank XYZ's reserve balance held at the Federal Reserve is lower than the reserve requirement, and Bank XYZ needs to borrow funds from those member institutions of the Federal Reserve who have excess funds in their reserve. Let x be the rate at which Bank XYZ borrows from these excess funds.

Determine x.

(A) 3.20%

(B) 3.25%

(C) 3.30%

(D) 3.55%

(E) 3.65%

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以下為參考資料[1]的重點擷取:

定義：Interest Rate Swap 是一個兩方的協議，一方付支付固定利率，而另一方支付浮動利率作為交換。(或者浮動對浮動，這裡只討論固定對浮動。)

固定利率被稱為swap rate。在swap一開始就被決定直到結束都不會變動。

浮動利率在一開始也被決定，如LIBOR plus 250 bps。

付swap rate的一方稱為payer，另一方則稱為receiver。

The two parties in the agreement are known as counterparties. The counterparty who agrees to pay the swap rate is called the payer. The counterparty who agrees to pay the variable rate, and thus receive the swap rate, is called the receiver.

The specified principal amount is called the notional principal amount or just notional amount. The word “notional” means in name only. The notional principal amount under an interest rate swap is never paid by either counterparty. Thereby, it is principal in name only. However, the notional amount is the basis upon which the exchange of payments is determined. One counterparty will owe a payment determined by multiplying the swap rate by the notional amount. The other counterparty will owe a payment determined by multiplying the variable interest rate by the notional amount.

The specified period of the swap is known as the swap term or swap tenor.

An interest rate swap will specify dates during the swap term when the exchange of payments is to occur. These dates are known as settlement dates. The time between settlement dates is known as the settlement period. Settlement periods are typically evenly spaced. For example, settlement periods could be daily, weekly, monthly, quarterly, annually, or any other agreed upon frequency. The first settlement period normally begins immediately with the first payment at the end of the settlement period. For example, if the settlement period is every three months, then the first swap payment is made at the end of three months.

In Section 1, we introduced the concept of variable rate loans. An interest rate swap can be used to change the variable rate into a fixed rate. In this case the borrower would enter into an interest rate swap with a third party. Entering into a swap does not change the terms of the original loan. A swap is a derivative instrument that is used to exchange variable rate payments for fixed rate payments. However, two parties can enter into an interest rate swap without any loan being involved. One reason for doing this is speculation. One counterparty is “betting” that the variable rates are going to increase from current expectations while the other counterparty is betting that the variable rates are going to decrease. Other reasons include managing the duration of a portfolio or to swap a series of cash flows linked to interest rates, but where the cash flows are not from a loan.

At the time that each exchange of payments is to occur, the two payments are netted and only one payment is made. For example, Tyler and Graham enter into an interest rate swap. Based on this swap, at the end of one year, Tyler owes Graham 32,000 and Graham owes Tyler 27,000. Rather than each counterparty making a payment, the two payments would be netted and Tyler would pay Graham 5,000. This is known as the net swap payment.

The vast majority of interest rate swaps have a level notional amount over the swap term. However, this is not always the case. For example, a swap could have a notional amount that follows the outstanding balance of an amortization loan. Such a swap is known as an amortizing swap as the notional amount is decreasing over the term of the swap. Similarly, a swap could have a notional amount that increases over time. This is known as an accreting swap.

A swap typically has the first settlement period beginning at time zero. However, a swap could be a deferred swap. For deferred swaps, the exchange of payments does not start until a later date. An example is a swap where settlements occur quarterly over a three year period, but the first settlement period does not start for two years. This means that the first exchange of payments will be at the end of two years and three months because settlement occurs at the end of the settlement period that starts at time 2 and ends at time 2.25. With a deferred swap, the swap rate R is determined at the time that the swap is initiated even though the first payment will not occur until after the deferral period. The swap term or swap tenor for a deferred swap includes the deferral period. For the example in this paragraph, the swap term would be five years.

There is no cost to either counterparty to enter into an interest rate swap. This is because the swap rate is determined such that the expected future payments for each counterparty has the same present value. This will be our basis for determining the swap rate, R. Since the actual payments are netted as noted above, this results in the present value of the net payments that each counterparty is expected to receive in the future being equal to zero. It should be noted that in practice customized swaps may not have a value of zero at inception, in which case a premium would be paid by one counterparty to the other counterparty. However, for the purpose of this study note, we assume the present value of the swap is always zero at inception.

Conclusion:

Interest swaps are valuable financial instruments. They can be used to manage the risk of future cash flows, manage the duration of a portfolio, or create liquidity. As future actuaries, you should now be able to not only do the calculations (swap rate, market value, cash payments under a swap, …) but should also understand the mechanics of the swap.

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Reference:

1.EDUCATION AND EXAMINATION COMMITTEE OF THE SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS STUDY NOTE INTEREST RATE SWAPS by Jeffrey Beckley, FSA, MAAA

2. wiki

https://en.wikipedia.org/wiki/Libor