**CFA Level 1 - Derivatives**

**Plain Vanilla Interest Rate Swap**

In general, an interest rate swap is an agreement to exchange rate cash flows from interest-bearing instruments at specified payment dates. Each party's payment obligation is computed using a different interest rate. Although there are no truly standardized swaps, a plain vanilla swap typically refers to a generic interest rate swap in which one party pays a fixed rate and one party pays a floating rate (usually LIBOR).

For each party, the value of an interest rate swap lies in the net difference between the present value of the cash flows one party expects to receive and the present value of the payments the other party expects to make. At the origination of the contract, the value for both parties is usually zero because no cash flows are exchanged at that point. Over the life of the contract, it becomes a zero-sum game. As interest rates fluctuate, the value of the swap creates a profit on one counterparty's books, which results in a corresponding loss on the other's books.

A portfolio manager with a $1 million fixed-rate portfolio yielding 3.5% believes rates may increase and wants to decrease his exposure. He can enter into an interest rate swap and trade his fixed rate cash flows for floating rate cash flows that have less exposure when rates are rising. He swaps his 3.5% fixed-rate interest stream for the three-month floating LIBOR rate (which is currently at 3%). When this happens, he will receive a floating rate payment and pay a fixed rate that is equivalent to the rate the portfolio is receiving, making his portfolio a floating-rate portfolio instead of the fixed-rate return he was receiving. There is no exchange of the principal amounts and the interest payments are netted against one another. For example, if LIBOR is 3%, the manager receives 0.5%. The actual amounts calculated for semiannual payments are shown below. The fixed rate (3.5% in this example) is referred to as the swap rate.

A typical exam question concerning interest rate swaps follows:

For each party, the value of an interest rate swap lies in the net difference between the present value of the cash flows one party expects to receive and the present value of the payments the other party expects to make. At the origination of the contract, the value for both parties is usually zero because no cash flows are exchanged at that point. Over the life of the contract, it becomes a zero-sum game. As interest rates fluctuate, the value of the swap creates a profit on one counterparty's books, which results in a corresponding loss on the other's books.

*Example*A portfolio manager with a $1 million fixed-rate portfolio yielding 3.5% believes rates may increase and wants to decrease his exposure. He can enter into an interest rate swap and trade his fixed rate cash flows for floating rate cash flows that have less exposure when rates are rising. He swaps his 3.5% fixed-rate interest stream for the three-month floating LIBOR rate (which is currently at 3%). When this happens, he will receive a floating rate payment and pay a fixed rate that is equivalent to the rate the portfolio is receiving, making his portfolio a floating-rate portfolio instead of the fixed-rate return he was receiving. There is no exchange of the principal amounts and the interest payments are netted against one another. For example, if LIBOR is 3%, the manager receives 0.5%. The actual amounts calculated for semiannual payments are shown below. The fixed rate (3.5% in this example) is referred to as the swap rate.

A typical exam question concerning interest rate swaps follows:

Q. Two parties enter a three-year, plain-vanilla interest rate swap agreement to exchange the LIBOR rate for a 10% fixed rate on $10 million. LIBOR is 11% now, 12% at the end of the first year, and 9% at the end of the second year. If payments are in arrears, which of the following characterizes the net cash flow to be received by the fixed-rate payer?

A. $100,000 at the end of year two.

B. $100,000 at the end of year three.

C. $200,000 at the end of year two.

D. $200,000 at the end of year three.

A. The correct answer is "C". What's important to remember is that the payments are in arrears, so the end-of-year payments depend on the interest rate at the beginning of the year (or prior year end). The payment at the end of year two is based on the 12% interest rate at the end of year one. If the floating rate is higher than the fixed rate, the fixed rate payer receives the interest rate differential times the principal amount ($10,000 x (0.12-0.10) = $200,000).

**Calculate the Payments on an Interest Rate Swap**

Consider the following example:

Notional amount = $1 million, payments are made semiannually. The corporation will pay a floating rate of three-month LIBOR, which is at 3% and will receive a fixed payment of 3.5%.

*Answer:*Floating rate payment is $1 million(.03)(180/365) = $14,790Fixed payment is $1 million(.035)(180/365) = $17,225

The corporation will receive a net payment of $2,435.

__Equity Swaps__An equity swap is an agreement between counterparties to exchange a set of payments, determined by a stock or index return, with another set of payments (usually an interest-bearing (fixed or floating rate) instrument, but they can also be the return on another stock or index). Equity swaps are used to substitute for a direct transaction in stock. The two cash flows are usually referred to as "legs". As with interest rate swaps, the difference in the payment streams is netted.

Equity swaps have many applications. For example, a portfolio manager with XYZ Fund can swap the fund's returns for the returns of the S&P 500 (capital gains, dividends and income distributions.) They most often occur when a manager of a fixed income portfolio wants the portfolio to have exposure to the equity markets either as a hedge or a position. The portfolio manager would enter into a swap in which he would receive the return of the S&P 500 and pay the counterparty a fixed rate generated form his portfolio. The payment the manager receives will be equal to the amount he is receiving in fixed-income payments, so the manager's net exposure is solely to the S&P 500. These types of swaps are usually inexpensive and require little in term of administration.

For individuals, equity swaps offer some tax advantages. The owner of $1 million worth of XYZ stock watches his stock value increase by 25% over 12 months. He wants to take some of the profit but does not want to actually sell his shares. In this case, he can enter into an equity swap in which he pays a counterparty (perhaps his brokerage) the total return he receives from his XYZ shares annually for the next three years. In return, he'll take the three-month LIBOR rate. In this scenario, the owner of XYZ does not have to report any capital gains on his stock and retains ownership of those stocks as well.

- A total return equity swaps includes capital gains and dividends paid on the underlying stock or stock index. No principal is exchanged and payments are set off by a notional amount.

**Calculate the Payments on an Equity Swap**

Consider the following example:

Notional principal amount = $1 million

Payments made semi-annual

Fund manager will pay the broker/dealer the return of the S & P 500 and will receive an interest payment of 5% every six months

Index is at 10,500 at the start of the swap

*Results:*Six months from now the index is at 11,000.

- The fixed payment the fund will receive is:

$1 million(0.05) 182/365 = $24,931.51 - The index payment the fund must make is:

(11,000/10,500 -1) $1 million = $47,619.04

The net payment the fund must make at the end of the first six months is $22,687.50 (47,619,.04 - 24,931.51).

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