Subject 2. Equivalence of swaps and other instruments

The equivalence of a swap to transactions (such as assets) we are already familiar with is important because it allows us to price and value the swap using simple instruments, such as the underlying currency, interest rate, or stock.

Swaps and assets.

Currency swaps are like issuing a bond denominated in one currency and using the proceeds to buy a bond denominated in another currency.

Interest rate swaps are like issuing a fixed rate bond and using the proceeds to buy a floating-rate bond or vice versa. The notional principal is equivalent to the face value on these hypothetical bonds.

Equity swaps are like issuing a bond and using the proceeds to buy stock or vice versa. For example, a pay-fixed, receive-equity swap looks like issuing a fixed-rate bond and using the proceeds to buy a stock or index portfolio. Equity swaps with both sides paying an equity return are like selling short one stock and using the proceeds to buy another stock. The stock position is not, however, a buy-and-hold position and requires some rebalancing.

Swaps and forward contracts

A swap can be viewed as combining a series of forward contracts into a single transaction. However, there are some small differences.

An interest rate swap is like a series of off-market FRAs, meaning that the rate on each FRA is set at the swap rate, not at the rate it would be set as if priced as an FRA with zero market value at the start. In addition, the first payment on a swap is just an exchange of known amounts of cash.

Currency swaps and equity swaps are similar to forward contracts, but the connection is not as straightforward as in interest rate swaps.

Swaps and options

Interest rate swaps are like being long (short) interest calls and short (long) interest rate puts. Buying a call and selling a put would:

  • force the transacting party to make a net payment if the underlying is below the exercise rate at expiration, or
  • result in receipt of a payment if the underlying is above the exercise rate at expiration.

The payment will be equivalent to a swap payment if the exercise rate is set at the fixed rate on the swap. Therefore, a swap is equivalent to a combination of options with expirations at the swap payment dates.

Currency swaps and equity swaps are also similar to combinations of options, but the connection is not as straightforward.

Practice Question 1

An interest rate swap is identical to:

I. Issuing a fixed-rate bond and using the proceeds to purchase a floating-rate bond.
II. Issuing a fixed-rate bond in one currency, converting the proceeds to the other currency, and using the proceeds to purchase a floating-rate bond denominated in the other currency.
III. Issuing a floating-rate bond and using the proceeds to purchase a fixed-rate bond.
IV. Issuing a floating-rate bond and using the proceeds to buy a stock index portfolio.
Correct Answer: I and III

Practice Question 2

An off-market forward contract is defined as a forward contract:

A. that does not trade on the market.
B. that has a value other than zero at inception.
C. that is closed by both parties before the contract expiry date.
Correct Answer: B

An off-market forward contract starts with a non-zero value.

An interest rate swap is like a series of off-market FRAs, meaning that the rate on each FRA is set at the swap rate, not at the rate it would be set as if priced as an FRA with zero market value at the start.

A series of FRAs would have different fixed rates unless the term structure is flat.

Practice Question 3

Which of the following combinations would not be a likely outcome by combining an interest rate swap with a currency swap?

A. A fixed rate in the U. S. dollar swapped for floating rate in a foreign currency.
B. A floating rate in the U. S. dollar swapped for fixed rate in foreign currency.
C. A fixed rate in the U. S. dollar swapped for floating rate in U.S. dollar.
Correct Answer: C

A fixed rate in U.S. dollar swapped for floating rate in U. S. dollar is just a plain vanilla interest rate swap. Hence, this structure would not involve a currency swap and it would not constitute a correct answer.

Practice Question 4

The spot price of a stock that does not pay dividends is $35, and the 1-year risk-free interest rate is 5.0%. An investor enters into a long forward contract for delivery in one year's time. The forward price is $38. This forward contract is a(n):

A. off-market forward contract.
B. standard forward contract.
C. premium forward contract.
Correct Answer: A

After one year, the accumulated value of the initial stock price is 35x1.05 = $36.75. This is the forward price of a market-priced forward contract, so the premium of this market forward is 38 - 36.75 = $1.25. An off-market forward contract starts with a non-zero value.

A regular forward contract does not involve an exchange at the beginning of the contract. At the beginning the contract has zero value.