Pricing and Valuation of Interest Rate Forward Contracts

Who do you think might use a forward rate agreement to deal with their interest rate exposure?

Incorrect.

That's right!

A bank that is planning to lend money may want to hedge the risk that interest rates will decline before the loan closes. By using an FRA, the bank can effectively lock in the rate on the loan. In exchange for receiving a fixed payment on the FRA, the bank would pay an unknown payment, offsetting the unknown payment it would receive on the loan. An investor that is looking to be protected against adverse stock price movements would not be interested in an FRA. Other types of derivatives, such as options on the stock itself, would be more appropriate.

FRAs are typically quoted based on the London Interbank Offered Rate, or LIBOR, on a Eurodollar deposit, which is simply a dollar-denominated loan between overseas banks. FRAs represent forward rates, and not spot rates, which should be intuitive given the term _forward rate_ agreement. If you were interested in locking in the 90-day LIBOR rate three months from now, you could go long a 90-day FRA where the underlying rate is 90-day LIBOR. Once the 90 days are up, you would make a fixed payment and receive a variable payment tied to the value of 90-day LIBOR on that date. But you could also create a synthetic FRA of this same transaction using two Eurodollar positions. How do you think you might accomplish this?

Incorrect.

Correct.

If you were to go long a 180-day deposit and short a 90-day deposit, you would have no net exposure to interest rate movements over the initial 90-day period, since any impact from rate changes on the two positions would be offset. At the end of 90 days, you would be left with a long position on a 90-day deposit, which would give you the same exposure to prospective rate changes as you would have had under a regular FRA. Going long and short a 90-day deposit would give you no net exposure over the initial 90 days, but then you would have no position left after that, which is not what you set out to accomplish.

For example, suppose that 90-day rate is $$z_{90} = 2.84 \%$$ and the 180-day rate is $$z_{180} = 3.06 \%$$. Recalling the implied forward rate calculation: $$\displaystyle (1+z_A)^A \times (1+IFR_A,_{B-A})^{B-A} = (1+z_B)^B $$ What rate are you locking in for that 90-day forward period?

A forward rate agreement, or FRA, is a __forward contract on an interest rate__, in contrast to other types of forward contracts where the underlying is actually an asset. Companies frequently use FRAs to deal with the uncertain path of interest rates. For example, a borrower can commit to paying a fixed interest payment in the future in exchange for receiving an unknown payment.

Nice work!

Not quite.

Since the 180-day rate exceeds the 90-day rate, the forward 90-day rate that links the two must be the highest of the three, logically. It's calculated as: $$\displaystyle (1+0.0284)^{90/360} \times (1+IFR_{90,90})^{90/360} = (1+0.0306)^{180/360} $$ From there, algebra leads to the periodic rate of 0.8102%, which annualized is about 3.28%.

To summarize: [[summary]]

An investor that owns a stock and wants to protect against a potential price decline

A bank that expects to fund a loan in three months

Go long a 90-day Eurodollar deposit and short a 90-day Eurodollar deposit

Go long a 180-day Eurodollar deposit and short a 90-day Eurodollar deposit

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Other responses

3.28

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