What can the buyer of a 6 x 12 FRA expect to receive (or pay) if the contracted rate is 10% and the settlement rate is 12%? Assume contract notional is $100m.

What can the buyer of a 6 x 12 FRA expect to receive (or pay) if the contracted rate is 10% and the settlement rate is 12%? Assume contract notional is $100m.

A. Pay $1,000,000

B. Receive $1,000,000

C. Pay $943,396

D. Receive $943,396

View Answer

Answer: D

Explanation:

The buyer of the FRA gets to borrow $100m at 10% per annum for 6 months at the end of 6 months from the contract date. Thus, the interest due is $100m * 10% * 6/12 = $5m. However, at the end of the 6 months (when the notional borrowing period begins), the spot rate is 12%. The interest due on a borrowing at the spot rate would be $100m * 12% * 6/12

= $6m. Since the buyer gets to borrow cheaper than the going rate, he or she has made a gain of $1m on the FRA. However, this amount is not due immediately, it is due at the end of the 6 month borrowing period (ie, 12 months from the date the contract was entered into). The seller of the FRA can make the buyer whole by paying the buyer the present value of $1m due in 6 months time, which is $1m/(1 + 12%*6/12) = $1m/1.06 = $943,396. Thus, Choice ‘d’ is the correct answer. Remember that the FRA gets settled at the beginning of the notional borrowing period as all future cash flows, and the applicable

discount rates are known with certainty. The buyer and the seller do not need to wait for the entire period to get over first. The cash settlement allows the buyer to borrow at the market rate and still have the same net borrowing cost as he or she had initially contracted for in the FRA.