How many off-market FRAs is a 2-year semiannual swap equivalent to? According to QBank it’s 3 but Practice Exam says it’s 4…
give some details please , which exam?
QBank (3 FRAs): ID#88216*, 88218** Schweser Practice Exam 2 (Vol 2) Q56 *Which of the following is equivalent to a pay-fixed swap with a tenor of two years with semi-annual swap payments and a fixed rate of 6% (exchanged for LIBOR)? The notional principal is $100,000,000. A) A strip of three forward rate agreements, which obligates the party to pay a fixed rate of 6% and receive six-month LIBOR on a notional principal of $100,000,000. B) A forward rate agreement, which obligates the party to pay a fixed rate of 6% and receive six-month LIBOR on a notional principal of $100,000,000. C) A strip of two forward rate agreements, which obligates the party to pay a fixed rate of 6% and receive six-month LIBOR on a notional principal of $100,000,000. The correct answer was A. The determination dates for the floating rate will be at months 6, 12 and 18 and the corresponding payment dates will be at months 12, 18 and 24. **Which of the following is equivalent to a receive-fixed swap with a tenor of one and a half years with semi-annual swap payments and a fixed rate of 5% (exchanged for London Interbank Offered Rate (LIBOR))? Assume that the notional principal is $10,000,000. A) A strip of two forward rate agreements, which obligates the party to receive a fixed rate of 5% and pay six-month LIBOR on a notional principal of $10,000,000. B) A forward rate agreement, which obligates the party to receive a fixed rate of 5% and pay six-month LIBOR on a notional principal of $10,000,000. C) A strip of three forward rate agreements, which obligates the party to receive a fixed rate of 5% and pay six-month LIBOR on a notional principal of $10,000,000. The correct answer was A. This is an example of two 6-month forward rate agreements (FRAs). The first FRA is entered into at time 0 with the payment determined at 6 months and paid at 12 months. The second FRA is entered into at 6 months with the payment determined at 12 months and paid at 18 months.
Haven’t seen this question, but the CFAI text notes that swap/fra equivalence is not immediately intuitive. 2 years of semi-annual swaps should mean 3 contracts to settle, because swaps pay in arrears. The swap will involve 4 payment dates, T.5, T1, T2, and T2.5, but the rates involved will be set at T0, T.5, T1, and T1.5. FRAs fix future unknown rates, but since the first 6 month rate (payable or swapable at T.5) is known and set at T0, there’s no meaningful contract to make. Hence, 4 swaps made in arrears, but 3 unknown future rates, and so 3 FRAs to equate to the fixed payer. Perhaps the Practice Exam is wrong?
Mimician, if you read the second question, it says 1.5 years, not 2 years…
lmb Wrote: ------------------------------------------------------- > FRAs fix future > unknown rates, but since the first 6 month rate > (payable or swapable at T.5) is known and set at > T0, there’s no meaningful contract to make. Thanks. So the 3 FRAs are 6x12, 12x18, and 18x24 which mimics swap payments at T1, T1.5, and T2 respectively? The first payment at T.5 is not counted, since 0x6 “FRA” is technically not a FRA? What is the implication for equivalence options then? Only 3 put-call combos expiring on T1, T1.5, and T2 as well? With the first payment ignored again? The CFAI text does not seem to be too explicit on this. Unless it’s explained somewhere else than p261 (Vol 6)?
Yes, that’s right about the FRAs. The options should have, as you say, termination dates matching the interest rate reset dates. What would the price be on an option expiring today to lock-in today’s rate just for today? Zero. However the option (without the obligation) to swap at a certain rate in the uncertain future is valuable, so you contract only for the remaining three reset dates.
Mimician Wrote: ------------------------------------------------------- > Only 3 put-call combos expiring on T1, T1.5, > and T2 as well? With the first payment ignored > again? Correction: should be EXPIRATION on T.5, T1, and T1.5, and PAYMENT on T1, T1.5, and T2 respectively.
Yes! Sorry, I half spotted that, but somehow didn’t concentrate, because I could see you had the right idea!
Right on! Should we also point out an inherit subtle difference between the swap and the FRAs: The FRA payments that matches the swap payments at T1, T1.5, and T2 are actually made at T.5, T1, and T1.5 (discounted to their PVs) respectively, since FRA pays at settlement. So in this way, the put-call options mimics the swap better than the FRAs?
Practically, yes, the options mirror payment dates. Of course in the perfect CFAI world it’s completely equivalent, thanks to the risk-free, so our ideal investor is indifferent to that “advantage”.