# FRA

Which of the following combinations of interest rate options would replicate a 6-month by 9-moth forward rate agreement to pay 5% fixed? A. Long a 6-month call on LIBOR and short a 6-month put on LIBOR. B. Long a 9-month call on LIBOR and short a 9-month put on LIBOR. C. Long a 6-month call on LIBOR and long a 6-month put on LIBOR. D. Short a 9-month call on LIBOR and short a 9-month put on LIBOR.

Hmm…I’ll go with B

It should be A. I look up on the web thought. Still need work on this. I found this good explanation on it. http://www.cboe.com/Products/InterestRateOptionsSpecs.aspx

Yeah, the correct answer is A.

huc3 is there an explanation from the question provider on why the answer is a?

an Long FRA is long a interest rate call and short a interest rate put. a Short FRA is short an interest rate call, long a interest rate puts. Both of these options have the same payoff as the FRA. This is mentioned in Schweser as well, but I am not sure about the time frames for the Call and the Put options.

yea i narrowed it down to a or b not sure how the time frames of the fra affect the option strategy

yea, please explain. we all got it to A or B. How does the expiration dates/time frame play into this.

pg 162 of Schweser says the following QUOTE: The combination of a Long Int Rate call + a Short Int. Rate Put Option has the same payoff as a FRA. To see this, consider a fixed rate payer is a 5% fixed rate, 1 M \$ notional, LIBOR based FRA. Like the Long call position the fixed rate payer will receive 1 M * (LIBOR - 5%). And like the Short Put - the fixed rate payer will pay 1 M * ( 5 - LIBOR ) Professor’s note: for the exam you need to know that a long rate interest call combined with a short int rate put can have the same payoff as a long position in an FRA. END QUOTE. – extrapolating since it is a 6 x 9 FRA – the Interest rate call and Interest Rate Put have to be for the 6 month period… even though the interest amount on the 1 M Notional is available at 9 month (expiration date of the FRA – we account for it as though it’s available at the 6th month – because we discount it at the forward rate, at the 6th month, as though we receive it in the 6th month itself. I hope this makes sense… and throws some light on this.

But of course the problem is that there isn’t the discounting in the options. Long a 6-month call on Libor and short a 6 month put is just a long ED futures position which just ain’t the same as a FRA (an FRA has convexity and the synthetic futures position doesn’t). Bad question.

Explanation: If LIBOR exceeds 5%, this combination will result in an inflow of funds just like an FRA. If LIBOR drops below 5%, this combination will result in an outflow of funds just like an FRA. Can someone explain?

LIBOR Is the stock price, 5% is the exercise / strike price. Call option payoff = Max (0, S-X) --> so it pays off when LIBOR - 5 > 0.

thanks cpk123

But what does your book have as the pay-off for an FRA? At expiration an FRA has payoff N(exp(K - R)*T - 1) for notional amount N, strike K, interest rate R, time period T. The call/put thing has payoff N*(K-R)*T. Pretty odd that they have a question like that and then in L II spend lots of time teaching you about convexity adjustments in hedging with Eurodollars.

Joey: In the book for an FRA payoff is Notional * (Forward - Agreed) * T/360 ------------------------------------------------ (1 + forward * T/360) PV (Interest rate Differential ) at the future rate. So that is about consistent with the above – which is the pay off of a Call option. The exp(K-R) -1 part is missing in the L1 Curriculum. CP

Libor is always for 3 month, right?

cpk123 Wrote: ------------------------------------------------------- > Joey: > > In the book for an FRA payoff is > > Notional * (Forward - Agreed) * T/360 > ------------------------------------------------ > (1 + forward * T/360) > > PV (Interest rate Differential ) at the future > rate. > > So that is about consistent with the above – > which is the pay off of a Call option. > > The exp(K-R) -1 part is missing in the L1 > Curriculum. > > CP No it’s not because " PV (Interest rate Differential ) at the future > rate." which should mean that you discount it. The whole point of an FRA is that an FRA is about hedging a LIBOR loan in which the interest rate is paid at the end of the period not at settlement date of the FRA. Since nobody wants to wait around, the money is settled at expiration of the FRA by PV’ing it back. That gives FRA’s convexity. There is no convexity in the put/calls.

Hannoversch LIBOR could be specified for any time period. 30 day, 60 day, 90 day… etc. etc. The appropriate one of interest for us should be provided in the exam. CP

JoeyDVivre Wrote: ------------------------------------------------------- > cpk123 Wrote: > -------------------------------------------------- > ----- > > Joey: > > > > In the book for an FRA payoff is > > > > Notional * (Forward - Agreed) * T/360 > > > ------------------------------------------------ > > (1 + forward * T/360) > > > > PV (Interest rate Differential ) at the future > > rate. > > > > So that is about consistent with the above – > > which is the pay off of a Call option. > > > > The exp(K-R) -1 part is missing in the L1 > > Curriculum. > > > > CP > > No it’s not because " PV (Interest rate > Differential ) at the future > > rate." which should mean that you discount it. > > The whole point of an FRA is that an FRA is about > hedging a LIBOR loan in which the interest rate is > paid at the end of the period not at settlement > date of the FRA. Since nobody wants to wait > around, the money is settled at expiration of the > FRA by PV’ing it back. That gives FRA’s > convexity. There is no convexity in the > put/calls. —I think it’s one of those “cute things” schweser did, I remember when I first read this payoff equivalence thing from schweser’s qbank, I did a mad search in the CFAI text to try to find this but came up empty…I saw a few questions in qbank on this, but none from the 5 CFAI sample exams I did, but that’s 4000 questions to 300 questions… I agree these two aren’t equal, the only way I tried to make sense of this was that if you put the payoff graph of a long call and short put together with the same strike price, then it’ll be a straight line with a positive slope (neglecting the out of money portions of the graph and not counting the cost of the options or assume the call and put have the same cost so that the short would cover the cost of the long), which would be the payoff of an FRA (not taking the discounting into consideration, but strictly from the point of view of +ve or -ve return based on underlying rate compared to exercise rate)…that’s a whack load of assumptions, so I think this is an approximation at best (if that), and wouldn’t worry too much about it on the actual exam, since from the 5 CFAI exams I’ve done, they seem to stick to what they had in the text pretty closely, and this was certainly not in the text, at least I didn’t find it…

Liaaba In the derivatives section, there is an LOS which reads as: Reading 76: Option Markets and Contracts The candidate should be able to: a. define European option, American option, moneyness, payoff, intrinsic value, and time value and differentiate between exchange-traded options and over-thecounter options; b. identify the different types of options in terms of the underlying instruments; c. compare and contrast interest rate options to forward rate agreements (FRAs); see the item c). So it must be there in the text book, chapter 76.