 # FRA credit risk Cal

Assume that in six months a manager will borrow \$1,000,000 at LIBOR for one year, and LIBOR is currently 5%. The manager enters an FRA with a reference rate of 5% and a notional principal of \$1,000,000. Since the reference rate 5% and the contract rate are the same, the value of the FRA at inception is zero. Three months into the contract, however, LIBOR has climbed to 6%. Assuming the risk-free rate is 4%, determine the amount of credit risk and who bears it.

correct : (1M x 1%)/Libor rate of 3 months Wrong : (1M x 1%)/(1+0.04)^0.25

Here is the correct answer: (1M x 1%)/(1+0.06)/(1+0.04)^0.25 the payoff needs to be discounted by going loan rate (current Libor) for one year. Then, discount at Rf for the months from now till the FRA contract starts.

(1M x 1%)/(1+0.06)/(1+0.04)^0.25 is wrong. Sorry my previous answer shall be (1M x 1%)/(1+0.06) / Libor rate of 3 months and this shall be the correct answer. Discount by risk-free rate is wrong (as in Schweser). Please refer back to L2.

There’s not enough information here to give a complete answer. You need to know what the the 3 month libor and 15 month libor rates are - (first to calculate the “new” 1yr FRA rate and then to discount the difference back to it’s present value.) If the yield curve is flat, the amount of credit risk is: (1M * 1%)/[(1.06)^15/12]. Rates have gone up, so this will be a positive value for the long - thus he bears the credit risk.

cfa321, You are right. It must be discounted by risk-free rate by 3 month libor rate and to discount by risk-free rate is just wrong (as in Schweser).

cfa321, Sorry it shall be : You are right. It must be discounted by 3 month libor rate and to discount by risk-free rate is just wrong (as in Schweser).

AMC, can you please refer to a source in CFAI did similar calcualtions differently?

Not in L3, it is in L2.

No, it must be discounted by the 15 MONTH libor rate - not the 3 month libor rate. If the curve is flat, it will be discounted by 1.06^1.25

happyking02 Wrote: ------------------------------------------------------- > AMC, can you please refer to a source in CFAI did > similar calcualtions differently? If you hold Schweser L2, you can check it. I am sorry my Schweser L2 was gifted to my friend.

AMC, thanks. I do not have Level II notes either. I just zipped an email to Schweser on this, let’s see how they respond.

cfa321 Wrote: ------------------------------------------------------- > No, it must be discounted by the 15 MONTH libor > rate - not the 3 month libor rate. If the curve > is flat, it will be discounted by 1.06^1.25 It shall be discounted first by one year Libor (6%) then discount by 3 month libor rate which is different from discounting by the 15 MONTH libor rate. 3 month libor rate can be derived from 15 months libor rate & 1 YEAR libor rate (here 6%) : 3 month libor rate = [1+15 months libor ratex (15/12)] / [1+1 YEAR libor rate (6%)]

cfa321 Wrote: ------------------------------------------------------- > No, it must be discounted by the 15 MONTH libor > rate - not the 3 month libor rate. If the curve > is flat, it will be discounted by 1.06^1.25 Yes, if the curve is flat, it can be discounted by 1.06^1.25 But if the curve is not flat, it shall be discounted first by 1.06 then by 3 month libor rate

Actuulay, the Libor Rate is calculate as following in L2, but it makes little difference 1+0.06 x (15/12) instead of 1.06^1.25

Guys - I want to ask a simpler questions. Did you see this in a L-3 sample exam somewhere? I am f*d if CFAI asks questions from L2 or L1. I took them in 2006 and never touched the book.

This is in a worked example in CFAI Vol 5 for sure. Examinable.

LIBOR is never used with “to the power of”. It is always *15/12 or whatever for LIBOR. Just an FYI.

bidder Wrote: ------------------------------------------------------- > This is in a worked example in CFAI Vol 5 for > sure. Examinable. Please advise where is the worked example. Thanks

bluedragon Wrote: ------------------------------------------------------- > Guys - I want to ask a simpler questions. Did you > see this in a L-3 sample exam somewhere? I am f*d > if CFAI asks questions from L2 or L1. I took them > in 2006 and never touched the book. Both 2008 & 2009 AM Exam have this kind of question.