# swap credit risk issue

RR Company entered a one-year interest rate swap four months ago; • RR receives floating payments based on LIBOR and pays a fixed rate of 5.5 percent; • the two-month LIBOR is 5.35 percent; • the eight-month LIBOR is 5.45 percent; • the next floating payment will be 5.4 percent; • assume semi-annual payments based on 30 days in a month, 360 days in a year. The PV of floating-leg : PV(floating-leg) =(1+(0.054*(180/360))*0.9911)=1.0179 The PV(fixed-leg) = ((1+(0.055*(180/360)*0.9911)+ ((1+(0.055*(180/360)))*0.9649)=1.0187 Where the PV factors for 2 and 8 months are, respectively: 1/(1+0.0535*(60/360))=0.9911 1/(1+0.0545*(240/360))=0.9649 I’m not sure why pv of fixed leg needs to consider eight months fixed payment, while floating leg is not considering eight months floating receive.? can anyone give the correct answer to this question? thanks

CP, can you help?

floating leg resets to PAR… Level II stuff.

hi, if it is reset to par, then PV(floating)=1*0.9911+1*0.9649, why the answer says you need consider next floating payment 5.4%. should we ignore the eight month payment/receive? it looks like the answer is wrong. thus pv(float)=(1+0.054*180/360)*0.9911 pv(fix)=(1+0.055*180/360)*0.9911

go back to your level II books please. what they have done is right. When the floating resets to par - you get 1\$ back and the 0.054 back. Both need to be discounted at the 0.9911 factor. Fixed - calculated to become the 1.0187. You are receiving floating, paying fixed - so 0.0009 is your swap payoff. Please do not (as usual) try to poke and find errors in the CFAI books. They are most often correct. If they are not, this is not the time - since you do not have enough time to get them to post an erratum before the exam. So read and use what they have given.

Yes, this is in level II. But I don’t think anyone is trying to poke and find errors in the CFAI books. The PV(fixed-leg) = ((1+(0.055*(180/360)*0.9911)+ ((1+(0.055*(180/360)))*0.9649)=1.0187 is wrong. It shall be : The PV(fixed-leg) = ((0.055*(180/360)*0.9911)+ ((1+(0.055*(180/360)))*0.9649)=1.0187 Though the calculation result is correct !

Dear Swap expert, RR is paying fixed rate and receiving floating, in fixed leg, after 2 months, he will pay 0.055 and after 8 months(the last payment), he will pay both principal 1 and interest 0.055. in floating leg, according to CP’s suggestion, after 2 months, due to rest to par, he will receive principal 1 and 0.054 back, then after 8 months(the last receive), he will receive principal 1 and X back (x is the floating rate 8 months later), since the question doesn’t give us the floating rate 8 month later, how will work out for the floating leg?

francisgy Wrote: ------------------------------------------------------- > Dear Swap expert, > > RR is paying fixed rate and receiving floating, > > in fixed leg, after 2 months, he will pay 0.055 > and after 8 months(the last payment), he will pay > both principal 1 and interest 0.055. > > in floating leg, according to CP’s suggestion, > after 2 months, due to rest to par, he will > receive principal 1 and 0.054 back, then after 8 > months(the last receive), he will receive > principal 1 and X back (x is the floating rate 8 > months later), since the question doesn’t give us > the floating rate 8 month later, how will work out > for the floating leg? You don’t. Work with what you are given.

OK, if I assume eight month floating rate=0.055. Then PV(floating leg) should be (1+0.054*180/360)*0.9911 +(1+0.054*180/360)*0.9649. So is it correct? why CP didn’t mention eight month reset to par and discount based on eight month interest rate? pls help

2 months (not 8 months) remains until next 1st reset day. So the discount factor is : 1/(1+0.0535*(60/360))=0.9911. Discount the floating payment (at t=6, next 1st reset day) 2 months back to t=4. PV of floating-leg : PV(floating-leg) =(1+(0.054*(180/360))*0.9911)=1.0179

francisgy Wrote: ------------------------------------------------------- > OK, if I assume eight month floating rate=0.055. > > Then PV(floating leg) should be > (1+0.054*180/360)*0.9911 > +(1+0.054*180/360)*0.9649. > > So is it correct? why CP didn’t mention eight > month reset to par and discount based on eight > month interest rate? pls help Because the LIBOR in floating is determined in arrears. You don’t know what the 8 month rate is going to be until 2 months from now. This was taught at level 2, you only need to take the PV of the next floating payment. Done.

Thanks, this is not resonable, now I change this question to two years swap, semi-annual payment, is PV(floating-leg) =(1+(0.054*(180/360))*0.9911)=1.0179? PV(fixed leg)= ((0.055*(180/360)*0.9911)+ ((0.055*(180/360))*0.9649)+0.055*(180/360)*D1+(1+0.055/2)*D2? D1 and D2 is the discount factor, 14 month later interest rate in two months term , 20 month later interest rate in two months term. everyone will like to be floating payer, because floating payer only pay once according to bubpdlog. fixed payer suffers four payment, the first three with interest rate, the fourth with principal. any expert pls share your knowledge

francisgy Wrote: ------------------------------------------------------- > everyone will like to be floating payer, because > floating payer only pay once according to > bubpdlog. fixed payer suffers four payment, the > first three with interest rate, the fourth with > principal. > > any expert pls share your knowledge floating payer pay on every reset date. i.e., pay a payment which is set on t=0 or reset at t =6, 12, 24 months. 1st floating payment (1+5.4%) at t=6 is set according to Libor at t=0, 2nd floating payment (1+ ? %) at t=12 is reset at t=6 according to Libor at t=6 …etc.,

Correction 1st floating payment (1+5.4% x 6/12) at t=6 is set according to Libor at t=0, 2nd floating payment (1+ ? % x 6/12) at t=12 is reset at t=6 according to Libor at t=6 …etc.,

Thanks, how about t=0, is it the 1st floating payment ? Thus I think 2nd floating payment (1+5.4%) at t=6 is set according to Libor at t=0, how about the rate to be used for t=0 floating payment, according to your logic, is it libor at t=-6? is 1st floating payment (1+X%) at t=0, x= libour at t=-6? My statement is correct. floating payer only pay once in a particular time period. for example current time is t=4, so only one floating payment is at t=6, discounted back to t=4 if current time is t=7, only one floating payment is at t=12, discounted back to t=7, the rate to be applied should be the current libor rate at t=7, not at t=6 as you said.

francisgy Wrote: ------------------------------------------------------- > Thanks, how about t=0, is it the 1st floating > payment ? > > Thus I think 2nd floating payment (1+5.4%) at t=6 > is set according to Libor at t=0, > > how about the rate to be used for t=0 floating > payment, according to your logic, is it libor at > t=-6? is 1st floating payment (1+X%) at t=0, x= > libour at t=-6? Value of I/R SWAP at t=0 is 0. i.e., the fixed swap rate is determined such that the swap value is 0 at t=0. So no payment (both floating & fixed). Please refer to L2.

thanks, you are right for this point, but I disagree with you for the rate to be used. Is My statement correct? floating payer only pay once in a particular time period. for example current time is t=4, so only one floating payment is at t=6, discounted back to t=4 , using the libor rate at t=4, not the one you mentioned (t=0). so back to the original question, 5.4% is used in the answer. if current time is t=7, only one floating payment is at t=12, discounted back to t=7, the rate to be applied should be the current libor rate at t=7, not at t=6 as you said.

You can say floating payer only pay once in a particular time period. My saying is that floating payer pay on every reset date It shall be same !

francisgy Wrote: ------------------------------------------------------- > if current time is t=7, only one floating payment > is at t=12, discounted back to t=7, the rate to be > applied should be the current libor rate at t=7, > not at t=6 as you said. The floating payment at t=12 is set at t=6, not at t=7 (reset period is agreed upon in the contract). It is the “value” at t=7 which reuire you to calculate.

francisgy Wrote: ------------------------------------------------------- > Thanks, this is not resonable, now I change this > question to two years swap, semi-annual payment, “semi-annual payment” here means reset floating rate every 6 months.