# SWAP RATE, comfused

Hey All, I have a question about reading 37. why we have different swap rate formula for interest swap in Level III from the one in CFA Level II . In CFA Level II: swap rate=(1-Zn)/(Z1+Z2…), {Zn=1/(1+Rn)} it means that we liquadate every period. PV of one period floating payment equate entire period fixed. While in Level III Reading 37, in Kaplan Notes, swap rate = [SUM(FDF*forwad rate)]/SUM(FDF), {FDF=Zn(mentioned)}, PV of entire period floating equate entire period fixed. I also read the fomular in book, it is almost the same, which just use Zero coupon bond instead of FDF. Quite confused, Any one helps. Thanks in advance for any insight, Baifan

Par = 1 Par = PV of coupons + PV of Principal if coupons are market coupons = swap rate (with several assumptions) (fixed rate) coupons can be also forward rates (in case of floater) 1=PV of coupons + PV of principal PV of coupons = 1 - PV of principal Coupon = forward rate PV of coupons = Sum(FDF x forward rate) FDF = Zn = Discount factor (your formula of Zn is wrong…) Principal = 1 swap is exchange of fixed coupons against floating coupons PV of fixed coupons = PV of floating coupons PV of fixed coupons = Sum(FDF x fixed coupon) = fixed coupon x Sum(FDF) fixed coupon = swap rate = PV of floating coupons / Sum(FDF)

“FDF = Zn = Discount factor (your formula of Zn is wrong…)” so Swap need not to mark to market every settlement day in this case? I am sure that In CFA Level II: swap rate=(1-Zn)/(Z1+Z2…Zn), {Zn=Discount factor} it means that we need to mark to market every period. So PV of one period floating payment equate entire period fixed payment.

sorry for confusion in my previous message, FDF=Zn=discount factor = 1/(1+Rn)^n I might have misunderstood the meaning of FDF and Zn in your message. Everything is valid with this in my previous message. “I am sure that In CFA Level II: swap rate=(1-Zn)/(Z1+Z2…Zn), {Zn=Discount factor}” here the discount factor = 1/(1+Rn)^n, where Rn is regular spot rate (not forward rate) the idea of discounting over 1 interest period using forward rate (which probably confuses you) when pricing a floater explains why floating rate bond equals par (with simplifying assumptions)

The way CFA level 2 and 3 calculate the swap rate is the same (although it took me a while to figure it out). I suggest not read Schweser books for that chapter because it’s way to simplified and misses a lot of key information. CFAI explains swaps clearly.

mik82 Wrote: ------------------------------------------------------- > The way CFA level 2 and 3 calculate the swap rate > is the same (although it took me a while to figure > it out). Thanks guys, can anyone point out why the way CFA level 2 and 3 calculate the swap rate is the same? (the key point to confuse me.)

baifan Wrote: > > Thanks guys, can anyone point out why the way CFA > level 2 and 3 calculate the swap rate is the > same? > > (the key point to confuse me.) mik82 or anyone please give me a hand, thanx.

anyone help?

swap rate=(1-Zn)/(Z1+Z2…+Zn), {Zi=discount factor} swap rate=[SUM(FDF*forwad rate)]/SUM(FDF), {FDFi=Zi(mentioned)} ==> (swap_rate)*(Z1+Z2+…Zn)+Zn = 1 (swap_rate)*(Z1+Z2+…Zn) = Z1*forwad_rate_1+…+Zn*forwad_rate_n ==> PV(received fixed rate counpon bond)= PV(received floating rate bond) PV(received fixed rate coupons) = PV(received floating rate counpons) The only difference is whether is the principal is paid or not. Notes: forward_rate_i could be derived from the discount factor Zi’s, vice versa.

At issue, a floating-rate bond has par value. That is, Z1*forwad_rate_1+…+Zn*forwad_rate_n+Zn=1. So the swap rates in the two approaches are the same.

Great!!! I got it. Thanx a lot.