Par yields are swap rates (FRM T3-13)

[my xls is here trtl.bz/2HPIDMX] The par yield is the coupon rate that prices a bond to par. It is also effectively the swap rate. Discuss this video here in our FRM forum: trtl.bz/2VMMOVa.

[@danielk.1026]

thank you so much for the distinction between par rates and ytm. Your videos are a great supplement to my university material

[@claudiaalves4760]

Awesome video and explanation! Thanks!!

[@ZakharovInvest]

Hello! This calculation only works if we consider yearly basis. I mean we can’t do this for 0.5 year or 1.5. So basically to get 1.5 par we need to take the average of 1 and 2 years par? How about 0.5 par?

[@daveyboybluey1]

Is it a rule that Swap rates HAVE to be below Spot rates by definition? If so - then something is odd. I’m comparing swap rates from spot rates using annual and continuous compounding to see the difference.
I'm finding that swap rates are higher than spot rates in the short end for cont. compounding. Have I stumbled across an edge case scenario?
Spot Rates Used 1y=1% // 2y=1.5% // 3y=2% // 4y=2.5% // 5y=3%.
I see the 3y Swap rate @2.01% when using DF that have continuous compounding.

[@mobileentertainment212]

In general do we e take par rates from market and bootstrap zeros or the other way round?

[@henrycosentino7818]

In what situation would one use a par rate vs spot rate in their analysis or valuation of bonds/fixed-income securities?

[@antoineboudreau2983]

Very good video!
If I may, I have a few questions: What is typically the use of the Par Yield - other than measuring a Swap rate (fix leg). Given the instrument priced is of the same characteristics than the term structure (eg., US-treasuries), could we theoretically use it as an arbitrage opportunity tool. For instance, using the example of the bond @ 103 (as a coupon paying x - 5-year treasury). For this particular bond, we would know its coupon right..?
My question :P: If this security, let's say, would be paying a $3.00 coupon versus a 2.36% par yield, could we infer from the par rate that she is undervalued.

[@vinitmehta21]

To answer your first question, government par curve is used to calculate Effective duration for callable bonds or MBS or any fixed income security whose cashflows are uncertain

[@elinab376]

Hello, there is a misunderstanding regarding the calculation of the par yield curve that you explain the 6th column. For example, in the 3d year, you calculate the par yield by (1- 0.96)/2.94 = 1.36 not 1.49. Why is that :) ?

[@bionicturtle]

Hi Elina, the df(3.0) = 1.015^-3 = 0.95632
, but as mentioned (at ruclips.net/video/Gfzfa81baNM/видео.html) is display-rounding to 0.96, so you'd be better to use (1 - 1.015^-3)/2.94. Thanks,

[@elinab376]

@@bionicturtle Hello again, thank you for the quick reply, but even if I calculate (1-1.016^-3)/2.94 I get 1.58 not your answer of 1.49? :)

[@bionicturtle]

@@elinab376 the 3.0 year zero rate is 1.50%, so I meant (1 - 1.015^-3)/2.94, as in 1/(1+1.50%)^3. Fixed above. The xls is available at the beginning of the description field.

[@elinab376]

@@bionicturtle Hello again, maybe I don't explain my misunderstanding the right way :) I downloaded the xls table and watched the whole video. So you explained that in order to get to calculate the par rates ( for the year 1,2,3,4 and 5 ) you use the same formula. For example, for year 5 that is 2.36% and you obtain this figure by using the df column. So that translates to (1- 0.89)/4.74. You get 2.36% but I get ( when I calculate this) - 2.32%. ANd I don't understand where am I doing wrong?

[@bionicturtle]

@@elinab376 again, the df column is rounded to 2-digits (I had limited width given the columns), if you opened the excel, you can change the format to see more decimals. More accurately, the 4.74 is actually 0.99602
+ 0.98030 + 0.95632 + 0.92385 + 0.88818 = 4.74465, such that (1 - 0.88818) / 4.74465 = 2.36%. I hope that clarifies!