Hi all
I understand that the the yields on zero coupon bills and notes serve as the spot rates for different time periods. However, I would like to know how do we determine the spot rate at time - Year 30 for constructing a spot rate curve?
Is the coupon % on 30 Year Treasury bond the spot rate of Year 30? Or is it calculated differently?
yes, if the bond is trading at par. Otherwise you would need to bootsrap the spot curve to derive the 30 year rate.
Howdy.
Alas, this isn’t true.
If the bond is trading at par then the coupon rate is the 30-year _ par _ rate, but not the 30-year spot rate. That’s why it’s called the par rate (and the resulting curve is called the par curve).
You need to do this under any circumstances.
Here’s a article I wrote on this topic that may be of some help: http://financialexamhelp123.com/par-curve-spot-curve-and-forward-curve/.
Yield on Zero coupon security = Spot Rate
Thank you for your comments!
Yes, to get the 30-year spot rate you’d have to compute the 6-month spot rate, then the 1-year spot rate, then the 18-month spot rate, then the 2-year spot rate, . . ., then the 29½-year spot rate, then the 30-year spot rate. That’s why the process is called bootstrapping: you have to calculate the rates one at a time, in order, just as you have to lace boots one eyelet at a time, in order.
Yes, the yield on a zero is the spot rate for that payment.
Yes, if a bond’s coupon equals its YTM, then it sells at par, and vice-versa.
My pleasure.
Thanks a ton!
Where do we get the first 6 month spot rate and the other par yields from? Auction of securties?
Is it possible to have different values for, lets say yield on a 2 year zero coupon bill (Year 2 spot) and the year 2 spot rate calculated using bootstrapping.
You are a legend magician!
You’re welcome.
The 6-month spot rate is the same as the 6-month par rate. If they auctioned 26-week T-Bills, it would be the YTM on those securities.
Not for long: arbitrage.
You flatter me.
Crystal clear so far. I am trying to understand the usages of the par and spot curves.
2… A side question but related: I think the Z-spread is a superior measure of gauging a bond than nominal spread. Is this correct, or do both guide us to the same conclusion?
Cool!
Correct.
I think that this is an overstatement: the spot curve and the par curve contain exactly the same information, merely in different forms. While it is true that the spot curve is used directly to calculate the Z-spread, the spot curve and the par curve are used equally to value bonds.
It is. The nominal spread considers only a single point on the (par) yield curve; the Z-spread accounts for the entire term structure of interest rates.
How would I value a 5 year 5% coupon rate corporate bond that pays coupon semi-annually using the par curve, when:
the bond was issued at par
the bond was issued at discount
the bond was issued at premium
It’s the same process under all three circumstances: discount the cash flows at the 5-year par rate. Remember that the par rate is the YTM for a 5-year bond, irrespective of the coupon rate. If the bond were issued at par, the par rate (YTM) will be 5%. If the bond were issued at a discount, the par rate (YTM) would be higher than 5%; if the bond were issued at a premium, the par rate (YTM) would be less than 5%.
Good, I have a real life question: Do we use the treasury spot rate or the swap spot rates to value fixed income securities - like corporate bonds etc. We study in level II that swap spot rate is superior and more favored. Can you explain why?
I’ve only seen Treasury rates used in practice, but I’d imagine that some people use swap rates, or LIBOR rates.
Swap rates are more difficult (for governments, for example) to manipulate artificially. The same was thought to be true of LIBOR rates, until two years ago (look here).
Swap rate is the fixed rate that the dealer pays but why is it also called the LIBOR rate that is floating?
I didn’t mean that swap rates were LIBOR rates (though I can see how what I wrote can be misinterpreted that way); what I meant was that some people may use either swap rates or LIBOR rates instead of Treasury rates.