# Yield Spot Rate Curve

Hello, I am not sure if this exact question is discussed earlier in the forum. Can anyone help me understand the below: a) What is the difference between Spot Rate Curve and Yield Curve? b) I have read yield spot rate curve must be used to value bonds. Why can’t we use yield curve?

By any chance do you mean “zero coupon” curve rather than “spot rate” curve?

Spot rate curve and zero-coupon curve I would say are essentially the same thing (although if I constructed such a Treasury curve from strips I would call it a zero-coupon curve and if I constructed it from bootstrapping I would call it a spot rate curve and they have to be close but they will surely be different). Anyway, a yield curve plots yield to maturity against time to matrurity for some class of similar bonds (like US Treasuries). A spot rate curve plots spot rates which are like zero-coupon bond yields against time to maturity. You should be able to calculate either of these from the other one. Note that, say, the 10-yr ytm of a Treasury bond can be either higher or lower (usually) than the 10-yr spot rate. If you don’t know why, you should read that section again until you do because it’s an important topic in CFA studies.

If both are Yields aganist time to maturity, why the 10-yr ytm of a treasury bond should be different from 10 yr Spot rate?.(if the difference is in the way you construct it)…

Also, if both are same, why yield curve can not be used for valuation of bonds…

The yield curve can be used in the valuation of bonds, just not in the straightforward way of the spot rate curve. Look up the difference between ytm and zero-coupon yield. Please.

The yield curve is not accurate to valuate bonds, because it gives one yield for bonds with the same maturity (but due to different cashflow/coupon scheme this can vary). So the spot rate curve is more appropriate to value bonds, as it discounts the cashflows at a unique interest rate that is applicable to the time period, when the cashflow is received. It is derived/bootstrapped from (theoretical) zero-coupon bonds, just as Joey says.

Zero coupon curve is more appropriate to value bonds. Why? Because everyone in the market is pricing it using the zero coupon curve, and if you price it differently (using the yield curve), you will be arbed out in the market. Now, why is everyone in the market using the zero coupon curve? Because you can replicate the bond cashflows with a portfolio of Treasury strips and create a risk free arbitrage opportunity.

First off, I can make an arbitrage-free yield curve from Treasury strips. Since it contains exactly the same information as the spot rate curve from the strips, I can use it to price bonds exactly as well as I can use the spot rate curve. You should check out that risk-free arbitrage opportunity - there are all kinds of issues related to bond pricing, liquidity premia, non-fungibility of principal, repo rates, etc. that make this not an especially easy game. Further, neither the yield curve or the spot rate curve is directly observable. For example, suppose we have a 5-year on-the-run bond trading at par with a coupon of 5% and a 30-yr bond with 5 yrs left to maturity with a coupon of 13%. These bonds will have very different YTM. In any event, all that we can observe are bond prices which are affected by all kinds of issues like liquidity, repo rates, futures deliverability, strippability, etc… and we need to estimate either curve. Everyone in the market is not pricing bonds using “the zero coupon curve” they are pricing bonds in 57 million different ways just like everyone is pricing stocks in 57 million different ways. That’s one reason we have liquidity in capital markets.