# Quick Fixed Income questions

I’m having trouble understanding LOS 54. What exactly is the spot rate cuve? Also, what is the difference between YTM and a spot rate?

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schweser does do a good job of explaining those in the beginning. and these are repeated items from Level 1 book.

ill be more specific. this is from investopedia: A yield curve constructed using Treasury spot rates, rather then yields. The spot rate Treasury curve can be used as a benchmark for pricing bonds. This type of rate curve can be built from on-the-run treasuries, off-the-run treasuries or a combination of both. Alternatively, the Treasury curve can be calculated by using Treasury coupon strips. i know YTM is the rate at which the cf’s are discounted to match the current market price of the bond. how does that relate to spot rate?

spot rate is the rate prevailing today for a zero coupon bond with maturity same as the cash flow being valued. So for a 7 year 9% bond - you will need 14 spot rates for each coupon payment + a spot rate for the return of principal.

…so spot rates are like the “individual” cash flow discount rates to get the PV, lets say par = 1000 = 9/(1+s1) + 9/(1+s2)^2 + 1000/(1+s2)^2 while YTM is the same single rate used for each time period to get the PV? 1000= 1/(1+ytm) + 1/(1+ytm)^2

yep…you got it right… If you take individual rates to discount each cash flow, then you are using sport rates. Spot rate are drived from zero coupon bonds. for instance, the rate on a zero coupon bond for 2 years will be the spot rate for two years. On the other hand, YTM is the ‘single’ rate that makes the PV of a bond equal to its current price.

For further understanding, if you have listed all the spot rates for some period of time, say 8 years, you would have the zero-coupon rates for 1-yr, 2-yrs, etc. If you add a constant number of basis points (discovered by trial and error) to each one of those rates you would get the Z-spread which is the spot rate for, say, a corporate bond or any non-treasury bond. Another thing is that forward rates are spot rates for future periods, so the prevailing 1-yr spot rate 2 years from now is a forward spot rate.