# Difference between YTM and Spot rate

I am confused with the difference between YTM and spot rate.

ex) Reading 35 Aribtrage-Free Valuation Framework #2

Why can’t we discount the cash flow to the YTM of 1.25%, 1.5%, 1.7% ?

I do not understand the part that 1) calculate each spot rate 2) discount with this number

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The YTM is The weighted average of each spot rate at different maturities. The spot rate is a single rate used to discount a coupon payment for a determined maturity and the yield to maturity is the rate that makes future cash flows equal to the bond market price

The YTM is a single interest rate used to discount all payments (coupons and principal) on a bond.

A spot rate is an interest rate used to discount a single payment (known as a spot payment).

A bond’s YTM is an average of the spot rates for each of the payments. I don’t know what

weighted average means.TheSimplify the complicated side; don't complify the simplicated side.

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Thank you for the definition.

Could you clarify more detail about the definition?

I am reading the curriculum and schweser notes, but it does not seem to have a concrete definition (or either I lack the knowledge to understand)

Suppose that the 1-year spot rate is 1%. This means that a payment of, say, $100 one year from today will have a present value of $100 / 1.01

^{1}= $99.0099.Suppose that the 2-year spot rate is 2%. This means that a payment of, say, $100 two years from today will have a present value of $100 / 1.02

^{2}= $96.1169.Suppose that the 3-year spot rate is 2.5%. This means that a payment of, say, $100 three years from today will have a present value of $100 / 1.025

^{3}= $92.8599.A 3-year, annual pay, 6% coupon, $1,000 par bond will have a value today of:

$60/1.01 + $60/1.02

^{2}+ $1,060/1.025^{3}= $1,101.39.That bond has a YTM of 2.4531%, because:

$60/1.024531 + $60/1.024531

^{2}+ $1,060/1.024531^{3}= $1,101.39.A spot rate applies to one payment at a given maturity. A YTM applies to all payments at all maturities.

Simplify the complicated side; don't complify the simplicated side.

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by weighted average I mean, that the YTM is going to be closer to the spot rate where you discount the most of the cash flow (ex. Principal), if the bond is a 3 year bond and the spots are 3%, 4% and 5% and the bond is bullet payment, the YTM is going to be between 3% and 5%, but closer to 5% cause the weight of the principal payment

It is certainly

weighted average.aWhen you wrote

weighted average, you made it sound as if there’s only one. That’s what I was questioning.TheSimplify the complicated side; don't complify the simplicated side.

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Oh my bad, yes is a weighted average