# 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 The weighted average means.

Simplify 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 / 1.011 = \$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 / 1.022 = \$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 / 1.0253 = \$92.8599.

A 3-year, annual pay, 6% coupon, \$1,000 par bond will have a value today of:

\$60/1.01 + \$60/1.022 + \$1,060/1.0253 = \$1,101.39.

That bond has a YTM of 2.4531%, because:

\$60/1.024531 + \$60/1.0245312 + \$1,060/1.0245313 = \$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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S2000magician wrote:

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 The weighted average means.

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

Julio77 wrote:
S2000magician wrote:
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 The weighted average means.

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 a weighted average.

When you wrote The weighted average, you made it sound as if there’s only one.  That’s what I was questioning.

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

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

S2000magician wrote:

Julio77 wrote:
S2000magician wrote:
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 The weighted average means.

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 a weighted average.

When you wrote The weighted average, you made it sound as if there’s only one.  That’s what I was questioning.

Oh my bad, yes is a weighted average