 # 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

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.

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.

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

Interesting!