Question about YTM

[Dermot81]

I have a question. In the Schweser notes it says, "The yield to maturity assumes cash flows (from coupon payments) will be reinvested at the YTM."

This isn't making any sense to me. I thought the all of the coupon payments were being discounted. Where in the equation for YTM does it show the coupon payments being compounded and reinvested? There is no compounding going on in the equation.

I thought the YTM is just like an IRR problem, with different cash flows (coupons) being discounted to the present along with one lump sum (par) at the end.

Thanks in advance!

 

[exemplaria]

You are correct when you say the YTM is like the IRR. When using IRR, CF are assumed to be reinvested at the IRR. When using NPV, CF are assumed to be reinvested at the discount rate. I know it's not obvious, because it doesn't seem to be a part of the equation, but it is true.

Look at it like this: Assume a 10% bond at par maturing in 2 years. Therefore, you pay $1000 now, get $100 in one year, and $1100 in 2 years. This bond has a YTM of 10%. Now assume you don't reinvest the $100 received at the end of year 1. In 2 years you would have $1200. But if you discount the $1200 back 2 years to a present value of $1000, you get a rate of 9.54%. You need to reinvest that $100 at 10% to achieve the YTM of 10%. Doing this, in 2 years you'd have $1210. Discount that to a PV of $1000, and you have a rate of 10%. Clear as mud, right? Hope that helps.

 

[Dermot81]

Very interesting. Good example.

Thanks, makes sense now!