YTM and Reinvestment Risk.

Hi, this has been at the back of my mind for a while now and i came across this question again:

Q: “Holding all other characteristics the same, the bond exposed to the greatest level of reinvestment risk is most likely the one selling at a premium.”

A: A bond selling at a premium has a higher coupon rate and, all else being equal, bonds with higher

coupon rates face higher reinvestment risk. The reason is that the higher the coupon rate, the more

dependent the bond’s total dollar return will be on the reinvestment of the coupon payments in order to

produce the yield to maturity at the time of purchase.

My confusion: Isn’t YTM the effective yield which one receives for holding the bond till maturity? Why should the lender/investor need to reinvest the coupons elsewhere? The YTM is already the return that one receives for investing in the bond.

It all depends on how you treat cash flows from an investment.

Some people consider them still to be part of the investment, so that the reinvestment income you earn on those cash flows is considered part of the total return on the original investment.

Other people conseder them to have been removed from the investment, so that the total return is calculated only on the value still remaining in the investment.

The former view seems more prevalent.

I would also love to hear more clarification on this if you happen to have time.

I thought I understood the topic well, but now I’m realizing I’m a little confused.

Supposing the market rate drops significantly after hold-to-maturity invester purchases a bond. Assuming he does in fact hold until maturity, will he not see the same bond return as he did at purchase time (ie. the bond’s effective rate or yield at time of purchase)??

But then I thought the YTM ASSUMES all coupons are reinvested?? Basically I’m wondering the difference between two investers, both holding to maturity, one invester re-invests coupons, while the other does not - and how that will affect their returns.


I think you are overthinking this. As coupon rate increases, you get a higher cashflow periodically to re-invest, and those big amounts of cashflows will have a big weight on your total overall return. Additionally, a premium bond tends to have a lower YTM. You re-invest your coupons at the YTM rate, so you get a lower YTM for all the bigger cash flows you receive, hence the higher re-investment risk.

Remember that a zero-coupon bond (t-bill for example) has 0 re-investment risk.

Am I just dumb? I thought coupon payment stayed the same regardless of the purchase price of the bond?