Question, is it right to say that : “The roll down return demonstrates how the price of a bond typically moves closer to par regardless of yield curve changes over the strategy horizon.”

Answer : No. The roll down return is equal to the bond’s percentage price change assuming an unchanged yield curve over the strategy horizon. The roll down return results from the bond “rolling down” the yield curve as the time to maturity decreases. As time passes, a bond’s price typically moves closer to par.

Anyone can explain the difference ? If the bond roll down the yield curve, it means that maturity decreases (time passes) and it should be moving closer to par. I don’t get the difference between the question and the answer.

Beginning of next year without yield curve change the expected value is 97.5 per 100.

Roll down yield (97.5-95)/95.

How do you price a security? Theoretically it is the present value of cash flows. I’m going to leave this up to you now, why would the price of the bond move towards par?

Btw the opposite is true as well, if the bond were priced at a premium rather than a discount. Remember that is determined by the coupon rate and the market (irr) rate.

Bonds moving towards par is called “pull to par” not roll down. I don’t know why the answer discusses it, maybe to help explain why it’s not the appropriate answer?

Anyways, roll down is simply the capital appreciation that comes from the bond rolling down the yield curve assuming the yield curve doesn’t change.

roll down return is the price change return over a period of time given an unchanged yield curve. That has nothing to do with the fact that bond prices move towards par over time (all else equal).

The question says regardless of yield curve changes. The answer says assuming no changes. I.e. if there are significant changes in the yield curve, the bond’s price doesn’t move in the same linear fashion towards par.

If the yield curve shifts, the IRR (market rate) changes. If that goes up, your bond price could decrease regardless of the fact that its approaching maturity. Think back to the way you calculate the price, sum of Coupon_{t}/(1+IRR)^{t}_{ }+ Par/(1+IRR)^{t}.

If IRR is unchanged that roll down return shows the increase of price as it moves to maturity (the par payment is the biggest payment so the less periods you’re discounting it by the greater the price if the curve is unchanged). However if IRR increases by 10%, it might not matter that there’s one less period that you’re discounting by because you discount rate is so much higher, or if it decreases by 10% the bond might significantly increase in value faster than anticipated. So the whole key is that rolldown return is the return from an unchanged yield curve.

PreDRaR66 is right, the key to this answer is that " regardless of yield curve changes" is wrong and it should be “assuming an unchanged yield curve”. Pull to par and roll-down are different but it’s about the yield curve assumption here.