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These three sources all say that the bond roll-down effect is negative if the bond is trading at a premium:

It seems to me this is mixing up roll-down and pull-to-par. As long as the yield curve is not inverted (i.e. is upward sloping to the right), then as time passes, the yield of the bond decreases. Doesn't that mean that roll-down (isolated from the pull-to-par effect) has a positive effect on bond price, regardless of whether the bond is at a premium or discount?

If a premium bond's price is declining over time with no change to the yield curve, couldn't that simply mean that the pull-to-par effect (negative) is stronger than the roll-down effect (positive)?

And, if the yield curve is steep enough, couldn't that make the roll-down stronger than pull-to-par, meaning that a premium bond's price could increase?

Or, since all three sources above agree, maybe I'm just missing something important. What is it?

Quote from the first source above:

Roll-down return works in two ways. The direction depends on whether the bond is trading at a premium or at a discount to its face value.

If the bond is trading at a discount, the roll-down effect will be positive. This means the roll-down will pull the price up towards par. If the bond is trading at a premium the opposite will occur. The roll-down return will be negative and pull the price of the bond down back to par.

Thanks. This is my first question in this community.

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  • $\begingroup$ Fwiw, I agree with you. Roll down and pull to par are different concepts. But a lot of semi-quantitative sources throw these terms around quite loosely. $\endgroup$
    – dm63
    Commented Oct 6, 2023 at 15:40
  • $\begingroup$ @dm63 Thanks. It seems pretty bad to throw the term around loosely on the very page that they're defining it, especially since those are the main search results for the term. Another problem might be that all these sources basically copy each other. $\endgroup$
    – B R O
    Commented Oct 6, 2023 at 16:11
  • $\begingroup$ Roll-down, cost-of-carry and potentially even pull-to-par are often very crudely defined. In my book on IR derivatives I define these concepts so that I can use them appropriately without ambiguity. Roll-down is a market-movement scenario where the future curve is the same curve as the spot curve but observed from that point in time. Since it is arbitrarily determined from a curve shape you can arbitrarily construct any spot curve to produce any roll-down effect. Whether the bond starts at a premium or not. If it doesn't just raise its coupon. The answer is False. $\endgroup$
    – Attack68 ♦
    Commented Oct 7, 2023 at 15:14

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