I understand that the Price/Yield curve relationshp of a bond is convex. The line tangent (slope) to any point on the price/yield curve is the duration. And this duration changes as you move along the curve. The change in duration for change in yield is the convexity.

Does duration change linearly? I would think no because some parts of the price/yield curve may be steeper than other parts but I’m not really sure. If you’re on the flat part of the price/yield curve, you may get small changes in duration even for larger changes yield. I’m not sure…

Duration _ **is not** _ the slope of the price/yield curve, nor the negative of that slope. **Dollar duration** is the (negative of the) slope of the price/yield curve, because it gives the *change in price* for a *change in yield*. (Effective) duration gives the _ **percentage** _ change in price for a change in yield; if you must think of it as the slope of a line tangent to something, it’s the (negative of the) slope of a line tangent to the ln(price)/yield curve (i.e., the natural logarithm of price vs. yield). You probably don’t want to think of it that way.

Yes. And yes.

It doesn’t. For a normal bond, the plot of convexity vs. yield looks much like the plot of duration vs. yield: larger at low yields, smaller at high yields.