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I read the following paragraph from investopedia: https://www.investopedia.com/terms/c/convexity.asp If a bond's duration increases as yields increase, the bond is said to have negative convexity. In other words, the bond price will decline by a greater rate with a rise in yields than if yields had fallen. Therefore, if a bond has negative convexity, its duration would increase—the price would fall. As interest rates rise, and the opposite is true.

If I understand correctly, for a vanilla bond with coupon, its duration is always a negative value, right? When investopedia says "If a bond's duration increases as yields increase", it is saying the absolute value of duration increases, is that right?

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    $\begingroup$ Duration is expressed as the inverse for conveience or you’d see a lot of negative signs. A normal bond therefore has “positive” duration which means prices rise as yields fall. Price Change=-1*duration*rate change $\endgroup$
    – Bond wiz
    Commented Jun 10, 2020 at 20:56

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If you're long a normal Vanilla bond, you're always long Duration and long Convexity. You get negative convexity if you are short the bond.

Convexity has an effect on the rate at which you make or lose money:

Negative convexity (you are short the bond) means that the rate at which you lose money increases as yields decrease. And the rate at which you make money decreases as yields go up. So being short convexity is not as good as being long convexity.

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