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I think I figured it out. Sinking fund structures experience negative convexity when they are priced above par, but when priced below par they experience positive convexity. This would be because the issuer is obliged to pay back part of the principal at par, so this would benefit the holder when the price is at a discount to par. In other words, the sub-par bond holder would receive par for part of his bonds, making them more valuable (i.e. supporting the price). Convexity must turn negative above par for the same reason.

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