An easy way to analyze the impact on convexity is to think about the impact on duration. If the change causes duration to increase, it would cause the convexity to increase too, and if it causes the duration to decrease, it would reduce convexity as well.An increase in yields reduces duration, and therefore reduces convexity.
An increase in maturity increases duration, and therefore increases convexity.
An increase in the coupon rate reduces duration, and therefore reduces convexity.
An increase in duration increases convexity.
Therefore statements II and IV represent situations where convexity increases.
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