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We derive analytics of duration and convexity for the convertible puttable bond, which offers investors a significant upside potential embedded in the long call as well as downside protection of a long put. The inclusion of a long put in this bond makes the bond relatively more convex than a conventional pure bond, therefore, increasing both duration as well as convexity of this bond. We find that convexity of the convertible puttable bond is the highest when compared to other classes of convertibles as money managers pay a premium to acquire the convexity embedded in this hybrid financial instrument.