Question

"The second derivative of the bond price with respect to the yield is the rate of...

"The second derivative of the bond price with respect to the yield is the rate of change of the slope of the tangent line that is tangent to the curve on the bond price-yield map."

True or false?

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Answer #1
  • true. The bond curve is a function of bond price and bond yield . If bonds duration increases as yield increases, the shape of the bond will be concave. If yield increases (2% to 5%), the price falls ($100 to $80) .therefore, it will be negative sloping .Higher the coupon rate the lower the bonds convexity.
  • The first derivative is the slope of the Bond price-yield curve which is a tangent to the bond curve. It is the change in the Price per unit of yield. Also called as modified duration. MOD DUR = %age change in price / %age change in yield. MOD DUR=
  • Convexity is the rate of change of the modified duration. Therefore it is the rate of change of price per unit of yield with respect to yield. Convexity = .
  • Hence,The second derivate of the bond price with respect to the yield is the rate of change of slope of the tangent line that is tangent to the curve on the bond price yield map.
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