A 10-year sold-at-par German bonds yield to maturity (YTM) is near zero. According to the WSJ calculation, at a yield (i.e., YTM) of 0.09%, more than 11 years worth of income would be wiped out if the 10-year bond drops in price by just one point (i.e., 1%). Yields wouldnt even have to rise that much: a move one point lower (in price) equates to only a 0.1-percentage-point rise in the yield, to 0.19%. For simplicity, assume that the German government bond is paying annual coupons.

a) What is the Macaulay duration of the bond approximately? (Note: No calculation needed here. Please simply explain your rationale to estimate the Macaulay duration. The precise calculation of Maucaulay duration is required in Question (c) below.) What about its modified duration approximately? Please explain.

b) Assume that this bonds convexity is 320. If the yield increases by 50 basis points (0.5%), how much is the percentage bond price change based on linear rule with convexity adjustment?

c) If we use the Duration Formula to do the calculation (Recalled Some Formulas for Duration that we discussed to deal with long-maturity bonds in the 1st slide of Topic #4 Interest Rate Risk), what is the precise calculation result of the Macaulay Duration?