Question: 4. Your colleague Roger calculated a set of key rate 01s (KR01) for a bond and shared them with you, below, but he forgot to include the bond's specifications. He informs you that, although he selected only four key rates (two, five, 10 and 30 year), neighboring rates are shifted in a linear (interpolation) manner such that the entire term structure is characterized by the model. Here are the four key rates (KR01s), along with the bond's price of $94,000.00. Which is nearest to the bond's modified duration? a. 7.5 years b. 12.1 years c. 18.6 years d. 23.0 years Answer: 4. B. 12.1 years The sum of KRO1s will approximate the bond's DV01 (it will not be exact as a simultaneous shift of the key rates is not identical to a parallel shift--specifically, neighboring rates will shift less than one basis point--but it will be a good approximation). In this case: Estimate of bond's DV01 = 3.09 + 9.44 + 52.01 + 49.19 = $113.73; therefore, Since DV01 = Price * Modified Duration / 10,000, an estimate of bond's modified duration = DV01 * 10,000 / Price = $113.73 * 10,000 /$94,000 = 12.099 years ... which is also the sum of the individual key rate durations, where, for example key rate duration [2 years] = 3.09*10,000/$94,000 = 0.33 years.