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Solution_for_probelm_5_in_tutorial_8

Solution_for_probelm_5_in_tutorial_8 - Problem 5 dividend...

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Problem 5: dividend is increasing in 𝑔 = 1.04 , interest rate 𝑖 = 0.08 Calculate the Macaulay duration (MD). Solution: According to definition 𝑀𝐷 = 𝑘𝑣 𝑘 𝑔 𝑘−1 𝑘=1 𝑣 𝑘 𝑔 𝑘−1 𝑘=1 = 𝑘𝑣 𝑘 𝑔 𝑘 𝑘=1 𝑣 𝑘 𝑔 𝑘 𝑘=1 = 𝑘𝑣 𝑗 𝑘 𝑘=1 𝑣 𝑗 𝑘 𝑘=1 = � 𝑘𝑣 𝑗 𝑘 𝑘=1 × 1 − 𝑣 𝑗 𝑣 𝑗 , 𝑤ℎ𝑒𝑟𝑒 𝑣 𝑗 = 𝑣𝑔 Consider the function 𝑆 ( 𝑥 ) = 𝑘𝑥 𝑘−1 𝑘=1 , then � 𝑆 ( 𝑡 ) 𝑑𝑡 𝑥 0 = � � 𝑘𝑥
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