1. Duration, Convexity, and Price Approximation (25 points) A specially designed financial asset called XYZ generates a series of cash flows as follows (Table 1). Assume the yield to maturity is 2.75% and the interests are accumulated quarterly (i.e., quarterly compounding). Table 1 t (year) 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 CF ($) 100 100 200 200 300 300 400 400 500 500 1000 1000 5000 10000

(1) Calculate the price of Asset XYZ with yield of 2.75% (i.e., the present value). (3 points) (2) Calculate the Macaulay duration and modified duration of Asset XYZ. (7 points) (3) Calculate the duration of Asset XYZ by changing the yield up and down 25 basis points with the following formula: (5 points) Duration= (P_--P_+)/(2P_0 (y)). (4) Calculate the convexity of Asset XYZ by changing the yield up and down 25 basis points with the following formula: (3 points) Con= (P_++P_--2P_0)/(P_0 (y)^2 ). (5) Using the duration you calculated in (3) and the convexity you calculated in (4), estimate the relative price change of Asset XYZ with 250 basis points decrease in yield. Then estimate the price of Asset XYZ with 250 basis points decrease in yield. (3 points) (6) Comparing with the actual price of Asset XYZ with 250 basis points yield decrease, is the estimation in (5) a good approximation? (4 points)

Little bonus question: (3 points) Calculate convexity for the asset using the formula Convexity=1/((1+y)^2m^2 ) _(n=1)^T[w_n(n^2+n)] where n is # of periods and m is # of compounding per year. The your solution closed to your answer in (4)?