Duration, Convexity, and Price Approximation (25 points) A specially designed 4-year asset called XYZ generates a series of cash flows as follows (Table 1). Assume the yield to maturity is 4.75% and the interests are accumulated quarterly (i.e., quarterly compounding). 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 3.75 4 CF 150 300 450 700 850 1000 1500 2000 2500 3000 4000 8000 9000 12000 15000 20000 (1) Calculate the price of Asset XYZ (i.e., the present value). (2) Calculate Macaulay duration for Asset XYZ. (3) Calculate modified duration for Asset XYZ. (4) Given the duration you calculated in (3) and convexity 11.8739, estimate the relative price change of Asset XYZ for a 250 basis points decrease in yield. Then approximate the new price of Asset XYZ given a 250 basis points decrease in yield. (5) Comparing with the actual price of Asset XYZ with 250 basis points yield decrease, is this approximation a good one?