The 1yr, 2yr, 3yr, 4-yr, and 5yr spot rates are 456, 556, 5%, 5.5%, and ll, respectively. All the rates are discretely compou nded. Consider a 5yr, 10% annual coupon paying bond. Assume all the bonds have a face value of $1,000. [Note: it does not matter what face value you assume to answer the questions below] [a] Calculate the duration and convexityr of this bond. [5 points] [b] HOW many 2yr and ityr zero coupon bonds should you buy or sell to immunize a portfolio consisting of 5,000 of these coupon bonds? Use duration and convexity to answer this question. [5 points] {c} Do Principal Components Analysis of I"Interest Rate Data." [5 points] [d] What are the factor durations of the coupon bonds with respect to the level and the slope factor? [5 points] {c} How many 2yr and day zero coupon bonds should you buy or sell to immunize a portfolio consisting of 5,000 of the coupon bonds? {5 points} [f] Using regrsion analysis, find out the effect of the level, slope, and curvature factors together have on the 1yr, 2yr, 3yr, ailyr, and 5yr rates. [5 points} [g] Just like above, use the 2yr and 4yr zero coupon bonds to immunize the portfolio. [5 points} [h] Why is it better above to use Principal Components Analysis than Regression Analysis to immu nize the bond portfolio against interest rate changes? [Read your textbookto answer this question} [5 points]