(1) Duration approximation. The effective duration of the pool was reported by the state auditor as 7.4 years in December 1994. This high duration is the result of two factors: the average duration of individual securities of 2.74 years (most of the securities had a maturity below 5 years), and the leverage of the portfolio, which was 2.7 at the time. In 1994, interest rates went up by about 3%. Compute the loss predicted by the duration approximation and compare your result with the actual loss of $1.64 billion. You can use the formula AP = -D*(AY/(1+Y))*P Or use the effective duration format and suppose the effective duration of the pool was 7.4 years. Then the formula is AP = -D*Ay*P Predicted Loss = (2) Computation of portfolio VAR. The yields data file contains 5-year yields from 1953 to 1994. Using this information and the duration approximation, compute the portfolio VAR as of December 1994. Risk should be measured over a month at the 95% level. Report the distribution and compute the VAR: - using a normal distribution for yield changes (Delta-Nomial method), and - using the actual distribution for yield changes (Historical-Simulation method). Compare the VAR obtained using the two methods. a. Delta-Normal method: AP Assume 7.4 years is the effective duration, and using the formula\" r = = - D * Ay to calculate monthly return from the excel file, and then find out the descriptive statistics: the mean for the monthly return on 5-year Treasury issues is the stande deviation is Therefore, the VAR(1month @ 95%) = VAR(1year@95%) = b. Historical simulation method Sorting the returns data from a) on the excel sheet, since there is a total of 504 returns observation, 5% of 504 is 25.2. So using the 25th lowest return as the threshold, its monthly return is VAR(1month@95%) VAR(1year@95%) =