FIN 5530: Final Exam - Advanced Financial Risk Management and Decision Analysis Final Exam Dr. Abraham FIN 5530 Answer all questions 1. The DEAR for a bank is $6,500. What is the VAR for an 8 - day period? A 16 - day period? Why is the VAR for a 16 - day period no t twice as much as that for a 8 - day period? VAR for an 8 - day period Value at risk (VAR) = DEAR x √ N = 6,500 x √ 8 = 6,500 x 2.828 = $18,384.77 VAR for a 16 - day period Value at risk (VAR) = DEAR x √ N = 6,500 x √ 16 = 6,500 x 4 = $26,000 The reason that VAR 16  (2 x VAR 8 ) is because [16] ½  (2 x [8] ½ ). The interpretation is that the daily effects of an adverse event become less as time moves farther away from the event. 2. Bank Y has an inventory of 14 - year zero - coupon bonds with a face value of $400 million. The bonds currently are yielding 8.5 percent in the over - the - counter market. a. What is the modified duration of these bonds? Modified duration = (MD) = D/(1 + r) = 14/(1.085) = 12.9032 . b. What is the price volatility if the potential adverse move in yields is 25 basis points? Price volatility = (MD) x (potential adverse move in yield) = (12.9032) x (.0025) = 0.03225 or 3.225 percent . c. What is the DEAR? Daily earnings at risk (DEAR) = ($ Value of position) x (Price volatility) Dollar value of position = $400m. / (1 + 0.0 85 ) 14 = $12 7 , 656 , 712 . Therefore, DEAR = $ 12 7 , 656 , 712 x 0.03225 = $ 4 , 116 , 928 3. X Inc., a publicly traded manufacturing firm in the United States, has provided the following financial information in its application for a loan. All numbers are in thousands of dollars.