AP/ADMS 4504 M&N Fixed Income Securities and Risk Management

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AP/ADMS 4504 M&N Fixed Income Securities and Risk Management Final Exam Solutions Winter 2022 All of the questions in this exam are independent. Question 1 (21 marks) (a) Use the following daily... yield observations to calculate a daily standard deviation of yields. The daily yield changes are assumed to be continuously compounded. Then construct a 4-day moving-average equal weight volatility forecast for Day 5, assuming that the average daily yield change is zero. Please do not annualize your volatility estimates. (7 marks) Day Yield (%) 0 6.8112 1 6.7881 2 6.8203 3 6.8066 4 6.8122 5 6.8216 Answer X  100[ln(6.7881%)]  0.3397, X 1 6.8112% 2 X  100[ln(6.8066%)]  0.2011, X  100[ln(6.8203%)]  0.4732, 6.7881%  100[ln(6.8122%)]  0.0822, 3 6.8203% 4 6.8066% and X 5  100[ln(6.8216%)]  0.1379. X  0.0305. 6.8122% (0.3397  0.0305)2  (0.4732  0.0305)2  (0.2011  0.0305)2 Variance  (5  1)  (0.0822  0.0305)2  (0.1379  0.0305)2 (5  1)  0.1002 percentages squared, standard deviation   0.3166%. For Day 5, the 4-day moving-average uses the yield changes on Days 2, 3, 4, and 5. Assuming a zero average daily yield change, i.e., , the moving- average daily variance on Day 5 is computed as (in percentages squared): 0.47322  (0.2011)2  0.08222  0.13792  4  1 0.096711. The daily standard deviation on Day 5 is:  31.0984%. (b) Assume normally distributed yield changes. The daily standard deviation of yields is 1.5179%. With a probability of 95%, the range for future annual yields is [3.12%; 8.88%]. What is the 68.3% confidence interval of future annual yields? There are 250 trading days in a year. (5 marks) Answer [Show More]

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