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AP/ADMS4504A Fall 2009 Assignment #2 Solutions 20 4.692 21 4.687 22 4.521 23 4.435 24 4.424 25 4.440 26 4.516 27 4.448 28 4.427 29 4.390 30 4.457 Answer In the table below: in Column (3), X t = 100 × [Ln(y t /y t-1 )], where y t is the daily yield recorded in Column (2); and Column (4) contains the values of 2 t ) X X ( , where X , the sample mean, is calculated as: (1.742717)/30 = 0.058091 (there are 30 observations in our sample, so T, the sample size, is equal to 30). (1) Day (2) Yield (%) (3) X t (%) (4) (Percentages squared) 0 4.380 1 4.393 0.296364 0.056774 2 4.430 0.838722 0.609385 3 4.428 -0.045157 0.010660 4 4.522 2.100636 4.171990 5 4.648 2.748265 7.237034 6 4.656 0.171969 0.012968 7 4.595 -1.318795 1.895816 8 4.562 -0.720763 0.606614 9 5.208 13.243478 173.854437 10 4.454 -15.639334 246.409144 11 4.404 -1.128935 1.409031 12 4.659 5.628761 31.032369 13 4.904 5.125037 25.673938 14 4.820 -1.727727 3.189146 Page 2
AP/ADMS4504A Fall 2009 Assignment #2 Solutions 15 3.933 -20.337144 415.965597 16 4.907 22.126027 486.993782 17 4.650 -5.379554 29.567981 18 4.814 3.466112 11.614607 19 4.766 -1.002096 1.123997 20 4.692 -1.564845 2.633921 21 4.687 -0.106621 0.027130 22 4.521 -3.605951 13.425205 23 4.435 -1.920559 3.915057 24 4.424 -0.248335 0.093897 25 4.440 0.361011 0.091761 26 4.516 1.697227 2.686767 27 4.448 -1.517209 2.481570 28 4.427 -0.473240 0.282313 29 4.390 -0.839293 0.805297 30 4.457 1.514667 2.121613 Total 1.742717 1,469.9998 Sample mean 0.058091 It follows that the variance of daily yields is: squared. s percentage 689648 . 50 1 30 9998 . 469 , 1 iance var = = The standard deviation of daily yields is thus: %. 119666 . 7 689648 . 50 = The annual standard deviation is either: %. 021032 . 136 365 % 119666 . 7 = × Or %. 571807 . 112 250 % 119666 . 7 = × Finally, as to the 10-day moving-average volatility forecast, we will use Day 15 to illustrate the calculations. The volatility forecast for Days 16 - 30 can be obtained similarly. To compute the daily volatility on Day 15 using a 10-day moving-average

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