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Unformatted text preview: AP/ADMS4504 Assignment #2 Solutions Winter 2010 Question 1 Pricebased vs. yieldbased volatility (16 marks) This question has two independent parts, (a) and (b). (a) Use the daily yields in the following table to compute a daily standard deviation of yields. Next annualize the daily standard deviation just calculated first using 365 calendar days, then using 250 trading days in a year. Finally, construct a 3day moving average equal weight volatility forecast for each day in the period from Day 4 to Day 16, assuming that the expected value of the daily change in yield is zero. Please note : for this question 1) you may attach your Excel worksheet to your assignment, 2) please write down clearly the formulas used, and 3) keep at least 6 decimal places in both your calculations and your final answers. (9 marks) Day Yield (%) 0 3.750 1 3.752 2 3.749 3 3.746 4 3.744 5 3.748 6 3.751 7 3.752 8 3.750 9 3.751 10 3.747 11 3.746 12 3.749 13 3.748 14 3.751 15 3.753 16 3.754 Answer AP/ADMS4504 Winter 2010 Assignment #2 solutions In the table below: in Column (3), X t = 100 [ln(y t /y t1 )], 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: (0.106608)/16 = 0.006663 (there are 16 observations in our sample, so T, the sample size, is equal to 16). (1) Day (2) Yield (%) (3) X t (%) (4) (percentages squared) 0 3.750 1 3.752 0.053319 0.002177 2 3.749 0.079989 0.007509 3 3.746 0.080053 0.007520 4 3.744 0.053405 0.003608 5 3.748 0.106781 0.010024 6 3.751 0.080011 0.005380 7 3.752 0.026656 0.000400 8 3.750 0.053319 0.003598 9 3.751 0.026663 0.000400 10 3.747 0.106695 0.012850 11 3.746 0.026692 0.001113 12 3.749 0.080053 0.005386 13 3.748 0.026677 0.001112 14 3.751 0.080011 0.005380 15 3.753 0.053305 0.002175 16 3.754 0.026642 0.000399 It follows that the variance of daily yields is: squared. s percentage 004602 . 1 16 069029 . Variance = = The standard deviation of daily yields is thus: %. 067838 . 004602 . = The annual standard deviation is either: %, 296035 . 1 365 % 067838 . = or %. 072613 . 1 250 % 067838 . = Finally, as to the 3day movingaverage volatility forecast, we will use Day 4 to illustrate the calculations. The volatility forecast for Days 516 can be obtained similarly. Page 2 AP/ADMS4504 Winter 2010 Assignment #2 solutions To compute the daily volatility on Day 4 using a 3day movingaverage window, we need to use the yield changes on Days 24. In particular, using the X t values in Column (3) of the table on Page 2 above, the movingaverage daily variance on Day 4 is calculated as: squared, s percentage 007829 . ) 1 3 ( ) 053405 . ( ) 080053 . ( ) 079989 . ( 1 T X Variance 2 2 2 T 1 t 2 t = + + = = = where the expected (mean) daily yield change is assumed to be zero....
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 Fall '10
 Nabil

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