ADMS4504-Assignment2-Sample2-Sol

ADMS4504-Assignment2-Sample2-Sol - AP/ADMS4504 Assignment...

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Unformatted text preview: AP/ADMS4504 Assignment #2 Solutions Winter 2010 Question 1 Price-based vs. yield-based 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 3-day 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 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: (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 3-day moving-average volatility forecast, we will use Day 4 to illustrate the calculations. The volatility forecast for Days 5-16 can be obtained similarly. Page 2 AP/ADMS4504 Winter 2010 Assignment #2 solutions To compute the daily volatility on Day 4 using a 3-day moving-average window, we need to use the yield changes on Days 2-4. In particular, using the X t values in Column (3) of the table on Page 2 above, the moving-average 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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ADMS4504-Assignment2-Sample2-Sol - AP/ADMS4504 Assignment...

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