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ADMS4504 3.0 Assignment #1 Page 1 AP/ADMS 4504 3.0 Fixed Income Fall 2010 Assignment #2 Solution Instructions: (1) This assignment is to be done individually . You must sign and submit the standard cover page supplied as the last page of this assignment. (2) This assignment is due on December 7 , 2010. (3) The work can be typed or handwritten. If it is handwritten and too difficult to read due to messiness and poor handwriting, it will receive zero credit. (4) You must show all details of your work to receive full credit. (5) This assignment contains 5 questions and carries a total of 40 points . Question 1 – Volatility Forecast (8 marks) The following table shows the daily yields for the past 31 days ( note: the table is also provided as an excel sheet Assignment2-Q1-Data.xls ). We assume that the daily changes are continuously compounded. Day 0 4.4548% Day 1 4.6733% Day 11 4.9635% Day 21 4.4523% Day 2 4.7119% Day 12 4.8092% Day 22 4.6470% Day 3 4.6002% Day 13 4.6953% Day 23 4.7757% Day 4 4.6793% Day 14 4.8121% Day 24 4.5458% Day 5 4.8615% Day 15 4.7429% Day 25 4.4397% Day 6 4.9468% Day 16 4.8378% Day 26 4.3307% Day 7 4.7503% Day 17 4.6868% Day 27 4.2366% Day 8 4.7266% Day 18 4.7736% Day 28 4.1120% Day 9 4.5893% Day 19 4.6957% Day 29 4.0105% Day 10 4.4304% Day 20 4.5673% Day 30 3.8827% (a) We assume an equal weight for all days and a zero 10-day moving average. Use a 10-day moving window to forecast the volatility for days 11-31 (e.g. for day 11 we use days 1-10; for day 12, we use days 2-11…). Show the general mathematical formula used even if you use Excel. (3 marks) (b) We assume a weight equal to [3.0872 x (0.7) k-1 ] where k = 1, 2,…,10 respectively for the most recent day, the second most recent day, … until the farthest day in the moving window ( note that the weights add up to 10 ). Use this weighted 10-day moving window to forecast the volatility for days 11-31 as in (a). Show the general mathematical formula used even if you use Excel. (3 marks)

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AP/ADMS4504 Winter 2010 Assignment #1 Solutions Page 2 (c) Draw the 10-day volatility forecasts computed in (b) and (c) on the same graph. Comment briefly on the two forecasting methods in light of the graph. (2 marks) Solution (a) Assuming that the m-day moving average is zero, the forecast equation for Day( t +1) volatility is: = + = + m i i t X m t 1 2 1 1 1 ) 1 ( σ where = 1 ln k k k y y X . For m = 10, and for example the volatility forecast for Day 11, we have: () % 1211 . 3 ... 9 1 1 10 1 ) 11 ( 2 1 2 10 10 1 2 11 = + + = = = X X X i i See the table below for the other equal-weight daily volatility forecasts. Day Equal weight Declining weight Day 11 3.1211% 3.1657% Day 12 4.6409% 7.1468% Day 13 4.7509% 6.2584% Day 14 4.7507% 5.4160% Day 15 4.7872% 4.7514% Day 16 4.6400% 4.0474% Day 17 4.6507% 3.5755% Day 18 4.5739% 3.4984% Day 19 4.6117% 3.1177% Day 20 4.5390% 2.7656% Day Equal weight Declining weight Day 21 4.4807% 2.8054% Day 22 2.5408% 2.5474% Day 23 2.7171% 3.2756% Day 24 2.7520% 3.1647% Day 25 3.0996% 3.9117% Day 26 3.1613% 3.5502% Day 27 3.2007% 3.3022% Day 28 3.1086% 3.0317% Day 29 3.2061% 3.0754% Day 30 3.2669% 2.9558% Day 31 3.3142% 3.1047% (b) Assuming that the m-day moving average is zero, and a weighted scheme ( w i ) 1 i m , the forecast equation for Day( t +1) volatility is: = + = + m i i t i X w m t 1 2 1 1 1 ) 1 ( where m w m i i = = 1 . For m = 10, and for example the volatility forecast for Day 11, we have: % 1657 . 3 ) 7 . 0 ( ... (0.7) 9 3.0872 (0.7) 1 10 3.0872 ) 11 ( 2 1 9 2 9 2 10 10 1 2 11 1 - i * = + + = = = X X X X i i See the table above for the other declining-weight daily volatility forecasts.

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