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ADMS4504 3.0 Assignment #1 Page 1 AP/ADMS 4504 3.0 Fixed Income Fall 2010 Assignment #1 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 October 26 , 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 (8 marks) A company issues a 5-year step-up note rating AA+/Aa2 paying semi-annual coupons. The coupon rate starts at 3.45% and goes up by 25 bps every year. The issue sells at par (i.e. \$100). (a) What is the BEY of this note? (2 marks) (b) Use a 20 bps rate shock to approximate the duration of the note. What is the approximate dollar price change if the yield declines by 100 bps? (2 marks) (c) What is the exact dollar price change if the yield declines by 100 bps? Comment on the findings. (2 marks) (d) Comment briefly (in no more than half a page) on the different risks associated with investing in this note. (2 marks) Solution (a) The step-up note price is given by: n n k k k y y C P ) 1 ( 100 ) 1 ( 100 1 0 + + + = = = . 225 . 2 ; 10 . 2 ; 975 . 1 ; 85 . 1 ; 725 . 1 10 9 8 7 6 5 4 3 2 1 = = = = = = = = = = C C C C C C C C C C We solve for the BEY either using the Solver in Excel or the CF functions on a financial calculator. The BEY is equal to 3.9306%. (b) The duration estimate with a rate shock of 20 bps is given by:

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AP/ADMS4504 Winter 2010 Assignment #1 Solutions Page 2 525 . 4 002 . 0 100 2 10 . 99 91 . 100 ) )( ( 2 0 * = × × = Δ = + y P P P D The approximate dollar price change for a 100 bps decline in the yield (i.e. 2.9306%) is simply 525 . 4 %) 1 ( * 0 = × × = Δ D P P . (c) Using the price formula in (a) with a yield of 2.9306%, the new price is \$104.642, thus the exact dollar price change is \$4.642. There is a small difference with the result in (b) because duration is a better measure for small rate shocks while 100 bps is not a small shock. (d) The note presents the following risks: Interest rate risk with duration of 4.525 years, yield curve risk, a very small default and credit risk because it is rated AA+/Aa2, reinvestment risk, liquidity risk, event risk and inflation risk (see textbook for more details on each risk).
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