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L15_wk06_soln - ACST201 Financial Modelling Gail Curry...

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1 (c) Macquarie University 2015 1 ACST201 Financial Modelling Gail Curry Week 6 DISCOVERING DURATION Consultation Sachi 11 am-1pm Monday E4A 615 Colin 5 pm -6 pm Wednesday E4B 104 Syazreen 10 am-11 am Thursday E4B 104 Poon 12 noon- 1 pm Thursday E4B 104 email address for queries [email protected] (c) Macquarie University 2015 2 (c) Macquarie University 2015 3 About learning “Schools teach you to imitate. If you don’t imitate what the teacher wants you get a bad grade. Here, in college, it was more sophisticated, of course; you were supposed to imitate the teacher in such a way as to convince the teacher you were not imitating.” Robert M Pirsig, “Zen and the Art of Motorcycle Maintenance” (1974) Revision - Weighted average Twenty students sat a test which was marked out of 10. Their results are as follows: Score out of 10: 9 7 6 5 Number of students: 8 7 4 1 NOTE: with NO WEIGHTING the average of the scores is : 9+7+6+5 = 6.75 4 (c) Macquarie University 2015 4 Taking into account the weights where the weights are the number of students achieving these scores: Weighted average of the scores: (9 × 8)+(7 × 7)+(6 × 4)+(5 × 1) = 7.5 (8+7+4+1) (c) Macquarie University 2015 5 (c) Macquarie University 2015 6 Bonds: two types of risk (1) Reinvestment risk : risk that interest rates fall, so coupons must be reinvested at lower rates (2) Interest rate risk : risk that interest rates rise, causing the value (market price) of the investment to fall
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2 (c) Macquarie University 2015 7 n half-years Purchase date Sale date P 1 P 2 +c Outgo (purchase price P 1 ) Income (coupons, interest on reinvested coupons, sale price P 2 ) BOND HOLDING PERIOD c c c …... c c 1 2 n-3 n-2 n-1 n ..... 0 (c) Macquarie University 2015 8 BALANCING INTEREST RATE RISK & REINVESTMENT RISK Suppose you have just purchased a 10-year 8% T- bond, and the current yield is 9% pa (coupon rate & yield are both semi-annual) 10-year 8% T-bond, the current yield is 9% pa What is the bond’s purchase price? Purchase price = 4 a 20 + 100 v 20 at 4.5% = 52.0317 + 41.4643 = $93.496 (per $100 face value) (c) Macquarie University 2015 9 (c) Macquarie University 2015 10 Now suppose interest rates rise immediately, and then remain unchanged indefinitely, so that the reinvestment rate, and the sale yield if you want to sell the bond, are j 2 = 10% (c) Macquarie University 2015 11 What will be your HPY (in j 2 form) if you plan to sell the bond after: (a) 1 year? (b) 5 years? (c) 9 years? The sale price is the present value, at the sale yield rate (j 2 = 10%), of the remaining future cash flows – eighteen coupon payments of $4 each and the maturity amount of $100. Sale price (P) = 4 a 18 + 100 v 18 at 5% = 46.7583 + 41.5521 = $88.310..(per $100 face value) (c) Macquarie University 2015 12 If sell after 1 Year: the bond has nine more year to run.
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3 Each of the two coupons is reinvested, from the date it is received until the sale date, at the rate of j 2 = 10%. The accumulated value of the coupons at sale is: 4 s 2 at 5% = $8.200 Total accumulated value of the bond investment on sale date = accumulated value of re-invested coupons + sale price = 8.200 + 88.310 = $96.510 (c) Macquarie University 2015 13 If sell after 1 Year: the bond has nine more year to run.
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