assignmnt1Sol

assignmnt1Sol - ACTSC445/845 ASSIGNMENT 1–SOLUTION. (1)...

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Unformatted text preview: ACTSC445/845 ASSIGNMENT 1–SOLUTION. (1) (10 points) A 5-year bond with semiannual coupons is redeemable at par. The annual effective yield is 7% and the coupons are 5% a year. Find the price of this bond per $100 par value. Is it sold at a discount or a premium? Solution 0.1. We have • 10 coupons ( n = 10 ), • F = C = 100 , • coupon rate r = 0 . 05 / 2 = 2 . 5% , • The yield to mature per payment period: i = 1 . 07 . 5- 1 = 0 . 03441 . The price is P = 2 . 5% × 100 × a 10 | i + 100(1 + i )- 10 = 2 . 5 × 1- i- 10 i + 100 × (1 + i )- 10 = 92 . 15 The bond is sold at a discount since P < 100 . This is expected since r < i . (2) (10 points) A corporate bond with face value 100 pays semiannual coupons at a coupon rate of 8% (annualized rate). The bond is priced to yield 6% compounded semiannually. The bond matures on June, 1 , 2008 and is purchased with a settle- ment date of Oct, 1 , 2003. Determine the full price of the bond as of the settlement date and the price quoted (clean price). (using Actual/Actual basis, i.e. actual days for holding the bond and actual days for each coupon period) Solution 0.2. • the number of total coupons in the future: 5 × 2 = 10 , • the number of days between last coupon day and today: 30( june ) + 31( july ) + 31( Aug ) + 30( sept ) = 122 • the number of days between last coupon day and next coupon day: 30( june ) + 31( july ) + 31( Aug ) + 30( sept ) + 31( Oct ) + 30( Nov ) = 183 • The value of the bond at the last coupon day = 4 a 10 | 3% + 100 × 1 . 03- 10 = 108 . 53 • Full price (dirty price) at 1 /Oct/ 2003...
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This note was uploaded on 10/30/2009 for the course ACTSC 331 taught by Professor David during the Spring '09 term at Waterloo.

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assignmnt1Sol - ACTSC445/845 ASSIGNMENT 1–SOLUTION. (1)...

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