2010SpringA1Sol

# 2010SpringA1Sol - ACTSC445/845 ASSIGNMENT 1SOLUTION. (1)...

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ACTSC445/845 ASSIGNMENT 1–SOLUTION. (1) See excel fle (2) The Following table gives the price at di±erent dates For a three-year 4% bond that pays semi-annual coupons and has a Face value oF 10 , 000. i date price 1 01/Jan/2007 (issue date) 10,188.40 2 01/July/2007 10,129.22 3 01/Jan/2008 10,129.12 4 01/July/2008 10,119.37 5 01/Jan/2009 10,069.05 6 01/July/2009 10,024.08 (a) (10 points) Compute the yields y i on the bond (expressed on annual rate, with semi annually compounding) obtained iF the bond is bought at time i , For i =1 , 2 , 3 , 4 , 5 , 6. (b) (10 points) Consider a 6-month T-bill on date i with a Face value oF \$10 , 000, For i , 2 , 3 , 4 , 5 , 6. Let r c,i be the (Canadian) quoted yield on T-bill issued on day i . ²ind the value oF r c,i such that T-bill i has the same e±ective annual yield as the bond in part (a) bought at time i . (c) (10 points) ²or each i , 2 , 3 , 4 , 5 , 6 fnd the US quoted yield r D,i equivalent to the Canadian quoted yield r c,i Found in part (b). Solution 0.1. (a) Let B i be the price of the bond at time i ( i , 2 . . . 6) . We have B i = 200 a 7 - i | y i 2 + 10 , 000(1 + y i 2 ) - (7 - i ) Using a Fnancial calculator (or Excel), we have y 1 =3 . 334845% ,y 2 . 456019% 3 . 327327% , y 4 . 178770% 5 . 292403% 6 . 509948% (b) Let P i be the price for the T -Bill issued on date i , r i be the e±ective annual

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## This note was uploaded on 10/19/2010 for the course ACTSC 445 taught by Professor Christianelemieux during the Spring '09 term at Waterloo.

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2010SpringA1Sol - ACTSC445/845 ASSIGNMENT 1SOLUTION. (1)...

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