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# sol2 - ACTSC 445 Asset-Liability Management Department of...

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ACTSC 445: Asset-Liability Management Department of Statistics and Actuarial Science, University of Waterloo Solutions for Unit 2 Exercises 1. (i) The bank discount yield is r D = (10000 - 9700) 10000 × 360 91 = 11 . 87% . (ii) We have that r C = 300 9700 × 365 91 = 12 . 41% . (iii) The effective annual yield is r = (10000 / 9700) 365 / 91 - 1 = 12 . 99% . 2. We have that P (1 + r C ( n/ 365)) = F and P = F (1 - r D ( n/ 360)) . Therefore F P = 1 + r C ( n/ 365) = 1 1 - r D ( n/ 360) , and thus r C = 1 1 - r D ( n/ 360) - 1 365 n = 360 360 - n × r D - 1 365 n = n × r D 360 - n × r D 365 n = 365 r D 360 - n × r D . 3. Using formula (1), we have that r D + 0 . 0011 = r C = 365 r D 360 - 93 r D . Hence we have (360 - 93 r D )(0 . 0011 + r D ) = 365 r D (1) 360 × 0 . 0011 + r D (360 - 93 × 0 . 0011 - 365) - 93 r 2 D = 0 (2) 93 r 2 D + 5 . 1023 r D - 0 . 396 = 0 . (3) Therefore r D = - 5 . 1023 ± 5 . 1023 2 + 4 × 93 × 0 . 396 186 r D = 0 . 043353616 . We can now compute the price: assuming a face value of 10 000, we have P = 10 000(1 - 0 . 043353616 × (93 / 360)) = 9888 . 0032 . 4. We are looking for the rate y so that 9200 = 375 a 8 y + 10 000(1 + y ) - 8 . 1

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using Excel’s Goal Seek, we find that y = 4.9871%. 5. Using the formula P = 3 . 5 a n 0 . 04 + 100 × 1 . 04 - n where n is the number of coupon-paying periods until maturity (so it goes from 2, 4, 6, 8 until 10), we
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sol2 - ACTSC 445 Asset-Liability Management Department of...

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