# AssignmentOneAnswers - ActSc 445/845 Assignment One Due...

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ActSc 445/845 Assignment One Due Date: Tuesday, October 5, 2010. 1. For a T-Bill with a given price P , face value F>P , and maturity of n< 360 days: (a) Show that the rates r D (bank discount yield) and r C (yield quoted in Canada) satisfy the relation r D <r C ; (b) Let r be the T-Bill’s e±ective annual yield. Is it possible to have r<r C ? Justify your answer. Answer: (a) We have that: P = F ° 1 r D · n 360 ± = F 1+ r C · n 365 Solving for r C in terms of r D yields r C = 365 360 r D n r D Since r D = F P F · 360 n , we have that n · r D < 360 and therefore 365 360 nr D > 1, which implies r C >r D . (b) This is not possible. We can prove that r C ° r . We have P = F (1 + r ) n/ 365 = F 1+ r C · n 365 So that: r C = 365 n ° (1 + r ) n/ 365 1 ± So that f ( r )= r r C satis²es f (0) = 0 and f ° ( r )=1 (1 + r ) n/ 365 1 ± 0 so that f ( r ) ± 0, i.e. r ± r C . 1

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2. You purchased a Canadian T-Bill with face value 1000 on March 1, 2010. The T-bill is expiring on September 1, 2010 and is quoted at 3.2%. On May 1, 2010, this T-Bill is quoted at a rate r so that it has the same price as a US T-Bill with the same expiration date and face value which is currently quoted at 3.0%. If you sell your T-bill on May 1, 2010, what will be the eFective annual return on your investment?
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## This note was uploaded on 02/23/2012 for the course ACTSC 445 taught by Professor Christianelemieux during the Fall '09 term at Waterloo.

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AssignmentOneAnswers - ActSc 445/845 Assignment One Due...

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