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Unformatted text preview: 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 effective 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 6 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 satisfies f (0) = 0 and f ( r ) = 1- (1 + r ) n/ 365- 1 > so that f ( r ) > 0, i.e. r > r C . 1 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 effective annual return on your investment?1, 2010, what will be the effective annual return on your investment?...
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- Fall '09
- Forward rates, RC