- a) (2 marks) Please retrieve the following zero rates from the Bank of Canada’s web-site and use the data for the zero yield curve dated October 10th, 2018. You can find the information at https://www.bankofcanada.ca/rates/interest-rates/bond-yield-curves/
b) (5 marks) Using the zero rates retrieved in part a), compute the par yield curve.
c) (5 marks) Using the Government of Canada bond yields as of October 10th, (that can also be obtained from the Bank of Canada web-site), compare your par curve yield rates, for the 2, 3, 5, 7 and 10 year maturity terms. What can you conclude?
d) (3 marks) From the Bank of Canada website, obtain the closing yield to maturity of the on-the-run 3 year bond (GoC 0.75% due Sept. 1, 2021). Using this yield to maturity, calculate the bonds’ clean price as of October 10th, 2018 (this would be the settlement date for this bond). Note: this is a semi-annual pay bond
e) (5 marks) Using the Bank of Canada zero coupon rates from October 10th, 2018, calculate the theoretical arbitrage free price of the 3 year GoC 0.75% due Sept. 1, 2021. What do you observe? Note: this is a semi-annual pay bond
- Calculate Macaulay duration, modified duration and convexity for each of the following bonds. Assume that all bonds have a principal value of $1,000 at maturity.
Part A (6 marks)
a) 2.0 year, 9% annual-pay coupon bond priced at par.
b) 2.0 year, zero-coupon bond priced at $708.42. (assume annual compounding)
c) 2.5-year, 9% annual-pay coupon bond priced at par.
d) 2.5-year, 7% semi-annual pay coupon bond priced at par.
Part B (4 marks) Given your calculations in part a) above, answer the following:
a) (1 mark) Briefly explain which 2.5 year (c or d) bond has the greatest sensitivity to interest changes.
b) (2 marks) Briefly explain which 2.5 year bond (c or d) has the greatest non-symmetric capital gain and capital loss characteristics.
c) (1 mark) If you were an institutional investor and anticipated that the yield curve would have a uniform parallel shift downwards in the near future, which 2 year bond (a or b) would you select?
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