12. (8 points) You are given the following:
Time to Maturity Effective Annual Spot Rate
0.5 years 5.00%
1.5 years 5.50%
2.5 years 6.10%
3.5 years 6.25%
4.5 years 6.50%
•the valuation date is December 31, 2004
•liability cash flows are as follows:
Time of Cash Flow Liability Amount
June 30, 2005 25
June 30, 2006 20
June 30, 2007 15
June 30, 2008 10
June 30, 2009 5
•the Macauley duration of the liabilities is 1.75 years
•the convexity of the liabilities is 5.5 years
•the universe of publicly traded bonds at 100 par value as at
December 31, 2004 is as follows:
Bond Maturity Annual Coupon Effective Annual Yield
A June 30, 2005 10.0% 5.00%
B June 30, 2006 7.5% 5.50%
C June 30, 2007 6.5% 6.50%
D June 30, 2008 5.0% 6.50%
E June 30, 2009 4.0% 6.50%
(a) Calculate the Macauley duration of Bond B.
(b) Compare immunization and cash flow matching strategies.
(c) Construct an immunized portfolio using Bond A and Bond E that protects against
interest rate movements.
(d) Determine a cash flow matched portfolio using the universe of available bonds.
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Course 6: Spring 2004 - 4 - GO ON TO NEXT PAGE
Afternoon Session
13. (6 points) A bond portfolio consists of three bonds, each issued at the same par value.
You are given the following projected results over a one-year planning horizon under
three different interest rate scenarios.
Scenario Bond Total Annual Return % Duration
1 X 11.9 2.3
Y 10.1 1.4
Z 10.7 1.1
2 X 8.2 2.3
Y 8.4 1.4
Z 8.3 1.1
3 X 5.7 2.3
Y 6.1 1.4
Z 5.6 1.1
Each of the three scenarios is equally likely to occur and the total portfolio consists of
one of each of the bonds.
(a) Describe Strategic Frontier Analysis.
(b) Using the Strategic Frontier Analysis, plot the graph and evaluate each of the
bonds.
(c) Describe Relative Return Value Analysis.
(d) Using the Relative Return Value Analysis, plot the graph and evaluate each of the
bonds.
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Course 6: Spring 2004 - 5 - STOP
Afternoon Session
14. (5 points) You are given the following with respect to a Treasury instrument:
•days to maturity: 110
•bid: 4.48%
•ask: 4.46%
•change: +0.02%
•ask yield: 4.50%
(a) Calculate as of today:
(i) Market Price
(ii) Bond Equivalent Yield
(iii) Effective Annual Yield
(b) Describe the characteristics of U.S. Treasuries and how they are made available to
markets.
(c) Describe the characteristics of Agency Securities and how they are made
available to markets.
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