大家复习北美精算师考试辛苦不？期待你们10月的考试合格后的呐喊声给高顿网校小编哦！
　　11. (6 points) You are given the following with respect to a one-period interest rate
　　contingent claim:
　　?  martingale probability: 50%
　　?  variance of the security: 0.2755%
　　?  risk- free rate: 5%
　　?  payment if interest rates go up: 105
　　?  payment if interest rates go down: 95
　　(a) Calculate the martingale security price.
　　(b) Calculate the “true” market price of risk.
　　(c) Calculate the “true” probability.
　　Show all work.
　　Course 6: Spring 2004 - 3 - GO ON TO NEXT PAGE
　　Afternoon Session
 
　　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.
　　Show all work.
　　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 o
　　ccur 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 *uate each of the
　　bonds.
　　(c) Describe Relative Return Value Analysis.
　　(d) Using the Relative Return Value Analysis, plot the graph and *uate each of the
　　bonds.
　　Show all work.
　　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
　　?  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.
　　Show all work.
　　高顿网校之名人话语汇总：青年人如果有青年的精神，这精神就是乐观。——茅盾