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SOA北美精算师2005年5月考试真题荟萃放送Course6（*9课）

来源：高顿网校 2014-08-07

　　SOA北美精算师2005年5月考试真题荟萃放送Course6（*9课）是高顿网校小编们每个工作日都会坚持更新的历年大纲。
　　Course 6: Spring 2005 - 1 - GO ON TO NEXT PAGE

　　Morning Session

　　COURSE 6

　　MORNING SESSION

　　SECTION A – WRITTEN ANSWER

　　Course 6: Spring 2005 - 2 - GO ON TO NEXT PAGE

　　Morning Session

　　**BEGINNING OF EXAMINATION**

　　MORNING SESSION

　　1. (5 points) Your company is evaluating active and quasi-passive investment strategies for

　　bond portfolio management.

　　(a) Define each quasi-passive indexation approach.

　　(b) Describe the advantages and disadvantages of each quasi-passive indexation

　　approach.

　　(c) Explain the reasons your company would consider an active investment strategy.

　　(d) Describe the sector and security strategies that an active investment manager

　　would use to select individual bonds.

　　2. (7 points) Your company is offering a 15-year term-certain immediate annuity with

　　payments linked to the CPI. Policyholders can withdraw funds on demand at market

　　values.

　　The universe of available investments consists of the following:

　　? Short-term T-bills

　　? Real return public bonds

　　? Corporate bonds

　　? Real estate

　　(a) Outline the advantages and disadvantages of each investment for backing this

　　annuity.

　　(b) Recommend an investment strategy using the investments available.

　　(c) Describe the major components of an accumulated cash flow scenario-based

　　model.

　　(d) Outline the major components of the investment policy statement for this product.

　　Course 6: Spring 2005 - 3 - GO ON TO NEXT PAGE

　　Morning Session

　　3. (5 points) You are given the following information:

　　Bond Term Effective Duration Effective Convexity

　　A 5 3.1 -41.7

　　B 5 4.5 23.4

　　C 5 4.2 21.3

　　D 5 2.7 64.5

　　The option and price characteristics of Bonds A, B, C and D are as follows:

　　? one bond is option-free with a current price above par

　　? one bond is option-free with a current price below par

　　? one bond is callable, priced at par

　　? one bond is putable, priced at par

　　(a) Determine the option and price characteristics corresponding to each of Bonds A,

　　B, C and D. Explain your answer.

　　(b) Assess the limitations of duration as an interest rate risk measure.

　　(c) Define convexity. Compare effective convexity and modified convexity.

　　(d) Calculate the approximate percentage price change for Bonds A and B assuming a

　　decrease in yield of 0.50%.

　　Show all work.

　　Course 6: Spring 2005 - 4 - GO ON TO NEXT PAGE

　　Morning Session

　　4. (10 points) You are given the following with respect to treasury securities as of today,

　　May 13, 2005:

　　Security Years to Maturity

　　Annual Coupon Rate

　　Paid Semi-annually Yield-to-maturity

　　A 0.5 0% 3.0%

　　B 1.0 0% 3.2%

　　C 1.5 6% 3.5%

　　D 2.0 5% 3.6%

　　(a) Calculate the spot rate for each maturity date.

　　(b) Explain how arbitrage profits could be made from coupon stripping.

　　(c) Calculate the one-year forward rate, one year from today.

　　(d) With respect to the pure expectations theory

　　(i) Describe the theory

　　(ii) Describe the interpretations of the theory that have been put forth by

　　economists

　　(iii) Explain the shortcomings of the theory

　　(e) With respect to other theories of term structure of interest rates:

　　(i) Briefly describe each theory

　　(ii) Using each theory, compare the one-year spot on May 13, 2006, with the

　　one-year forward rate calculated in (c)

　　Show all work.

　　Course 6: Spring 2005 - 5 - GO ON TO NEXT PAGE

　　Morning Session

　　5. (5 points) You are given the following information with respect to Stock XYZ:

　　? price: 50

　　? variance: 4%

　　? dividend rate: 0%

　　The risk-free rate compounded continuously is 6%.

　　You are also given the following selected values from the Standard Normal Cumulative

　　Distribution Function:

　　Z N(Z) Z N(Z) Z N(Z)

　　.01 0.5040 .11 0.5438 .21 0.5832

　　.02 0.5080 .12 0.5478 .22 0.5871

　　.03 0.5120 .13 0.5517 .23 0.5910

　　.04 0.5160 .14 0.5557 .24 0.5948

　　.05 0.5199 .15 0.5596 .25 0.5987

　　.06 0.5239 .16 0.5636 .26 0.6026

　　.07 0.5279 .17 0.5675 .27 0.6064

　　.08 0.5319 .18 0.5714 .28 0.6103

　　.09 0.5359 .19 0.5753 .29 0.6141

　　.10 0.5398 .20 0.5793 .30 0.6179

　　(a) List the assumptions required for put-call parity.

　　(b) Use the Black-Scholes formula to calculate the price of a one-year European call

　　option on Stock XYZ with a strike price of 52.

　　(c) Calculate the price of a one-year European put option on Stock XYZ with a strike

　　price of 52.

　　Show all work.

　　Course 6: Spring 2005 - 6 - GO ON TO NEXT PAGE

　　Morning Session

　　6. (6 points) You are given the following with respect to a portfolio of bonds:

　　Bond

　　Annual

　　Coupon Par

　　Market

　　Value

　　Option

　　Features

　　Years to

　　Maturity

　　A 4.50% 100 100 none 2

　　B 6.00% 100

　　callable in one

　　year at 101 2

　　You are given the following with respect to a binomial lattice:

　　? rL : 4%

　　? σ : 15%

　　? time interval between nodes: 1 year

　　(a) Calculate the one-year spot rate.

　　(b) Calculate the two-year spot rate.

　　(c) Calculate the one-year implied forward rate.

　　(d) Calculate the value of the option in Bond B.

　　Show all work.
　　迁延蹉跎，来日无多，二十丽姝，请来吻我，衰草枯杨，青春易过。——高顿网校考试箴言

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