以下则是高顿网校小编在8月31日上午10点35分为大家编写的历年精算师北美考场SOA：2003年5月Course6真题（六）。
　　26-30. Questions 26 through 30 consist of an assertion in the left-hand column and a reason in the
　　right-hand column. Code your answer to each question by blackening space:
　　(A) If both the assertion and the reason are true statements, and the reason is a correct
　　explanation of the assertion.
　　(B) If both the assertion and the reason are true statements, but the reason is NOT a
　　correct explanation of the assertion.
　　(C) If the assertion is a true statement, but the reason is a false statement.
　　(D) If the assertion is a false statement, but the reason is a true statement.
　　(E) If both the assertion and the reason are false statements.
 
　　26.
　　ASSERTION
　　Mean reverting interest rate
　　generators tend to produce interest
　　rates at or close to their upper or
　　lower bounds.
　　BECAUSE
　　REASON
　　Mean reversion factors tend to
　　increase volatility.
 
　　27.
　　ASSERTION
　　Under FASB 115, reported
　　earnings from assets classified as
　　available-for-sale will be impacted
　　by unrealized gains or losses.
　　BECAUSE
　　REASON
　　Under FASB 115, assets classified
　　as available-for-sale are valued on a
　　market value basis.
 
　　28.
　　ASSERTION
　　In equilibrium, it is rare for
　　collateralized mortgage obligations
　　(CMOs) to trade rich compared to
　　collateral.
　　BECAUSE
　　REASON
　　Collateral spreads quickly tighten as
　　more CMOs are issued.
 
　　29.
　　ASSERTION
　　Reducing the C-2 component of
　　risk-based capital (RBC) through a
　　YRT reinsurance agreement may
　　not decrease the total RBC
　　requirements of a life insurance
　　company.
　　BECAUSE
　　REASON
　　The covariance adjustment between
　　the C-1, C-2 and C-3 components
　　of the RBC requirements can be
　　negative for a life insurance
　　company.
 
　　30.
　　ASSERTION
　　The valuation of derivatives
　　generally assumes that the derivative
　　security can be replicated using a
　　self-financing portfolio of traded
　　securities.
　　BECAUSE
　　REASON
　　Derivative valuation models generally
　　assume that there are market frictions
　　such as transaction costs.
　　**END OF MORNING SESSION OF THE EXAMINATION**
　　COURSE 6
　　AFTERNOON SESSION
　　SECTION C-WRITTEN ANSWER
　　Course 6: Spring 2003 - 1 - GO ON TO NEXT PAGE
　　**BEGINNING OF THE AFTERNOON SESSION OF THE EXAMINATION**
 
　　8. (4 points) You are given the following with respect to shares of Bre-XYZ:
　　State of Economy Probability Share Price on May 1, 2004
　　Boom 0.20 100
　　Normal Growth 0.65 50
　　Recession 0.15 20
　　?  share price on May 1, 2003: 45
　　?  semi-annual cash dividend: 2
　　?  rate of inflation: 2.5%
　　(a) Calculate the expected holding-period return.
　　(b) Calculate the standard deviation of the holding-period return.
　　(c) Calculate the purchasing power of 1,000 to be received in 10 years.
　　Show all work.
　　Course 6: Spring 2003 - 2 - GO ON TO NEXT PAGE
 
　　9. (8 points) You are given the following with respect to European style options on a common
　　stock:
　　?  strike price: 100
　　?  current market price of the underlying stock: 95
　　?  standard deviation of the underlying stock returns: 0.14
　　?  dividend rate of the underlying stock: 3% payable continuously
　　?  time to maturity for the options: 3 months
　　You are also given the following selected values from the Standard Normal Cumulative
　　Distribution Function:
　　Z N(Z)
　　0.1 0.5398
　　0.2 0.5793
　　0.3 0.6179
　　0.4 0.6554
　　0.5 0.6915
　　0.6 0.7257
　　0.7 0.7580
　　0.8 0.7881
　　0.9 0.8159
　　1.00 0.8413
　　The risk-free rate is 3%.
　　(a) List the assumptions underlying the Black-Scholes option model.
　　(b) Calculate the value of the call option ignoring the dividend.
　　(c) Calculate the value of the put option ignoring the dividend.
　　(d) Calculate the value of the call option including the dividend.
　　(e) Calculate the value of the put option including the dividend.
　　Show all work.
　　Course 6: Spring 2003 - 3 - GO ON TO NEXT PAGE
　　Course 6: Spring 2003 - 4 - GO ON TO NEXT PAGE
 
　　10. (6 points) You are given the following with respect to an option-free bond portfolio:
　　?  the value of the bond portfolio using the current yield curve is 800
　　?  the value of the bond portfolio using the current yield curve with a parallel shift
　　upwards of 20 basis points is 788
　　?  the value of the bond portfolio using the current yield curve with a parallel shift
　　downwards of 20 basis points is 813
　　(a) Using the methodology outlined in the Fabozzi textbook, estimate the value of the bond
　　portfolio for a parallel shift upwards of 200 basis points in the yield curve.
　　(b) Explain how the inclusion of convexity impacts your estimate.
　　Show all work.
 
　　11.
　　(a) (4 points) Describe the issues and practical considerations in immunizing a portfolio of
　　insurance liabilities.
　　(b) (1 point) Describe cash flow matching.
　　(c) (1 point) Describe contingent immunization.
 
　　12. (6 points)
　　(a) With respect to corporate bonds, describe the role of the corporate trustee.
　　(b) Differentiate the levels of security offered by various corporate bonds.
　　Course 6: Spring 2003 - 5 - GO ON TO NEXT PAGE
　　Course 6: Spring 2003 - 6 - GO ON TO NEXT PAGE
 
　　13. (6 points) You are given the following for an insurance company that currently offers term
　　insurance and fixed deferred annuities:
　　?  corporate pre-tax target return on capital of 18%
　　?  risk-based capital (RBC) formula:
　　1 5 . * asset default risk component d 2 + mortality risk component 2 i
　　Asset Default Risk Component (C-1)
　　Asset Class Amount (millions) RBC Factor
　　Historical
　　Mean Return
　　Bond 600 1% 7%
　　Real Estate 300 7% 8%
　　Common Stock 100 20% 10%
　　Mortality Risk Component (C-2)
　　Amount (millions) RBC Factor
　　Net Amount at Risk 10,000 0.1%
　　The industry-wide ratio of C-1 to C-2 is 1.5.
　　The risk-free rate is 6%.
　　(a) Describe the shortcomings of this RBC formula.
　　(b) Calculate the RBC-adjusted spread for this company’s asset portfolio.
　　(c) Evaluate the competitive advantage of the company’s product lines from a cost of
　　capital perspective.
　　Show all work.
　　Course 6: Spring 2003 - 7 - STOP
 
　　14. (4 points)
　　(a) Describe and compare the various prepayment models used to *uate a block of
　　mortgage-backed securities (MBS) pass-throughs.
　　(b) Describe the effects of prepayment rates on the cash flows of MBS pass-throughs.
　　要想一下子全知道，就意味着什么也不会知道。——高顿网校生活感悟

 

 
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