SOA真题北美精算师资格考试Course6之2005年5月（第六节）请读完，非常经典的大纲，很受启发的吧。
　　10. (8 points) An investment house has provided an investor with the following:
　　Scenario Probability Fund A Return Fund B Return
　　1 50% 25% 20%
　　2 30% 10% -20%
　　3 20% -30% 25%
　　The annual T-bill return is 3%.
　　(a) Calculate the correlation coefficient between Fund A and Fund B using the given
　　scenarios.
　　(b) Determine the optimal risky portfolio, Portfolio P. Calculate the expected return
　　and standard deviation of Portfolio P.
　　(c) Calculate the slope of the Capital Allocation Line supported by T-bills and
　　Portfolio P.
　　(d) The investor has the following utility function:
　　( U=E r)?0.025σ 2
　　Calculate the amount the investor would invest in each of:
　　(i) Fund A
　　(ii) Fund B
　　(iii) T-bills
　　(e) Another investment house has developed a portfolio, Portfolio Q, using Fund A
　　and Fund B. The expected return of Portfolio Q is 10% and the standard
　　deviation is 12%. Explain if the investor should invest in Portfolio Q rather than
　　Portfolio P.
　　Show all work.
　　Course 6: Spring 2005 -37- GO ON TO NEXT PAGE
　　Afternoon Session
　　11. (5 points) With respect to numerical interest rate risk management techniques,
　　(i) List and define the common techniques
　　(ii) Describe the key shortfalls of each common technique
　　Base your answer on the Canadian Institute of Actuaries Educational Note “Measurement
　　of Exposure to Interest Rate Risk”.
　　12. (6 points) Company ABC has an international fund that is benchmarked against an
　　external index. You are given the following with respect to a benchmark portfolio and
　　ABC’s fund manager’s portfolio:
　　Market
　　Benchmark
　　Weight
　　Return on
　　Equity Index
　　Currency
　　Appreciation
　　Fund Manager’s
　　Weight
　　Fund Manager’s
　　Equity Return
　　Asian 40% 10% 20% 35% 12%
　　European 25% 5% -10% 7%
　　Australian 35% 7% 25% 20%
　　(a) Describe the risks that are unique to international investments.
　　(b) The fund manager’s portfolio return matched the return of the index. Determine
　　the amount that the fund manager invested in the European and Australian
　　markets.
　　(c) For your portfolio, calculate the individual impacts of each of the following:
　　(i) Currency selection
　　(ii) Country selection
　　(iii) Stock selection
　　Show all work.
　　Course 6: Spring 2005 -38- GO ON TO NEXT PAGE
　　Afternoon Session
　　13. (5 points) You are given the following with respect to an 8-year, 6%, sequential-pay
　　CMO:
　　Tranche Initial Balance
　　1 20,000
　　2 35,000
　　3 65,000
　　? The annual payment required to amortize the CMO over eight years is 19,324.31.
　　? The actual cash flows are as follows:
　　Year
　　Interest
　　Payment
　　Required Principal
　　Payment
　　Additional
　　Principal Payment
　　Outstanding
　　Balance
　　0 120,000.00
　　1 7,200.00 12,124.31 1,078.76 106,796.93
　　2 6,407.81 12,916.50 1,877.61 92,002.82
　　3 5,520.17 13,804.14 2,345.96 75,852.72
　　4 4,551.16 14,773.15 2,443.18 58,636.39
　　5 3,518.18 15,806.13 2,141.51 40,688.75
　　6 2,441.32 16,882.99 1,190.29 22,615.47
　　7 1,356.92 17,967.39 185.92 4,462.16
　　8 267.73 4,462.16 0.00 0.00
　　(a) Describe the types of CMO structures.
　　(b) Calculate the outstanding balance for each tranche at the end of each year.
　　(c) Calculate the interest allocated to each tranche for each of the first three years.
　　Show all work.
　　Course 6: Spring 2005 -39- STOP
　　Afternoon Session
　　14. (4 points)
　　(a) Describe the criteria for selecting an interest rate generator.
　　(b) Describe the characteristics of
　　(i) a lognormal process
　　(ii) a mean reversionary lognormal process
　　(c) Describe the steps used in the Markov chain process to generate interest rates.
　　15. (4 points)
　　(a) Describe the advantages and disadvantages of using stochastic simulation when
　　pricing derivative securities.
　　(b) Describe the techniques that are available to reduce variance when using Monte
　　Carlo simulation.
　　**END OF EXAMINATION**
　　普通人只想到如何度过时间，有才能的人设法利用时间。——高顿网校极品语录