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SOA真题北美精算师资格考试Course6之2005年5月（第六节）

来源：高顿网校 2014-08-07

　　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

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