大家复习北美精算师11月份的考试辛苦不？期待你们2015年初考试合格后的呐喊声！精算师（北美考区）SOA往年真题精华—May2004Course6（六），请先苦后甜吧。
　　30. X. Price sensitivity techniques I. Maturity gap management
　　Y. Cash flow techniques II. Key rate duration
　　III. Convexity
　　31. X. Z Bonds I. No reinvestment risk during the
　　accretion phase.
　　Y. Accretion-directed Classes II. Do not extend even if there are no
　　prepayments.
　　III. Price is highly sensitive to interest
　　rate movements.
　　Course 6: Spring 2004 - 34 - GO ON TO NEXT PAGE
　　Morning Session
　　USE THIS PAGE FOR YOUR SCRATCH WORK
　　Course 6: Spring 2004 - 35 - GO ON TO NEXT PAGE
　　Morning Session
　　32. You are given the following information with respect to a portfolio:
　　?  duration: 3
　　?  dispersion: 0.75
　　?  all cash flows are positive
　　Time ( t ) ( PV CFt )
　　1 1
　　2 X
　　3 Y
　　4 0
　　5 1
　　Determine the minimum value of Y .
　　(A) 0
　　(B) 3
　　(C) 4
　　(D) 9
　　(E) 26
　　Course 6: Spring 2004 - 36 - GO ON TO NEXT PAGE
　　Morning Session
　　USE THIS PAGE FOR YOUR SCRATCH WORK
　　Course 6: Spring 2004 - 37 - GO ON TO NEXT PAGE
　　Morning Session
　　33. You are given the following with respect to a multiplicative binomial model:
　　?  the current short rate is 4%
　　?  rates are twice as likely to rise as they are to fall
　　?  the volatility parameter is 20%
　　Determine the expected short rate two periods from now.
　　(A) 3.65
　　(B) 4.13
　　(C) 4.31
　　(D) 4.55
　　(E) 4.65
　　Course 6: Spring 2004 - 38 - GO ON TO NEXT PAGE
　　Morning Session
　　USE THIS PAGE FOR YOUR SCRATCH WORK
　　Course 6: Spring 2004 - 39 - STOP
　　Morning Session
　　34. You are given the following with respect to a mutual fund:
　　?  annual expense ratio: 1%
　　?  gross annual rate of return: 10%
　　The back-end load fee starts at 4% and reduces by 0.5% on each anniversary.
　　An investor makes an initial investment of 5,000 on January 1, 2002.
　　Calculate the realized gain if the investor sells the shares on December 31, 2004.
　　(A) 941
　　(B) 1,216
　　(C) 1,281
　　(D) 1,313
　　(E) 1,455
　　Course 6: Spring 2004 - 40 - GO ON TO NEXT PAGE
　　Morning Session
　　COURSE 6
　　AFTERNOON SESSION
　　SECTION C – WRITTEN ANSWER
　　Course 6: Spring 2004 - 1 - GO ON TO NEXT PAGE
　　Afternoon Session
　　**BEGINNING OF EXAMINATION**
　　AFTERNOON SESSION
　　8. (4 points) Describe the practical difficulties that may be encountered while implementing
　　an asset allocation optimization model.
　　9. (5 points) You are given the following information about a universe of securities:
　　?  Rf : 0.0300
　　?  ( ) E RM : 0.0700
　　?  2
　　s M : 0.0450
　　The market covariance grid is:
　　Security Market Weight Covariance Matrix
　　A 0.35 9% 2% 2% 8%
　　B 0.25 2% 12% 1% 2%
　　C 0.25 2% 1% 3% 5%
　　D 0.15 8% 2% 5% 12%
　　(a) Calculate the market price of risk.
　　(b) Calculate the contribution to the variance of the market portfolio for securities
　　B and D.
　　(c) Calculate the equilibrium expected rate of return for securities B and D.
　　Show all work.
　　Course 6: Spring 2004 - 2 - GO ON TO NEXT PAGE
　　Afternoon Session
　　10. (6 points) You are given the following with respect to T-bills issued on February 1,
　　2004:
　　Term to Maturity Spot Price
　　1 month 98.50
　　2 months 98.40
　　3 months 98.20
　　4 months 98.00
　　A futures contract is available for delivery of a 3-month T-bill on March 1, 2004.
　　(a) Compare forward contracts to futures contracts.
　　(b) Determine the implied price of the futures contract.
　　(c) Recommend an arbitrage strategy to be implemented on February 1, 2004 if the
　　market price of the futures contract at that time is 97.5. Calculate the profit and
　　cash flows each month until all contracts are mature.
　　Show all work.
　　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
　　事在勉强而矣，勉强求学则见闻广而智力明，勉强修养，则德日起而大有功。——高顿网校生活感悟

 

 
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