以下是SOA往年真题May2004Course6（第三部分）——2014年份北美精算师，珍惜大好的学习时光，且学且珍惜。
　　stroyed in the
　　ordinary course of doing business
 
　　11. X. Callable Bonds I. Bond price at low yields is
　　approximately equal to the price of
　　an option- free bond.
　　Y. Putable Bonds II. Negative convexity at low yield
　　levels and positive convexity at high
　　yield levels.
　　III. Positive convexity at all yield levels.
　　Course 6: Spring 2004 - 18 - GO ON TO NEXT PAGE
　　Morning Session
 
　　12. X. Lattice methods I. Allow for more realistic jumps in
　　interest rates of varying amounts
　　along a single path.
　　Y. Simulation methods II. Easier to use to value instruments
　　that have embedded American-style
　　options.
　　III. Easier to use when more than one
　　factor changes at the same time.
 
　　13. X. Forward contracts I. Dealer or broker
　　Y. Futures contracts II. Bid-ask spread
　　III. High liquidity
　　14. X. Agency CMOs I. Usually rated by bond rating
　　agencies.
　　Y. Whole-loan CMOs II. Do not employ credit enhancement
　　techniques.
　　III. Employ credit enhancement
　　techniques.
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　　Morning Session
　　10-16. Each of questions 10 through 16 consists of two lists. In the list at the left are two items,
　　lettered X and Y. In the list at the right are three items, numbered I, II, and III. ONE of
　　the lettered items is related in some way to EXACTLY TWO of the numbered items.
　　Indicate the related items using the following answer code:
　　Lettered Item
　　Is Related to Numbered Items
　　(A)
　　X
　　I and II only
　　(B)
　　X
　　II and III only
　　(C)
　　Y
　　I and II only
　　(D)
　　Y
　　I and III only
　　(E)
　　The correct answer is not given by (A), (B), (C) or (D).
　　15. X. Horizon matching I. Active management.
　　Y. Contingent immunization II. Reduces impact of non-parallel
　　move of yield curve.
　　III. Always duration matched.
　　16. X. Value-at-risk model I. Measures the maximum loss in value
　　a company’s portfolio is likely to
　　sustain over a period of time as a
　　result of changes in market prices.
　　Y. Stress test II. Measures a company’s exposure to
　　extreme movements in stock prices.
　　III. Uses average historical correlations
　　among asset prices.
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　　Morning Session
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　　Course 6: Spring 2004 - 21 - GO ON TO NEXT PAGE
　　Morning Session
　　17. You are given the following:
　　?  issues traded: 4,800
　　?  advances: 2,600
　　?  declines 1,500
　　?  unchanged: 650
　　?  new highs: 150
　　?  new lows: 50
　　?  advancing volume (000): 470,000
　　?  declining volume (000): 235,000
　　?  total volume (000): 740,000
　　Calculate the “trin” statistic.
　　(A) 0.87
　　(B) 1.02
　　(C) 1.15
　　(D) 1.17
　　(E) 2.00
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　　Morning Session
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　　Course 6: Spring 2004 - 23 - GO ON TO NEXT PAGE
　　Morning Session
　　18. An investor purchases 50 shares of a stock on January 28, 2004.
　　You are given the following:
　　?  annual interest on borrowed funds: 7%
　　?  value of each share on January 28, 2005: 100
　　?  investor’s return from January 28, 2004 to January 28, 2005: 30%
　　Calculate the original purchase price of each share, if the initial margin percentage is
　　75%.
　　(A) 66.23
　　(B) 80.48
　　(C) 81.63
　　(D) 85.06
　　(E) 86.02
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　　Morning Session
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　　Course 6: Spring 2004 - 25 - GO ON TO NEXT PAGE
　　Morning Session
　　19. You are given the following:
　　?  target return on capital: 15%
　　?  net spread for residential mortgages: 1%
　　?  net spread for mortgage bonds: 0.9%
　　?
　　;  pre-tax return: 21%
　　?  risk- free rate: 6%
　　?  MCCSR factors:
　　BBB mortgage bonds: 2%
　　BB residential mortgages: 4%
　　Calculate the MCCSR-adjusted spread for residential mortgages and mortgage bonds,
　　respectively.
　　(A) (0.40%, 0.30%)
　　(B) (0.40%, 0.60%)
　　(C) (0.64%, 0.72%)
　　(D) (0.70%, 0.60%)
　　(E) (0.76%, 0.78%)
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　　Morning Session
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　　Course 6: Spring 2004 - 27 - GO ON TO NEXT PAGE
　　Morning Session
　　20. You are given the following:
　　Risk Amount
　　C-1 80
　　C-2 100
　　C-3 90
　　C-4 10
　　Using Zeppatella’s formula for incremental RBC, determine (Wa, Wi), where Wa is the
　　weight associated with assets and Wi is the weight associated with insurance.
　　(A) (0.743, 0.437)
　　(B) (0.793, 0.467)
　　(C) (0.793, 0.507)
　　(D) (0.862, 0.507)
　　(E) (0.862, 0.682)
　　Course 6: Spring 2004 - 28 - GO ON TO NEXT PAGE
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　　Course 6: Spring 2004 - 29 - GO ON TO NEXT PAGE
　　Morning Session
　　21-24. Questions 21 through 24 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.21.
　　ASSERTION
　　Given the choice, investors prefer
　　a portfolio on a higher
　　indifference curve.
　　BECAUSE
　　REASON
　　Higher indifference curves
　　correspond to higher levels of
　　utility.
　　22.
　　ASSERTION
　　A callable bond is negatively
　　convex.
　　BECAUSE
　　REASON
　　A call option increases a bond’s
　　effective duration when interest
　　rates fall.
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　　Morning Session
　　23.
　　ASSERTION
　　Modified duration is an
　　inappropriate measure for bonds
　　with embedded options.
　　BECAUSE
　　REASON
　　Modified duration assumes a flat
　　yield curve.
　　24.
　　ASSERTION
　　Dividend scale guarantees are put
　　options within a participating life
　　insurance policy.
　　BECAUSE
　　REASON
　　A put option gives the purchaser
　　the right to sell at a fixed price.
　　Course 6: Spring 2004 - 31 - GO ON TO NEXT PAGE
　　Morning Session
　　25-31. Each of questions 25 through 31 consists of two lists. In the list at the left are two items,
　　lettered X and Y. In the list at the right are three items, numbered I, II, and III. ONE of
　　the lettered items is related in some way to EXACTLY TWO of the numbered items.
　　Indicate the related items using the following answer code:
　　Lettered Item
　　Is Related to Numbered Items
　　(A)
　　X
　　I and II only
　　(B)
　　X
　　II and III only
　　(C)
　　Y
　　I and II only
　　(D)
　　Y
　　I and III only
　　(E)
　　The correct answer is not given by (A), (B), (C) or (D).
　　25. X. Refunding Provision I. Will not provide protection against
　　the issuance of common stock to
　　retire debt.
　　Y. Call Provision II. Bonds cannot be redeemed for any
　　reason.
　　III. Provides re
　　demption protection
　　against the issuance of debt ranking
　　equal to or superior to the debt to be
　　redeemed.
　　26. X. Multivariate density estimation
　　(MDE)
　　I. Chooses points which are as
　　uniformly distributed as possible.
　　Y. Low-discrepancy method II. Can only be used for classes of
　　financial instruments for which
　　liquid markets exist.
　　III. Nonparametric, model-free
　　approach.
　　Course 6: Spring 2004 - 32 - GO ON TO NEXT PAGE
　　Morning Session
　　27. X. Amortized cost method I. Assets held to maturity
　　Y. Market value method II. Assets available for sale
　　III. Assets for trading
　　28. X. Return simulation I. Evaluates the current level of yields
　　by producing spot, discount, and
　　forward rate structures.
　　Y. Term-structure analysis II. Predicts bond and portfolio behavior
　　given alternative interest rate
　　scenario projections.
　　III. Values Treasury securities.
　　29. X. Duration bets I. Pure index match
　　Y. No duration bets II. Minor mismatches
　　III. Full-blown active
　　Course 6: Spring 2004 - 33 - GO ON TO NEXT PAGE
　　Morning Session
　　25-31. Each of questions 30 through 31 consists of two lists. In the list at the left are two items,
　　lettered X and Y. In the list at the right are three items, numbered I, II, and III. ONE of
　　the lettered items is related in some way to EXACTLY TWO of the numbered items.
　　Indicate the related items using the following answer code:
　　Lettered Item
　　Is Related to Numbered Items
　　(A)
　　X
　　I and II only
　　(B)
　　X
　　II and III only
　　(C)
　　Y
　　I and II only
　　(D)
　　Y
　　I and III only
　　(E)
　　The correct answer is not given by (A), (B), (C) or (D).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
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　　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
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　　Morning Session
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　　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
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　　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
　　Af
　　ternoon 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.
　　高顿网校之名人语录：青年人满身都是经历，正像春天的河水一样丰富。几乎所有的伟业都是由青年人创造的。——迪斯累里