所有的北美精算师伙计们，还是在卖力的复习么？对，好样的！北美精算师考试SOA：真题系列May2004Course6（一），请接着。
　　COURSE 6
　　MORNING SESSION
　　SECTION A – WRITTEN ANSWER
　　Course 6: Spring 2004 - 1 - GO ON TO NEXT PAGE
　　Morning Session
　　**BEGINNING OF EXAMINATION**
　　MORNING SESSION
 
　　1. (4 points) Outline the key characteristics of securities regulations and restrictions in
　　effect in the United States.
 
　　2. (6 points) You are given the following:
　　Scenario 1 Scenario 2 Scenario 3
　　Probability 45% 40% 15%
　　Stock A Return 30% 2% -10%
　　Stock B Return -8% 15% 5%
　　Stock C Return 8% 4% -10%
　　T-bills Return 3% 3% 3%
　　An investor has:
　　?  7,000 invested in Stock A which he cannot sell
　　?  a risk aversion of 4
　　?  3,000 of additional funds to invest
　　(a) Calculate the expected return and standard deviation of each available investment.
　　(b) The investor can invest the additional funds in only one investment.
　　(i) Calculate the risk and reward of each investment strategy.
　　(ii) Rank each of the investment strategies. Explain your answer.
　　Show all work.
　　Course 6: Spring 2004 - 2 - GO ON TO NEXT PAGE
　　Morning Session
 
　　3. (9 points) You are given the following:
　　?  two types of bonds are available with par values of 100:
　　(i) 5-year zero coupon callable bonds, callable at 80 after two years of call
　　protection
　　(ii) 10-year zero coupon putable bonds, putable to issuer at 40 after three years
　　(iii) market prices are given in the table below:
　　Market Date Price
　　Callable Bond Putable Bond
　　December 31, 2003 70 50
　　December 31, 2004 100 50
　　December 31, 2005 90 60
　　December 31, 2006 70 60
　　?  An investor’s strategy is:
　　(i) invest any proceeds received from callable bonds into putable bonds
　　(ii) invest any proceeds received from putable bonds into callable bonds
　　The investor’s initial investment on December 31, 2003 was split between one
　　callable bond and one putable bond. Both bonds purchased had two years of
　　protection remaining at time of purchase.
　　December 31 of each year is the only day for purchasing, calling or putting bonds.
　　Bonds are called or put whenever the opportunity arises.
　　Today’s date is December 31, 2004.
　　(a) Contrast put options with call options.
　　(b) Describe the risks associated with the embedded options in the initial investment.
　　(c) Calculate the holding period return if all bonds are sold on December 31, 2006.
　　Assume no transaction costs.
　　(d) Contrast options with futures.
　　(e) Describe how futures could be used to improve the holding period return.
　　Show all work.
　　Course 6: Spring 2004 - 3 - GO ON TO NEXT PAGE
　　Morning Session
 
　　4. (6 points) You are given the following information about three collateralized mortgage
　　obligations (CMOs):
　　?  CMO A is backed by 7.5% pass-throughs consisting of the following tranches:
　　?  3-year sequential-pay
　　?  5-year very accurately defined maturity (VADM)
　　?  7-year sequential-pay
　　?  10-year sequential-pay
　　?  17-year Z bond
　　?  CMO B is backed by 7.5% pass-throughs consisting of the following tranches:
　　?  3-year planned amortization classes (PAC)
　　?  7-year PAC
　　?  7-year companion
　　?  10-year PAC
　　?  16-year PAC
　　?  20-year companion
　　?  CMO C is backed by 7.5% pass-throughs consisting of the follo wing tranches:
　　?  3-year sequential-pay
　　?  7-year sequential-pay
　　?  10-year sequential-pay
　　?  17-year sequential-pay
　　U.S. federal authorities are expected to increase interest rates by 50 basis points.
　　Describe how each structure will be affected by the
　　increase.
　　Course 6: Spring 2004 - 4 - GO ON TO NEXT PAGE
　　Morning Session
 
　　5. (8 points) You are given the following with respect to two public companies:
　　?  the common shares of each company are currently trading at 30 as of
　　December 31, 2003
　　?  neither company pays shareholder dividends
　　?  there are no taxes or transaction costs
　　?  an industry analyst has projected the possible stock prices over the next two
　　years as a function of the performance of the US economy:
　　US Economy Company A Company B
　　2004 2005 December
　　31, 2004
　　December
　　31, 2005
　　December
　　31, 2004
　　December
　　31, 2005
　　Expansion Expansion 32 33 33 36
　　Expansion Recession 32 30 33 30
　　Recession Expansion 30 29 29 29
　　Recession Recession 30 30 29 27
　　(a) Determine if the analyst’s projections allow for arbitrage.
　　(b) Using the analyst’s projections, determine the value of a European put option on
　　Company B’s stock if the option expires on December 31, 2005, and has an
　　exercise price of 30.
　　(c) Determine how an investor could replicate the payoff of a one- year European call
　　option with an exercise price of 31 on Company A’s stock using a portfolio of the
　　two companies common shares.
　　Show all work.
　　Course 6: Spring 2004 - 5 - GO ON TO NEXT PAGE
　　Morning Session6. (5 points) You are given the following:
　　Features
　　Bond Maturity (years) Annual Coupon Rate (%) Embedded Options
　　A 10 5% None
　　B 10 5% Put Option
　　C 10 7% None
　　D 10 7% Call Option
　　W 20 8% None
　　X 20 8% Put Option
　　Y 20 10% None
　　Z 20 10% Call Option
　　(a) Describe how bond features affect interest rate risk.
　　(b) An investor only buys bonds that have at least two of their features with high
　　sensitivity to interest rate changes. Identify the four bonds that this investor will
　　buy. Explain your answer.
 
　　7. (5 points)
　　(a) Describe the advantages of simulation techniques and lattice methods.
　　(b) Outline the issues that arise when implementing simulation techniques for a
　　mortgage-backed securities portfolio.
　　(c) Describe how lattice methods are used in a simulation model when *uating a
　　mortgage-backed securities portfolio.
　　Course 6: Spring 2004 - 6 - GO ON TO NEXT PAGE
　　Morning Session
　　COURSE 6
　　MORNING SESSION
　　SECTION B – MULTIPLE CHOICE
　　Course 6: Spring 2004 - 7 - GO ON TO NEXT PAGE
　　Morning Session
　　1. You are given the following bond portfolio:
　　S&P
　　Rating
　　Percentage
　　of Portfolio
　　AAA 10%
　　AA+ 10%
　　BBB+ 10%
　　A+ 25%
　　D 2%
　　CC 3%
　　BBB- 15%
　　BB+ 5%
　　A 20%
　　Determine the percentage of the portfolio that is investment grade.
　　(A) 65%
　　(B) 75%
　　(C) 90%
　　(D) 95%
　　(E) 100%
　　Course 6: Spring 2004 - 8 - GO ON TO NEXT PAGE
　　Morning Session
　　USE THIS PAGE FOR YOUR SCRATCH WORK
　　Course 6: Spring 2004 - 9 - GO ON TO NEXT PAGE
　　Morning Session
　　2. You are given the following information for a mutual fund:
　　?  net asset value (NAV) at December 31, 2003: 28
　　?  income distribution per share in 2004: 0.4
　　?  assets at December 31, 2004: 620,000
　　?  liabilities at December 31, 2004: 14,600
　　?  shares outstanding: 20,000
　　No securities were sold throughout the year. There are no capital gain distributions and
　　no fees in the year.
　　Calculate the effective annual interest rate of return for the mutual fund.
　　(A) 6.7%
　　(B) 8.1%
　　(C) 8.8%
　　(D) 9.5%
　　(E) 12.1%
　　Course 6: Spring 2004 - 10 - GO ON TO NEXT PAGE
　　Morning Session
　　USE THIS PAGE FOR YOUR SCRATCH WORK
　　Course 6: Spring 2004 - 11 - GO ON TO NEXT PAGE
　　Morning Session
　　3. A one-period securities market model is given by ( S 0) = [1 1 1].
　　( )
　　2 1.6 0
　　1 0 0.8
　　0 0 1
　　S x
　　? ?
　　=?? ÷÷
　　? ÷
　　è ?
　　Determine the range of values for x so that this model is arbitrage free.
　　(A) x > 4
　　(B) x < 4
　　(C) x > 0
　　(D) x < 0
　　(E) no such x exists
　　Course 6: Spring 2004 - 12 - GO ON TO NEXT PAGE
　　Morning Session
　　USE THIS PAGE FOR YOUR SCRATCH WORK
　　Course 6: Spring 2004 - 13 - GO ON TO NEXT PAGE
　　Morning Session
　　4. You are given the following:
　　?  expected return of market portfolio: 7.0%
　　?  variance of market portfolio: 10.0%
　　?  variance of Security A: 19.0%
　　?  covariance of Security A and market portfolio: 25.0%
　　?  risk- free rate: 5.0%
　　Calculate the expected return of Security A using CAPM.
　　(A) 7.6%
　　(B) 10.0%
　　(C) 14.2%
　　(D) 17.5%
　　(E) 22.5%
　　Course 6: Spring 2004 - 14 - GO ON TO NEXT PAGE
　　Morning Session
　　USE THIS PAGE FOR YOUR SCRATCH WORK
　　Course 6: Spring 2004 - 15 - GO ON TO NEXT PAGE
　　Morning Session
　　5-9. Questions 5 through 9 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.
　　.
　　ASSERTION
　　The original loan-to-value ratio
　　overestimates the measurement
　　of defaults for home mortgages.
　　BECAUSE
　　REASON
　　As home mortgages become more
　　seasoned, default rates tend to
　　decline.
　　6.
　　ASSERTION
　　Preferred stock payments are taxdeductible
　　for the issuing
　　corporation.
　　BECAUSE
　　REASON
　　Preferred stock payments are
　　treated as dividends.
　　Course 6: Spring 2004 - 16 - GO ON TO NEXT PAGE
　　Morning Session
　　7.
　　ASSERTION
　　An option-adjusted spread (OAS)
　　value by itself does not provide
　　sufficient information to
　　determine whether a bond is rich
　　or cheap.
　　BECAUSE
　　REASON
　　OAS is the spread to short-term
　　interest rates that equates the
　　theoretical price of a bond to its
　　market price.
　　8.
　　ASSERTION
　　Interest rate caps and floors
　　should not be used when the
　　holding period of the underlying
　　asset or liability is flexible or
　　subject to change.
　　BECAUSE
　　REASON
　　Termination of interest rate caps
　　and floors involves exit costs.
　　高顿网校之谚语相赠：青年人肩上的重担忽然卸去时，他勇敢的心便要因着寂寞而悲哀了!——冰心