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【SOA真题】May2004Course6①——北美精算师

来源：高顿网校 2014-07-16

　　今天下午，众位高顿网校小编们集合汇总了【SOA真题】May2004Course6①——北美精算师，供大家参考哦。
　　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 Session
　　高顿网校之名人哲理：别人可以违背因果，别人可以害我们，打我们，毁谤我们。可是我们不能因此而憎恨别人，为什么？我们一定要保有一颗完整的本性和一颗清净的心。

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