SOA真题NovemberCourse8I（共1篇）
1.SOA真题NovemberCourse8I 篇一
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, 70 50
december 31, 2004 100 50
december 31, 2005 90 60
december 31, 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