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course 8: fall 2003 1 go to next page
finance
morning session
**beginning of examination**
finance
morning session
questions 1-5 pertain to the case study.
each question should be answered independently.
1. (8 points) mr. newman has just given j. peterman the unaudited line-of-business and
consolidated financials of nada for along with projections for 2003-. in
addition, nada has supplied peterman with an extensive business plan detailing the
growth potential and opportunity for each of its business units.
the business plan contains an emphasis on growing the gic business. mr. newman
plans to do this through the addition of funding agreements with 12-day put options.
the funding agreements will be sold to institutional investors other than retirement
plans.
peterman is concerned about nada’s growing reliance on gic sales. peterman has
questions about the profitability, liquidity, and investment risks of the gics.
mr. newman has asked you to address the rating agency’s concerns.
(a) explain why peterman may have concerns about increased funding agreement
sales and their effects on profitability, liquidity, and investment risk.
(b) peterman has recently adopted a view of interest rate risk similar to moody’s
investor service. summarize moody’s view of interest rate risk, and describe the
impact that such views could have on peterman’s evaluation of nada’s current
and planned gic business.
course 8: fall 2003 2 go to next page
finance
morning session
questions 1-5 pertain to the case study.
each question should be answered independently.
2. (10 points) in preparation for the upcoming rating agency meeting with j. peterman,
chief actuary kramer has been asked to look into improving the rbc ratio of the term
life block. his preference is to change the asset mix backing the product.
manzier reinsurance has offered to coinsure 35% of nada’s term life block.
(a) (1 point) calculate the required capital for year-end 2003 for the term life block
of business prior to any reinsurance. show your work.
(b) (2 points) propose terms for the reinsurance transaction with manzier that would
optimize nada’s rbc ratio for the term life block of business.
(c) (3 points) calculate the required capital for year-end 2003 for the term life block
if the reinsurance deal you proposed is consummated. show your work.
(d) (2 points) calculate the impact of your proposed reinsurance arrangement on
nada’s year-end 2003 rbc ratio. assume no change to available surplus.
show your work.
(e) (2 points) predict manzier’s response to the terms of the reinsurance arrangement
proposed in part (b).
course 8: fall 2003 3 go to next page
finance
morning session
questions 1-5 pertain to the case study.
each question should be answered independently.
3. (12 points) nada’s business plan projects increased sales of gics beginning in 2003.
to achieve this plan, the marketing department has instituted a commission scale for
gic products sold in 2003, as follows:
•a commission payment of 1% of deposits for gics with 5-year interest rate
guarantees
•a commission payment of 0.2% of deposits for gics with 1-year interest rate
guarantees
•commissions are paid at the time of sale to the broker.
von nostrum has recommended that nada start deferring acquisition costs with respect
to its new business. elaine benes has put you in charge of creating a methodology to
capitalize and amortize acquisition costs in accordance with u.s. gaap.
you start by focusing on the gic line. assume the following:
•nada’s gics are fas 97 investment contracts.
•all gics are sold at the beginning of the year.
•there are no withdrawals prior to maturity.
•interest earned is paid to the contract holder on december 31 of each year.
•for assets backing the gic business sold in 2003, nada expects to earn an
investment return of 4.295%.
•expenses are 5 basis points per year.
(a) describe the procedure for determining the capitalization of the acquisition
expenses and the subsequent amortization of the dac asset for the gic line.
(b) calculate the dac asset for new business planned to be written in 2003 for the
gic line. show your work.
(c) calculate the amortization schedule for the dac asset from part (b). show your
work.
course 8: fall 2003 4 go to next page
finance
morning session
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
course 5
morning session
application of basic actuarial principles
section a-written answer
course 5: fall 2003 - 2 - go on to next page
morning session
**beginning of examination 5**
morning session
1. (5 points) a large employer is considering offering a private pension plan.
(a) describe the reasons for offering such a plan.
(b) describe the process involved in designing and implementing such a plan.
2. (5 points)
(a) for basic group term life insurance, briefly describe each of the following items:
(i) typical plan designs offered
(ii) eligibility provisions
(iii) continuity of coverage provisions
(b) briefly describe how supplemental group term life insurance is different from
basic group term life insurance with respect to:
(i) typical plan designs offered
(ii) eligibility provisions
(iii) continuity of coverage provisions
course 5: fall 2003 - 3 - go on to next page
morning session
3. (5 points)
(a) describe the reasons a life insurance company may reinsure its risk.
(b) abc life insurance company has a 40% quota share reinsurance treaty on a first
dollar basis. its retention limit is $500,000 per policy.
policy 1 policy 2
net amount at risk $750,000 x
amount retained r y
amount reinsured on a first dollar basis s z
amount reinsured on an excess basis t $100,000
calculate the missing values in the table above.
show all work.
4. (5 points) explain the u.s. laws and regulations with respect to market conduct that
apply to a life insurance company and its agents.
5. (6 points) mary and john, respectively 45 and 42 years old, are considering the purchase
of a non-participating whole life, joint last-to-die policy, paid-up at first death with:
•a 5 year term individual rider life insurance convertible and renewable up
to age 65 for mary and john;
•a critical illness rider covering 50 illnesses for mary and john;
•a disability income rider providing a lifetime benefit with a 2 week
waiting period for mary and john.
(a) describe briefly the policy and its riders.
(b) describe alternatives to each coverage that could reduce the cost to mary and
john.
course 5: fall 2003 - 4 - go on to next page
morning session
6. (7 points) for a defined benefit pension plan, you are given:
pension plan formula:
1.5% of final year’s salary for each year of service up to 10 years, plus
2.0% of final year’s salary for each year of service after 10 years.
interest rate 6%
salary growth rate 4%
pre-retirement decrements none
assumed retirement age 65
12
a&&65 12
assets at 1/1/2003 300,000
assets at 1/1/ 320,000
contribution made on 12/31/2003 5,000
funding method projected unit credit
employee age at hire age on 1/1/2003 salary on 1/1/2003
a 30 40 30,000
b 30 60 50,000
(a) calculate the unfunded accrued liability at 1/1/2003.
(b) the actual accrued liability on 1/1/2004 is 350,000.
calculate the total experience gain/loss as of that date.
show all work.
course 5: fall 2003 - 5 - go on to next page
morning session
7. (5 points) for a property and casualty insurance policy issued january 1, , you are
given:
effective date rate change
may 1, 2000 +5%
november 1, 2000 +10%
calendar year
earned premium
expected effective incurred losses, trended
and developed through december 31,
2000 120,000 100,000
130,000 110,000
2002 140,000 120,000
expense ratio: 30%
present average manual rate: 45
assume all policies have a one-year term and the premium is uniformly
distributed.
calculate the indicated average gross rate as of january 1, 2003.
show all work.
course 8: fall 2004 - 1 - go to next page
retirement benefits,
comprehensive segment – u.s.
morning session
**beginning of examination 8**
comprehensive segment – u.s.
morning session
1. (9 points) a pension committee member at your u.s. based client believes that the
interest rate for the defined benefit plan valuations is too low. he supports his view by
stating that a higher interest rate would lower the cost of the plan. a second committee
member argued against raising the assumption.
the chairman of the pension committee has asked you to lead a discussion at the next
pension committee meeting regarding the interest rate assumptions for funding purposes
and for accounting purposes, and their effect on the interested parties.
outline your discussion.
course 8: fall 2004 - 2 - go to next page
retirement benefits,
comprehensive segment – u.s.
morning session
questions 2 – 6 pertain to the case study
2. (12 points) the cfo of noc has decided to take a more active role in managing noc’s
pension plan assets. in reviewing the performance of the national oil full-time hourly
union pension plan, he is disturbed by the recent absolute performance. he proposes
that the assets should be moved to 100% domestic fixed income because that asset class
has outperformed the other asset classes in 2 of the last 3 years.
you are given:
calendar year rf rm β
4% 21% 0.9
2002 5% -5% 0.85
2001 4% 1% 0.8
additional information for 2003
target portfolio mix
for 2003 benchmark return in
2003
domestic large cap
equities
35% 30%
domestic small cap
equities
25% 47%
domestic fixed income 25% 4%
international equities 10% 39%
real estate 5% 9%
cash 0% 1%
(a) describe the features in a statement of investment policies and procedures that
could help the cfo in his evaluation of the plan’s performance.
(b) calculate the 2001, 2002 & 2003 risk adjusted rate of return for the fund.
(c) calculate the 2001, 2002 & 2003 treynor measure for the fund.
(d) evaluate the investment performance of the fund during 2003.
(e) critique the cfo’s proposal.
course 8: fall 2004 - 3 - go to next page
retirement benefits,
comprehensive segment – u.s.
morning session
questions 2 – 6 pertain to the case study
3. (8 points) the government of vosne is concerned that workers are harmed by switching
companies periodically throughout their careers. the government has asked for your
assistance in understanding this issue.
(a) describe the implications of switching employers on workers’ retirement benefits.
(b) suggest policies that could be adopted by the government of vosne to improve
the portability of private retirement benefits.
(c) describe how these policies address the issues identified in (a).
(d) describe the impact of these policies on noc.
4. (10 points) auditors in vosne have criticized its current pension accounting standards as
being misleading to readers of financial statements and contrary to the teachings of
financial economics.
the department of accounting standards is considering changes to the current
accounting rules to achieve the following goals:
• increased transparency;
• improved consistency with how financial economics measures “risk”; and
• more practical and usable information for financial statement readers.
(a) critique the current accounting rules in light of the department’s goals.
(b) recommend changes to the accounting rules to meet the department’s goals.
course 8: fall 2004 - 4 - go to next page
retirement benefits,
comprehensive segment – u.s.
morning session
questions 2 – 6 pertain to the case study
course 8: investment - 1 - go on to next page
november 2000
morning session
november 2000
course 8v
society of actuaries
course 8: investment - 2 - go on to next page
november 2000
morning session
** beginning of examination **
morning session
questions 1 – 3 pertain to the case study.
each question should be answered independently.
1. (10 points) the board of directors of lifeco was recently given a presentation on the
paper by robert van der meer and meye smink, strategies and techniques for asset-
liability management: an overview. as the newly appointed chief risk officer for
lifeco, the board has asked you to give a presentation.
(a) categorize and describe the alm strategies and techniques employed by lifeco
within the framework provided by van der meer and smink.
(b) assess the relative merits or return-driven versus value-driven strategies for
lifeco.
(c) formulate an alm strategy for lifeco (from the framework provided by
van der meer and smink) that reduces the total company exposure to interest rate
risk and provides an opportunity to increase company surplus.
(d) evaluate your proposed strategy using the criteria set out in the paper by
van der meer and smink.
course 8: investment - 3 - go on to next page
november 2000
morning session
questions 1 – 3 pertain to the case study.
each question should be answered independently.
2. (9 points) lifeco management wants to segment the group line of business for
asset/liability management purposes into:
(i) long term disability (ltd), and
(ii) other a&h.
the newly allocated balance sheet for ltd is shown below:
present value modified duration adjusted duration
assets 550.9 13.5 11.00
liabilities 532.0 8.1 5.37
economic value 18.9 169.47
the relative volatility of assets for other a&h is the same as for ltd. the relative
volatility of liabilities for other a&h is 1.
(a) construct the new other a&h allocated balance sheet.
(b) assess the limitations of only using the above measures in managing interest rate
risk.
(c) contrast the use of adjusted duration with the measures used by lifeco to
manage its exposure to interest rate risk.
(d) the portfolio manager for the group line of business argues that franchise value
should be considered in the liability target duration calculation. define franchise
value.
(e) explain the implications of using franchise value for determining target
durations.
course 8: investment - 4 - go on to next page
november 2000
morning session
questions 1 – 3 pertain to the case study.
each question should be answered independently.
3. (22 points) lifeco wants to establish a delta/gamma/vega/rho hedge on the equity
exposure of their variable annuity business, using positions in some or all of the
following assets.
asset price delta gamma vega rho
s&p 500 future 0 100 0 0 0
30-year treasury
bond future
0 0 0 0 -12,598
1-year put 51.98 -0.34608 0.00184 3.688 -3.98
1-year call 109.45 0.65392 0.00184 3.688 5.45
10-year put 42.88 -0.10529 0.00029 5.761 -14.82
10-year call 489.57 0.89472 0.00029 5.761 40.51
lifeco’s liabilities have the following sensitivities:
delta – 2,659.90
gamma 1.036
vega 1952
rho – 101,910,000
all deltas and gammas are per unit change in the s&p 500 index.
vegas are per 1% change in volatility
rhos are per 1% change in interest rates
current value of the s&p 500 is 1300
(a) (6 points) construct a hedge position using the above assets that minimizes the
cost of the hedge without regard to the operational guidelines.
(b) (1 point)
(i) assess whether the hedge determined in part (a) would be in violation of the
operational guidelines for use of derivatives.
(ii) recommend any necessary changes to the guidelines.
course 8: investment - 5 - go on to next page
november 2000
morning session
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