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【北美精算师】SOA真题2004年11月4CourseV

来源：高顿网校 2014-07-02

高顿网校小编提示：把握好精算师考试题型，才能在考试中合理分配时间，祝各位考生考试成功。

　　COURSE 8: Fall 2004 -1- GO ON TO NEXT PAGE

　　Investment

　　Morning Session

　　**BEGINNING OF EXAMINATION**

　　INVESTMENT

　　MORNING SESSION

　　Questions 1-4 pertain to the Case Study

　　1. (5 points) LifeCo’s ALM Report indicates a need to rebalance the assets supporting the

　　non-traditional life segment.

　　(a) Describe the constraints on asset sales when rebalancing this portfolio.

　　(b) Evaluate LifeCo’s investment strategy for this segment, and recommend any

　　necessary changes.

　　COURSE 8: Fall 2004 -2- GO ON TO NEXT PAGE

　　Investment

　　Morning Session

　　Questions 1-4 pertain to the Case Study

　　2. (9 points) LifeCo is considering selling its closed block of Institutional Pension (GIC).

　　Liability book value (in $ millions) $1,500

　　Maturity (in years) 2

　　Annual liability crediting rate 6.60%

　　1 year risk-free rate 1%

　　You are given the following information:

　　Scenario 1 Scenario 2

　　1 year risk-free rate 1 year forward 3% 2%

　　Withdrawal rate at the end of year 1 4% 2%

　　Withdrawal rate at the end of year 2 100% 100%

　　Probability 30% 70%

　　There are no new deposits.

　　(a) (4 points) Compare the option pricing method and the actuarial appraisal method

　　for estimating the fair value of liabilities.

　　(b) (2 points) Outline practical considerations in applying the option pricing method.

　　with the risk- free interest rate for discounting.

　　COURSE 8: Fall 2004 -3- GO ON TO NEXT PAGE

　　Investment

　　Morning Session

　　Questions 1-4 pertain to the Case Study

　　3. (9 points) You are LifeCo’s Investment Actuary and a member of the ALM Committee.

　　The Committee is currently reviewing the risk exposures of the Non-Traditional Life

　　portfolio as contained in your December 31 ALM Report.

　　? You have recently switched LifeCo’s ALM reporting to effective duration

　　from modified duration

　　? Your effective duration calculations use a base yield curve and a yield

　　curve shocked by 1 basis point

　　? No explicit hedge has been set up for the minimum credited interest

　　guarantees

　　? LifeCo’s head of Investments has proposed the sale of $50 million (in

　　present value) of 15-year zero-coupon bonds in order to increase cash

　　holdings to partially address the key rate duration mismatch

　　(a) Describe the limitations of LifeCo’s reported effective durations as an interest rate

　　risk measure.

　　(b) Estimate the economic impact of a 100bp drop in interest rates based on your

　　reported effective durations.

　　explain reasons for any differences to the ALM committee.

　　(d) Describe any interest rate ‘bets’ evident from the reported partial durations.

　　(e) Estimate the revised partial durations following this proposed transaction.

　　(f) Estimate the revised impact of margin squeeze following this proposed

　　transaction.

　　(g) Explain how the potential margin squeeze should be incorporated into any

　　assessment of interest rate bets.

　　COURSE 8: Fall 2004 -4- GO ON TO NEXT PAGE

　　Investment

　　Morning Session

　　4. (9 points) LifeCo wants to modify the design of its Equity Linked GIC product to reduce

　　the impact of a large decline in the stock market just before maturity. LifeCo believes

　　that these modifications should be done in such a way that the participation rate is as high

　　as possible and the profit margin remains the same.

　　The Company is also concerned about the cost of purchasing call options for the Equity

　　Linked GICs and is considering applying the dynamic hedging program it developed for

　　its Variable Annuities.

　　(a) Compare the options embedded in LifeCo’s Equity Linked GIC and Variable

　　Annuities.

　　(b) Recommend potential changes to the Equity Linked GIC product that would meet

　　LifeCo’s goals for the redesigned product.

　　(d) Evaluate LifeCo’s Variable Annuity dynamic hedging program as an alternative

　　to purchasing call options for its Equity Linked GIC product.

　　(e) Contrast the hedging of Equity Linked GICs as a stand-alone product to that of an

　　investment option of a Variable Universal Life product.

　　COURSE 8: Fall 2004 -5- GO ON TO NEXT PAGE

　　Investment

　　Morning Session

　　5. (8 points) You are constructing a model that will be used for dynamically hedging the

　　guaranteed minimum death benefits (GMDB) on a variable annuity portfolio. The

　　following models have been proposed:

　　(i) Lognormal

　　(ii) Regime Switching

　　(iii) Time Series Model with GARCH Volatility

　　(iv) Empirical

　　(v) Wilkie

　　(vi) Stable Distribution

　　(a) (3 points) Evaluate each model for modeling equity returns.

　　(b) (5 points) Assess the suitability of each model for dynamic hedging and

　　recommend a model to be used for dynamically hedging the GMDB.

　　COURSE 8: Fall 2004 -6- GO ON TO NEXT PAGE

　　Investment

　　Morning Session

　　6. (7 points) ABC Life has issued a 2-year GIC that has no policyholder options and pays

　　interest at maturity.

　　Single Premium 100 million

　　Payout in 2 years 110 million

　　Initial Assets (MV) 100 million of 3-year zero coupon corporate bonds

　　Treasury zero-coupon rates

　　Term, Years

　　Year 1 2 3

　　0 3% 4% 5%

　　1 4% 4% 4%

　　2 3% 4% 5%

　　Bond Spread Curve

　　1 year 2 year Corporate bond 3 year

　　spreads 0.1% 0.3% 0.5%

　　Assume:

　　? the bond spread curve does not change from issue

　　? expenses are negligible

　　? GIC issues occur at the beginning of the year

　　? payouts occur at the end of the year

　　(a) Compute the Total Returns in year 1 for both assets and liabilities using the Total

　　Return Approach.

　　(b) Disaggregate the Total Returns into their components, e.g. C-risks.

　　approach.

　　COURSE 8: Fall 2004 -7- GO ON TO NEXT PAGE

　　Investment

　　Morning Session

　　Daily return distribution

　　0 1 0 1 0 2 4 5

　　4 2 1 1 0 0

　　-5.00%

　　-4.50%

　　-4.00%

　　-3.50%

　　-3.00%

　　-2.50%

　　-2.00%

　　-1.50%

　　-1.00%

　　-0.50%

　　0.00%

　　0.50%

　　1.00%

　　1.50%

　　2.00%

　　2.50%

　　3.00%

　　3.50%

　　4.00%

　　4.50%

　　5.00%

　　Daily return

　　7. (9 points) The graph below shows the distribution of the daily returns of a particular

　　equity portfolio in one year with a total of 254 trading days. For example, there were 65

　　days with daily return between 0.00% and 0.50%. The average daily return is 0.04% and

　　the standard deviation of the daily return is 1.07%. The current value of the portfolio is

　　$10 million.

　　(a) Explain the objective of a Value at Risk (VaR) calculation

　　(b) Calculate:

　　(i) The one day VaR at a 95% confidence level using the above histogram.

　　(ii) The 10 day VaR at a 95% confidence level assuming a normal

　　distribution.

　　the Monte Carlo Simulation approach.

　　(d) Describe how to test the accuracy of the alternative models.

　　(e) List the limitations of VaR as a measure of risk, and explain how the Conditional

　　Tail Expectation approach and stress testing might complement VaR as a risk

　　measure.

　　(f) Calculate the 95% Conditional Tail Expectation based upon the distribution in the

　　graph above using interval midpoints as estimates of average values.

　　COURSE 8: Fall 2004 -8- STOP

　　Investment

　　Morning Session

　　8. (4 points) Acme Motors offers the following investment options to the participants in its

　　Defined Contribution plan:

　　1. A U.S. equity fund

　　2. An international equity fund

　　3. A fixed income fund

　　You are considering adding a Stable Value Fund option.

　　(a) Explain why a Stable Value Fund would be offered as an option.

　　(b) List the risks to Acme Motors and its participants associated with the Stable

　　Value Fund option.

　　Acme Motor’s DC plan’s stable value fund.

　　(d) Propose ways the issuer can manage these risks.

　　**END OF EXAMINATION**

　　MORNING SESSION

　　COURSE 8: Fall 2004 -9- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　**BEGINNING OF EXAMINATION**

　　INVESTMENT

　　AFTERNOON SESSION

　　Beginning With Question 9

　　9. (3 points) You are given a 5-year, BB rated zero-coupon bond with par value of 100.

　　You are given the following information

　　The 1-year transition matrix is:

　　Rating Initial at Year end (%)

　　Rating AA A BB B C Default

　　AA 95 3 2 0 0 0

　　A 2.5 93.5 2.5 1.5 0 0

　　BB 1 2 95.75 0.75 0.5 0

　　B 0 2 5 85 7 1

　　C 0 0 3 7 85 5

　　The 1-year forward zero-coupon curve is:

　　Category 1-Year 2-Year 3-Year 4-Year

　　AA 3.5 4.1 4.7 5.0

　　A 3.7 4.3 4.9 5.3

　　BB 4.0 4.7 5.3 5.7

　　B 5.6 6.0 6.8 7.4

　　C 10.0 12.0 11.0 9.0

　　Using the CreditMetrics approach:

　　(a) Calculate the possible 1 year forward values of the bond.

　　(b) Calculate the credit VaR at the 99% confidence level.

　　COURSE 8: Fall 2004 -10- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　10. (3 points) DM Life is considering hedging its credit risk with Credit Default Swaps

　　(CDS).

　　(a) Explain FAS 133’s rules for qualifying for hedge accounting.

　　(b) Formulate a hedge strategy that would qualify for hedge accounting under FAS

　　133.

　　COURSE 8: Fall 2004 -11- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　11. (3 points) An associate at your firm follows a select group of options. From time to time

　　he feels he can develop information and views in terms of expected return and risk that

　　are not reflected in current market prices.

　　(a) Explain why observed option prices might differ from those predicted by the

　　Black-Scholes model.

　　(b) Explain whether a Black-Scholes option model would be useful in evaluating a

　　specific option investment strategy.

　　COURSE 8: Fall 2004 -12- GO ON TO NEXT PAGE

　　Investment

　　12. (4 points) You are give the following statistics on a real estate portfolio.

　　Property

　　Type

　　Portfolio

　　Weighting

　　Index

　　Weighting

　　Portfolio

　　Returns

　　Index

　　Returns

　　Warehouse 15% 15% 5.50% 6.00%

　　Apartment 15% 15% 3.00% 4.00%

　　Retail 50% 40% 7.88% 7.50%

　　Office 20% 30% 4.25% 4.00%

　　Total 100% 100% 6.06% 5.70%

　　The real estate portfolio manager has made the following assertion:

　　“When it comes to real estate investing, I know exactly which properties are great

　　performers!”

　　He also provided the following two recommendations:

　　? Sell some of the apartment holdings because the occupancy rates are high in all of the

　　apartment buildings in the portfolio leaving little room left for any major price

　　appreciation.

　　? Invest in a retail complex being deve loped on the outskirts of town because of the

　　potential for price appreciation.

　　(a) Evaluate the validity of the real estate portfolio manager’s assertion.

　　(b) Critique each of the recommendations.

　　COURSE 8: Fall 2004 -13- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　13. (5 points) You are the Mortgage Backed Security analyst at ABC Life Insurance

　　Company. ABC’s chief economist, Jane Schmeau, is projecting that interest rates will

　　rise sharply over the next 12 months and then continue to rise steadily into the

　　foreseeable future. Ms. Schmeau makes the following statement:

　　“Because it is solely the current level of interest rates that determines the rate of

　　mortgage refinancing, the rate of mortgage prepayments will drop sharply in my

　　projected interest rate scenario”.

　　(a) (1 point) Assess Ms. Schmeau’s statement.

　　(b) (4 points) Describe the characteristics, advantages and disadvantages of each of

　　the following securities based upon Ms. Schmeau’s economic projection. Select

　　one of these bonds for purchase.

　　(i) A newly issued PAC with a 7 year average life, a collar of 100%-250%

　　PSA, and a 6 year lockout period

　　(ii) An intermediate pay sequential PAC with a 7 year average life and 6 years

　　of prepayment lockout

　　(iii) Z bond

　　(iv) Z-jump bond

　　COURSE 8: Fall 2004 -14- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　14. (7 points) Your company is considering adding a Market Value Ad justment (MVA) to its

　　SPDA. The SPDA has the following characteristics:

　　? surrender charges decline over 5 years

　　? minimum guaranteed credited rate of 3.0%

　　? initial crediting rate is 4.0% fixed for 5 years and reset annually thereafter

　　using a new-money rate

　　The MVA Factor being considered uses the following formula:

　　T t j

　　é+ ù-

　　ê? + ú?

　　for i > j

　　where:

　　i is the current market rate

　　j is the fixed crediting rate

　　T-t is the fixed rate period remaining

　　You asked a student to calculate the duration of the SPDA without the MVA. The

　　student’s immediate response is:

　　“This product is sold as a 5 year CD in the bank channel, it will behave like a

　　zero coupon bond with 5 year maturity and effective duration close to 5 years.”

　　(a) Assess the student’s response.

　　(b) Describe the benefit of the MVA feature from an ALM perspective.

　　(d) Describe in what situation a return of premium feature applied before the

　　surrender charge will be in-the- money with 4 more years of initial guarantee

　　remaining.

　　(e) Assess the impact on effective duration of the return of premium feature.

　　(f) Assess the impact of minimum guaranteed rate on the effective duration of the

　　SPDA with MVA.

　　COURSE 8: Fall 2004 -15- GO ON TO NEXT PAGE

　　Investment

　　15. (8 points) BMC Olympiad Inc. is looking for a potential acquirer within the next 12

　　months. You have been asked to assess the company’s near-term credit risk exposure

　　before proceeding with an appraisal analysis of BMC Olympiad’s operating businesses.

　　You are given the following information:

　　? Company’s credit rating: BBB

　　? Risk-free rate: 5% per annum compounded continuously

　　? Market value of company’s assets today: $21 billion

　　? Market value of company’s equity today: $5 billion

　　? Company’s debt due to be repaid including interest one year from now:

　　$17 billion

　　? Volatility of equity returns: 80%

　　? Volatility of asset returns: 20%

　　? A company with similar credit risk has five-year corporate zero-coupon

　　bonds trading at 350 basis points above risk-free rate

　　? Assumed recovery rate in the event of a default: 40% (as percent of bond’s

　　no-default value)

　　(a) Estimate the risk-neutral probability that the company will default on its debt

　　using Merton’s model.

　　(b) Determine the expected loss on the debt and the expected recovery in the event of

　　a default.

　　annualized risk- neutral default probability inherent in the company’s current

　　corporate bond pricing. Explain possible reasons for discrepancy between these

　　two estimates of default probabilities.

　　COURSE 8: Fall 2004 -16- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　16. (8 points) BH Life is a small insurance company that has sold a product with a minimum

　　return guarantee. The investment guarantee is equivalent to a European put option on

　　the S&P 500 index with a notional amount equal to 5,000 times the index.

　　You are given the following information:

　　? Risk free rate is 2.5%

　　? Current index value is 1200

　　? Strike price is 1100

　　? Time to maturity is 1 year

　　? Black Scholes value of the put option with implied volatility of 22% is

　　$242,900

　　? No dividends

　　? Trading costs equal 0.10%

　　? Proceeds are invested at the risk-free rate

　　? Risk- free rate and volatility do not change during the year

　　The firm wishes to delta hedge the risk on the put with quarterly rebalancing by using

　　shares of a fund tha t track the S&P 500.

　　(a) (2 points) Calculate the expected profit at the time the product is sold assuming that

　　expected volatility is 22% and the put option was priced using a volatility of 25% per

　　year.

　　(b) (1 point) Calculate the initial hedge position the firm should hold for delta neutrality if

　　the volatility assumed in their hedge is 22%.

　　course of the year the S&P 500 takes the following path given below, and that the

　　volatility assumed in their hedge is 22%. N(d1) factors are provided for European

　　options with the same maturity date and strike price and a volatility of 22%.

　　Time Index Level ( ) 1 N d

　　Point of sale 1200

　　End of Quarter 1 1250 0.8051

　　End of Quarter 2 1150 0.6700

　　End of Quarter 3 1050 0.3783

　　End of Quarter 4 1000

　　(d) (2 points) Describe other risk management strategies the firm can use.

　　COURSE 8: Fall 2004 -17- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　17. (4 points) You are considering investing in government issued fixed income securities in the

　　three countries listed below.

　　You are given the following information:

　　Country A B C

　　Continent Europe Asia Asia

　　Population 3M 400M 50M

　　Oil Exports 1B 150B 5B

　　Agriculture Exports 1B 150B 15B

　　Agriculture Domestic 3B 450B 40B

　　Manufacturing Exports 8B 150B 300B

　　Manufacturing Domestic 13B 600B 240B

　　Total GDP 26B 1500B 600B

　　Government type Stable Democracy Stable Democracy Emerging Democracy

　　Inflation Range 2%-20% 0%-30% 8%-16%

　　Infant deaths per 1000 1 3 5

　　Life expectancy 75 70 65

　　(a) Describe the risks of the potential investments and propose how to mitigate them.

　　(b) Rank the countries by their political stability and justify your ranking.

　　COURSE 8: Fall 2004 -18- GO ON TO NEXT PAGE

　　Investment

　　18. (6 points) You are a Risk Manager for a US-based trading company with international

　　operations. The company has the following risk exposures:

　　? a contract to deliver 1,000 ounces of gold semi-annually for one year at a maximum

　　price of $400 USD per ounce

　　? beginning of period 1 year LIBOR (in USD) on a $10,000,000 bank deposit payable

　　at the end of the year

　　? 7,000,000 Euro receivable from financing a customer purchase due in 1 year

　　You are given the following information:

　　? Available hedging instruments include currency forwards, USD swaps, and gold

　　options.

　　? Current exchange rate = .75 Euro / $1 USD

　　? Risk free rates USD Euro

　　6 month 2.5% 4.0%

　　1 year 3.0% 5.0%

　　Swap rates (USD) Floating rate Fixed Rate

　　6 month LIBOR 2.75%

　　1 year LIBOR 3.25%

　　? Option price per 1 ounce go ld contract with strike of USD 400:

　　Buy

　　Call

　　Sell

　　Call

　　Buy

　　Put

　　Sell

　　Put

　　6 month 4.0 3.6 6.0 5.2

　　1 year 6.0 5.6 8.0 7.2

　　(a) Describe the advantages of managing risk of strategic exposures in general as

　　defined in Chew.

　　(b) Propose a methodology to completely hedge the company against its strategic

　　risks.

　　COURSE 8: Fall 2004 -19- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　19. (6 points) BB No-Show Inc, a US company, is negotiating to buy a Japanese company.

　　The deal is expected to be closed in 3 months, with cash payment in Japanese Yen.

　　The chief financial officer of BB No-Show Inc has decided to buy an at-the- money call

　　option on Japanese Yen to hedge against a sudden increase in Yen relative to the US

　　dollar.

　　You are given the following information:

　　? Option type: at-the-money European call option.

　　? Maturity date of the option: 3 months (65 trading days)

　　? The option-holder has the right to buy 220 billion of Japanese Yen.

　　? US Treasury bond rates are 1% compounded continuously

　　? Japanese government bond rates are 0.05% compounded continuously

　　? Current exchange rate: 1 USD = 110 Japanese Yen

　　? Japanese Yen / USD exchange rate has daily volatility of 0.62%

　　An asset price S follows the stochastic process dS =mSdt+sSdz

　　(a) Apply Ito’s lemma to derive the process followed by G = S exp (r(T-t))

　　where r is the risk- free rate and (T-t) is the time to maturity.

　　(b) Interpret the derived stochastic process if G is a stock paying dividends at a

　　continuous rate.

　　spot foreign exchange rate.

　　(d) Calculate the value of the call option using the applicable Black-Scholes formula

　　for this call option on Japanese Yen.

　　COURSE 8: Fall 2004 -20- GO ON TO NEXT PAGE

　　Investment

　　Afternoon Session

　　20. (3 points) You are given the following information at time t = 0:

　　? Total assets supporting participating life = $74,081,822

　　? Total participating life liabilities = $66,673,640

　　? Maturity of policy = 10 years

　　? Guaranteed interest rate of the policy = 3% continuously compounded

　　? 10-year European call option values for an asset with current price

　　$74,081,822:

　　Strike price Call Value

　　$85,000,000 $8,520,220

　　$90,000,000 $7,625,000

　　$95,000,000 $4,502,535

　　$100,000,000 $1,204,330

　　$105,000,000 $820,300

　　Calculate the equilibrium participation level for policyholders.

　　**END OF EXAMINATION**
　　高顿网校小编赠语：期待考生们持续努力哦！一次性迈过这场精算师考试的这道坎！

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