2014年7月底*7最权威的北美精算师考试大纲：真题系列November2004CourseV（三）——北美精算师考试SOA，都在高顿网校！
　　COURSE 8: Fall 2004 -4- GO ON TO NEXT PAGE
　　Investment
　　Morning Session
　　Questions 1-4 pertain to the Case Study
 
　　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.
　　(c) Describe the process used to *uate the cost and efficiency of dynamic hedging.
　　(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.
　　(c) Outline the advantages of the Total Return Approach over the book-value
　　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
　　15
　　33
　　52
　　65
　　40
　　19
　　9
　　4 2 1 1 0 0
　　0
　　10
　　20
　　30
　　40
　　50
　　60
　　70
　　-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
　　Number of days
 
　　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.
　　(c) Evaluate the advantages and disadvantages of these methods of calculation and
　　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
　　Defin
　　ed 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.
　　(c) List the risks to the issuer of the underlying GIC or BIC contracts that support
　　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.
　　(c) Calculate the capital charge using the value obtained in (b).
　　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 *uating a
　　specific option investment strategy.
　　COURSE 8: Fall 2004 -12- GO ON TO NEXT PAGE
　　Investment
　　Afternoon Session
 
　　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
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　　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:
　　1
　　1
　　T t j
　　i
　　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.
　　(c) Compare the effective duration of SPDA with and without the MVA.
　　(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
　　Afternoon Session15. (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.
　　(c) Compare the default probability produced by Merton’s model versus the
　　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%.
　　(c) (3 points) Calculate the firm’s net gain or loss on the transaction, assuming that over the
　　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
　　Afternoon Session
 
　　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 fi
　　nancing 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.
　　(c) Calculate the market value of the risks in USD.
　　COURSE 8: Fall 2004 -19- GO ON TO NEXT PAGE
　　Investment
　　Afternoon Session
　　高顿网校之名人哲理：我的母亲是我见过的最漂亮的女人。我所有的一切都归功于我 的母亲。我一生中所有的成就都归功于我从她那儿得到的德、 智、体的教育。