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【北美精算师】November2001Course8V——SOA历年真题系列

来源：高顿网校 2014-07-02

　　以下则是高顿网校小编为您整理的一系列精算师考前珍贵资料，请笑纳。

　　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.

　　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.

　　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

　　3. (Continued)

　　(i) Calculate the 1-day, 99%VAR on the portfolio, before and after the hedge is

　　applied using delta and gamma to approximate it.

　　(ii) Assess the validity of these numbers.

　　(d) (4 points) LifeCo is worried about the liquidity of the 30-year Treasury bond

　　future.

　　(i) Analyse the effectiveness of the proposed hedges with respect to rho.

　　(ii) Propose alternative methods and alternative assets to improve rho exposure

　　coverage.

　　(e) (5 points) The newly appointed Chief Risk Officer is concerned about the use of

　　derivatives in the hedging strategy. Verify that the operational and credit risks of

　　managing derivatives have been adequately covered by LifeCo’s operational

　　guidelines for use of derivatives.

　　COURSE 8: Investment - 6 - GO ON TO NEXT PAGE

　　November 2000

　　Morning Session

　　4. (6 points) You have the following market information:

　　? Price of a 2-year zero coupon bond: 89

　　? 1-year short rate i0 b g: 7%

　　A new actuarial student in your company has implemented an interest rate model to price

　　interest rate derivatives. His model gives the following results:

　　Sample space i1

　　w1 6.0%

　　w 2 8.0%

　　(a) Describe the different types of model risk that must be considered when building

　　or using a model.

　　(b) Explain the concept of arbitrage-free in the context of an interest rate model for

　　pricing derivatives.

　　5. (4 points)

　　(a) Describe how the following factors will generally impact the Option-Adjusted

　　Spread (OAS) of a Planned Amortization Class (PAC) for a typical PAC bond.

　　(i) Average life of the PAC

　　(ii) Premium versus discount collateral

　　(iii) Lockout versus no lockout

　　(iv) Window length

　　(v) Whether or not a Z-bond funds the PAC

　　(b) Describe the shortcomings associated with OAS in evaluating mortgage-backed

　　securities.

　　COURSE 8: Investment - 7 - GO ON TO NEXT PAGE

　　November 2000

　　Afternoon Session

　　6. (5 points) You are given the following information on a European put option on a bond:

　　? Put option

　　? Maturity of option 1 year

　　? Strike price level 1000

　　? Underlying bond

　　? Cash price 1000

　　? Present value of bond coupon payments 100

　　? 1 year forward yield volatility 10%

　　? Modified duration 10 years

　　? Forward yield 7%

　　? Risk-free rates are flat at 5.13%

　　(a) Calculate the price of this option using Black’s model. Show your work.

　　(b) Contrast alternatives for calculating delta and gamma for this option with a stock

　　option.

　　7. (4 points)

　　(a) Describe the psychological factors that prevent rational investment decisionmaking.

　　(b) List five major anomalies which the standard paradigm of rationality fails to

　　explain. Give an example for each case and specify the key behavioral factors

　　that explain such anomalies.

　　** END OF EXAMININATION **

　　MORNING SESSION

　　COURSE 8: Investment - 8 - GO ON TO NEXT PAGE

　　November 2000

　　Afternoon Session

　　** BEGINNING OF EXAMINATION **

　　AFTERNOON SESSION

　　Beginning with question 8

　　8. (4 points) As a product development actuary you have been asked to research and

　　develop an Equity Indexed Annuity (EIA) product.

　　(a) Describe the basic product features of an EIA.

　　(b) Recommend and justify an investment strategy for the EIA product.

　　you have recommended in (b).

　　COURSE 8: Investment - 9 - GO ON TO NEXT PAGE

　　November 2000

　　9. (7 points) Consider a simple sequential Commercial Mortgage-Backed Securities

　　(CMBS) deal with the following senior/subordinated structure:

　　Class Rating Average Life Size

　　A-1 AAA 9.3 73.50

　　A-2 AA 10.0 5.50

　　A-3 A 10.0 6.00

　　B-1 BBB 10.0 4.75

　　B-2 BB 10.0 4.00

　　B-3 B 10.0 4.00

　　C Not Rated 10.0 2.25

　　Loan N/A 9.5 100.00

　　Collateral information:

　　Debt Service

　　Coverage

　　Ratio

　　(DSCR)

　　Loan-to-value

　　(LTV)

　　Net Operating

　　Income (NOI)

　　Volatility

　　Original 2.5 65% 6%

　　Stressed 1.2 90% 10%

　　? Collateral consists of 9% coupon, non-callable, 10-year balloon, commercial

　　mortgage loans with a 30-year amortization schedule.

　　? Subordinated class loss allocation: C, B-3, B-2, B-1, A-3, A-2.

　　(a) Describe how your Option Adjusted Spread (OAS) valuations would change by

　　rated class if the collateral weighted average DSCR and LTV ratios were to

　　change over the short term from original to stressed levels.

　　(b) Describe the relative impact of using the stressed NOI volatility assumption

　　versus the original assumption on your OAS valuations for the B classes.

　　COURSE 8: Investment - 10 - GO ON TO NEXT PAGE

　　November 2000

　　Afternoon Session

　　9. (Continued)

　　? The collateral is made up of lower quality commercial mortgage loans that

　　have prepayment penalties and are fully callable at par after five years without

　　penalty.

　　? The most senior class is priced at a discount.

　　Describe the impact of these assumptions on your OAS valuations for the most

　　senior class.

　　(d) (i) Explain the rationale for an issuer to use interest-only (IO) classes in a class

　　structure.

　　(ii) Describe the sensitivity of the OAS valuation of an IO class to default losses

　　and involuntary principal payments in a senior-subordinated CMBS deal.

　　COURSE 8: Investment - 11 - GO ON TO NEXT PAGE

　　November 2000

　　Afternoon Session

　　10. (7 points) You are the portfolio manager for a United Kingdom domiciled insurance

　　company. The portfolio currently has a U.S. asset of $300,000 with a volatility

　　(s) of 0.02 per day.

　　You have been asked to evaluate an investment in a Planned Amortization Class (PAC)

　　tranche of a collaterized mortgage obligation, where the mortgage collateral is residential

　　mortgages originated in the U.S. The PAC security you are considering is $200,000 and

　　has an asset volatility(s) of 0.015 per day.

　　The two assets have a correlation factor of 30%. The change in portfolio value is

　　normally distributed and asset returns have a bivariate normal distribution.

　　(a) Describe the factors affecting mortgage prepayment modeling.

　　(b) Describe, in general, the risks associated with political climate risk.

　　hedging this asset.

　　(d) Assess the benefit of diversification when adding this PAC security to the

　　portfolio, using a 5-day, 95% VAR. Show your work.

　　COURSE 8: Investment - 12 - GO ON TO NEXT PAGE

　　November 2000

　　Afternoon Session

　　11. (6 points) Your company has a portfolio of investment-grade bonds and mortgagebacked

　　securities (MBS) with an option-adjusted duration of 4 years. The portfolio

　　supports a closed block of single premium deferred annuities (SPDAs) with minimum

　　rate guarantees of 5%.

　　The company, using the portfolio yield method, declares the crediting interest rates

　　monthly. However, the V.P. of marketing strongly recommends that the credited rate be

　　based on current market rates.

　　The company's economist has forecast the following interest rates under two economic

　　scenarios:

　　Current

　　Environment

　　Recession

　　Scenario

　　Inflation

　　Scenario

　　10 Year T-Note Yield 6% 4% 8%

　　90 Day T-Bill Yield 5% 3% 11%

　　(a) Predict the effects on your company's asset portfolio and the SPDA block using

　　each interest rate crediting methodologies under the following:

　　(i) recession scenario

　　(ii) inflation scenario

　　(b) Explain why it may be disadvantageous to reposition the portfolio using outright

　　sales and purchases.

　　environment to:

　　(i) recession scenario

　　(ii) inflation scenario

　　(d) Describe the risks related to the options strategies used in (c).

　　COURSE 8: Investment - 13 - GO ON TO NEXT PAGE

　　12. (6 points) XYZ Life Insurance Company originates home equity loans to elderly

　　homeowners. The loan is not due for repayment until the borrower dies or moves out of

　　the property. The amount of the initial loan is based on the age of the borrower and the

　　property value. Interest and fees are accumulated until repayment. The only source of

　　repayment is the property.

　　A government institution provides insurance against the risk that the eventual repayment

　　amount is less than the loan balance at that time. The premium, which is added to the

　　loan balance, is an initial fee of 2% of the loan value and 0.5% of the outstanding loan

　　balance annually. The homeowner can repay in full at anytime without penalty.

　　The loan interest rate is reset every six months. The net rate of interest, after insurance

　　premium and expenses, is the rate on 6 month CD's plus 3%. Based on projected cash

　　flow, the company issues GICs of 1, 3 and 5-year maturities.

　　The following three strategies have been proposed:

　　(i) Issue fixed rate instead of variable rate loans.

　　(ii) Swap the variable interest rates for fixed interest rates.

　　(iii) Purchase insurance against the risk of homeowners dying earlier or later

　　than expected.

　　(a) Analyze the risks associated with the current strategy.

　　(b) Describe the risks associated with the three proposed strategies.

　　COURSE 8: Investment - 14 - STOP

　　November 2000

　　Morning Session

　　13. (7 points) You are given the following information about a European put option on a

　　non-dividend paying stock:

　　? Stock price 40

　　? Risk-free interest rate 7% (continuously compounded)

　　? Strike price 35

　　? Time to maturity 8 months

　　You are also given the following volatilities derived from actively-traded European call

　　options on the stock:

　　Strike Price

　　Time to maturity 30 35 40 45

　　3 months 0.290 0.225 0.180 0.150

　　6 months 0.280 0.230 0.230 0.160

　　1 year 0.275 0.236 0.221 0.180

　　(a) Calculate the price of this option using the Black-Scholes formula. Show your

　　work.

　　(b) Contrast the stock price distribution implied by the volatility matrix with the lognormal

　　distribution.

　　14. (5 points) The asset portfolio of a U.S. life insurance company includes real estate

　　properties. The portfolio manager is currently considering adding to the portfolio an

　　equity investment in an office building in Atlanta. The building is fully leased at fixed

　　rates with 10 years remaining on its leases and subject to a mortgage equal to 50% of its

　　current market value. The mortgage is for 10 years, interest-only, and interest is paid

　　monthly at 1 month LIBOR plus a fixed spread.

　　(a) Evaluate the risks of this specific investment.

　　(b) Propose approaches to reduce the risks identified in (a).

　　COURSE 8: Investment - 15 - STOP

　　November 2000

　　Morning Session

　　15. (7 points) The debt of Company X consists of one zero coupon bond with the following

　　payment probabilities at maturity:

　　Default Risk Probabilities

　　Real World Risk-Neutral

　　No default 85% 75%

　　Default with 70% recovery 10% 15%

　　Default with 35% recovery 5% 10%

　　Additional information is as follows:

　　? Debt maturity 5 Years

　　? Payment due at maturity 1000

　　? Risk-free rate 5% (continuously compounded)

　　Company Z has written a European option which will pay 1000 in 5 years in exchange

　　for Company X’s debt.

　　Assume Company X and Z have equal but independent default risk.

　　(a) Calculate the market's expected spread for the bond over the risk-free rate. Show

　　your work.

　　(b) Determine the possible payoffs at maturity of a European option written by

　　Company Z which will pay 1000 in 5 years in exchange for Company X's debt.

　　COURSE 8: Investment - 16 - STOP

　　November 2000

　　Morning Session

　　16. (6 points) You are given the following information about two estimations of the Market

　　Value (MV) of the total policy liabilities of a life insurance company:

　　Method used Estimation

　　MV (Liability) $2.0 billion

　　MV (Asset) – MV (Equity) $1.8 billion

　　(a) Contrast the two methods.

　　(b) Explain how the uncertainty of cash flows can be reflected in the estimation of the

　　market value under the MV (Liability) method.

　　17. (5 points)

　　(a) Describe the following fixed income risk measures:

　　(i) prepayment uncertainty,

　　(ii) volatility risk (vega),

　　(iii) zero volatility spread (ZVO),

　　(iv) spread duration.

　　(b) Your company’s fixed income portfolio contains MBS, CMBS, CMO, ARM,

　　callable and putable corporate bonds, and ABS. Explain the impact of each of the

　　risk measures above on the different fixed income asset classes.

　　** END OF EXAMINATION **

　　以上则是【北美精算师】November2001Course8V——SOA历年真题系列，请耐心看题、答题与牢记章节重点。

　　高顿网校之励志箴言：人生一世，总有些片断当时看着无关紧要，而事实上却牵动了大局。 —— 萨克雷

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