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2014年度北美精算师考试大纲——SOA真题November2001Course8V（*9部分）

来源：高顿网校 2014-07-28

　　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

　　N

　　ovember 2000

　　Morning Session

　　3. (Continued)

　　(c) (6 points)

　　(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.

　　(c) Assess the validity of the proposed model given the information above.

　　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.

　　(c) Describe how you would use OAS, considering the shortcomings.

　　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
　　高顿网校之名人心得：婴儿在母亲怀抱中哺育成长，从母亲获得最初的感情和思想……可以说精心培养儿童心灵的是妇女，是伟大的母亲。

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