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 *uating 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。