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　　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
　　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.
　　(c) Describe the potential risks associated with an EIA and the investment strategy
　　you have recommended in (b).
　　COURSE 8: Investment - 9 - GO ON TO NEXT PAGE
　　November 2000
　　Afternoon Session
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