北美精算师真题（2003年11月）Course8V（第四课），当然先把历年大纲的讲义看熟了。
　　16. (4 points) You are building a model for forecasting equity real estate values in portfolio
　　asset projections, given economic scenario inputs.
　　(a) List and justify the items you will need in order to build a robust model for equity
　　real estate values.
　　(b) Describe a method for determining the optimal level of equity real estate in your
　　company’s various portfolios.
　　COURSE 8: Fall 2003 - 13 - GO ON TO NEXT PAGE
　　Investment
　　Afternoon Session
 
　　17. (8 points) You are the Chief Risk Officer of Pusillanimous Re that provides annual
　　catastrophe reinsurance to the marketplace. You invest the asset portfolio in cash and
　　three zero-coupon bonds, each with 1-year time to maturity. You are given the following
　　information:
　　Reinsurance exposure: Excess cost layer between 100 million and 350 million of 1 billion
　　total earthquake exposure.
　　Cash Bond A Bond B Bond C
　　Market Value (millions) 2.0 2.2 2.0 1.8
　　Face Value (millions) 2.0 2.4 2.4 2.4
　　Expected default loss (%) 0 5 not given 15
　　Expected recovery rate (%) 100 not given 30 45
　　Historical default rate (%) 0 1 2 4
　　You are concerned about the default risk of your asset portfolio and the magnitude of
　　your liability exposure.
　　(a) Describe how you would calculate the 1-year default probability of Bond B using
　　(i) bond market prices, and
　　(ii) equity prices of the bond issuer.
　　(b) Calculate the 1-year expected default loss of Bond B implied by bond market
　　prices.
　　(c) Explain the reasons for the differences typically observed between the default
　　probabilities derived using historical default data and those derived from the bond
　　market prices.
　　(d) Compare and contrast the use of add-up credit default swaps (CDS) and first-todefault
　　CDS for management of the default risk in the asset portfolio.
　　(e) Describe how a first-to-default basket CDS on the asset portfolio can be valued
　　using a Gaussian copula approach.
　　(f) Explain how CAT bonds work and how they can be used to manage the option
　　structure of your liability risk exposure.
　　COURSE 8: Fall 2003 - 14 - GO ON TO NEXT PAGE
　　Investment
　　Afternoon Session
 
　　18. (4 points) The financial results at your insurance company over the past year have been
　　dismal. Your new CFO has asked you to determine the reasons behind this. She has
　　recently read about transfer pricing for banks, and is interested in applying this concept to
　　your company.
　　Total returns for your company:
　　Duration Credit Rating Return
　　Assets 10 A 5.70%
　　Liabilities 7 AAA (claims paying) 6.20%
　　Total return of generic assets over the past year:
　　Credit Rating
　　Duration A AA AAA
　　5 6.00% 6.50% 7.50%
　　6 5.90% 6.40% 7.40%
　　7 5.80% 6.30% 7.30%
　　8 5.70% 6.20% 7.20%
　　9 5.60% 6.10% 7.10%
　　10 5.50% 6.00% 7.00%
　　Your CFO wants to see the returns attributed to the following four sources:
　　1) Liability performance
　　2) Asset performance due to interest rate risk
　　3) Asset performance due to credit risk
　　4) Asset performance due to selection of individual securities
　　(a) Construct the appropriate benchmark portfolios from the generic assets provided.
　　(b) Attribute your company’s performance to the four sources described above, using
　　the benchmarks constructed in (a).
　　(c) Describe the considerations in benchmark selection when applying transfer
　　pricing to an insurance company.
　　COURSE 8: Fall 2003 - 15 - GO ON TO NEXT PAGE
　　Investment
　　Afternoon Session
 
　　19. (5 points) The current value of the assets and liabilities are respectively A0 and L0 . The
　　liability in five years is designated L5 . Senior management is concerned that the asset
　　portfolio could drop in value below the liability value in five years.
　　One method to model the asset returns would be using a multivariate normal model
　　and modified Cholesky decomposition with the following assumptions:
　　m = [0.12, 0.06, 0.085]=[equities, fixed income, real estate]
　　covariance matrix =
　　0.04 0.003 0.014
　　0.003 0.0025 0.0015
　　0.014 0.0015 0.01
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　　(a) Evaluate potential problems in using this method to model the asset returns.
　　(b) Explain and *uate the use of an option-based portfolio hedging strategy for a
　　portfolio of assets, A0 , and liabilities, L0 , where A0L0 , using
　　(i) a put, and
　　(ii) a call.
　　(c) Demonstrate that the strategies in (b) for the put and call options are equivalent,
　　assuming that cash flows are reinvested.
　　(d) Explain and *uate the use of dynamic hedging by replicating the put option
　　using a risky portfolio and a duration-matched Treasury portfolio.
　　COURSE 8: Fall 2003 - 16 - GO ON TO NEXT PAGE
　　Investment
　　Afternoon Session
　　正义是社会制度的首要价值，正像真理是思想的首要价值一样。——高顿网校为人处世

 

 
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