15. (4 points) A one-step binomial tree is used to model the impact of an important
　　announcement on the stock price of Company XYZ. There is a 50% chance that the
　　announcement will be positive for the company. The Company does not pay dividends.
　　Current stock price = $20
　　Stock price after good news = $30
　　Stock price after bad news = $15
　　Time period = 3 months
　　Risk-free rate (continuous compounding) = 5 %
　　(a) Calculate the price of a 3-month call option on the Company stock with strike
　　price equal to $22.
　　(b) The call writer decides to dynamically delta-gamma hedge the option based on a
　　standard lognormal model. Evaluate the effectiveness of this approach in this
　　context.
　　COURSE 8: Fall 2005 - 7 - GO TO NEXT PAGE
　　Investment
　　Afternoon Session
　　16. (8 points) You are consulting to a P&C company regarding the fair value of their
　　insurance liabilities. You are examining a single one-year policy with an uncertain claim
　　payment payable at the end of the year. Your analysis determines the following:
　　? The expected claim payment is $2,000.
　　? The expected annual return of the asset portfolio backing the liability is 7%.
　　? The one-year risk-free rate is 5%.
　　? The company’s tax rate is 35%.
　　? The ratio of equity to liabilities for similar products in the marketplace is 20%.
　　? The return on equity for similar products in the marketplace is 15%.
　　(a) Calculate the fair value of the liability at the beginning of the policy year using
　　the cost-of-capital approach.
　　(b) Calculate the Market Value Margin that will produce the same fair value when
　　discounting at the risk-free rate.
　　(c) Identify the assumptions underlying perfect markets that may not hold in the real
　　world with respect to insurance risks.
　　(d) List two reasons why U.S. Treasury securities may not be appropriate as the riskfree
　　rate for fair valuation.
　　COURSE 8: Fall 2005 - 8 - GO TO NEXT PAGE
　　Investment
　　Afternoon Session
　　17. (7 points) You have been asked to apply the Excess Spread approach to *uate the
　　static credited rate reset strategy and the dynamic reset strategy.
　　(a) Define Excess Spread and Required Spread on Assets (RSA).
　　(b) List the risks associated with an SPDA policy.
　　(c) List the steps when measuring interest rate risk with the Excess Spread approach.
　　(d) Calculate the Excess Spreads of the following two strategies:
　　? The static credited rate reset strategy:
　　RSA=80 bp
　　Spread on assets is 150 bp, credit risk is 5 bp, and expense is 15 bp.
　　? The dynamic reset strategy:
　　RSA=70 bp
　　Spread on assets is 160 bp, credit risk is 10 bp, and expense is 20 bp.
　　(e) Appraise the use of each of the two strategies for setting the SPDA credited rates.
　　COURSE 8: Fall 2005 - 9 - GO TO NEXT PAGE
　　Investment
　　Afternoon Session
　　18. (4 points) You are performing an actuarial valuation of a defined benefit pension plan.
　　Your results are showing the plan to be under-funded, with a funding ratio of 70%. The
　　plan sponsor wishes to find an asset portfolio using the surplus frontier approach that will
　　correct the problem.
　　You are given the following:
　　? Liability beta = 0.8
　　? Risk-free rate = 4.0%
　　? Market portfolio excess return over risk-free rate = 8%
　　? Alpha = 0
　　(a) Explain the Minimum Surplus Variance Portfolio.
　　(b) Compute the minimum asset beta required to give a positive surplus return.
　　(c) Assess the appropriateness of this strategy.
　　COURSE 8: Fall 2005 - 10 - GO TO NEXT PAGE
　　Investment
　　Afternoon Session
　　19. (7 points) You work for a publicly traded company with a defined-benefit pension plan.
　　Your CFO read recently that shifting pension assets from stocks to 100% bonds reduces
　　risk, and creates a tax arbitrage, resulting in gains to shareholders. You are given the
　　following:
　　Current pension assets = $10,000,000
　　Current pension liabilities = $10,000,000
　　Current pension asset allocation: 60% stocks, 40% bonds
　　Corporate tax rate = 35%
　　Personal tax rate on stocks = 18%
　　Personal tax rate on bonds = 28%
　　Estimated stock return = 11%
　　Estimated bond return = 7%
　　(a) Compare the Tepper arbitrage and the Black arbitrage.
　　(b) Compute the theoretical shareholder gain using both methods.
　　(c) Outline the challenges and arguments your CFO may face in moving to 100%
　　bonds.
　　COURSE 8: Fall 2005 - 11 - STOP
　　Investment
　　Afternoon Session
　　20. (3 points) As the CFO of your life insurance company, you have been asked to provide a
　　single measure of risk associated with a portfolio of whole life insurance products.
　　The current value of the portfolio is $61,125,856. Most of the value of the portfolio can
　　be explained by a set of monthly observable independent variables.
　　The 95% confidence level of VaR for the portfolio value over a two-year time horizon is
　　$30,170,914.
　　Critique this approach as a measure of portfolio risk.
　　**END OF EXAMINATION**
　　她们希望你总是伟大，总是漂亮。她们根本不会想到，天才总是病态的。——高顿网校之做人原则