1.A company anticipates the purchase British pounds in 6 months. The standard deviation ofthe change in British pounds over a 6-month period is calculated to be 9%. The company chooses to hedge their exposure by buying future contracts on EUR. The standard deviation ofthe change in the futures price over a 6- month period is calculated to be 10% and the correlation coefficient between British pounds and EUR is 0.70. Calculate the optimal hedge ratio.
　　A. 1.0
　　B. 0.90
　　C. 0.70
　　D. 0.63
　　2.The AT&T pension plan reports a projected benefit obligation of $17.4 billion. If the discount rate decreases by 0.5%, this liability will increase by $0.8 billion.Based on this information, the liabilities behave like a
　　A. Short position in the stock market
　　B. Short position in cash
　　C. Short position in a bond with maturity of about nine years
　　D. Short position in a bond with duration of about nine years
　　3.Bemard Madoff Investment Securities (BMIS) Form 13F filings were suspicious because they revealed that the portfolio was in:
　　A. Mostly cash at the end of each quarter.
　　B. Mostly S&P 100 stocks at the end of each quarter.
　　C. More than 95% NASDAQ stocks at the end of each quarter.
　　D. A 50-50 mix ofcash and S&P 100 stocks at the end ofeach quarter
　　Answer：
　　1.D
　　Optimal hedge ratio= 0.07 *0.09/0.10 =0.63
　　2.D
　　We can compute the modified duration ofthe liabilities as
　　D = -(ΔP/P)/ ΔY)= -(0.8/17.4) / 0.0005 = 9.2years .
　　So, the liabilities behave like a short position in a bond with a duration of around nine years.
　　Answers a) and b) are incorrect because the liabilities have fixed future payoffs， which do not resemble cash flow pattems on equities or cash. Answer c) is incorrect because the duration of a bond with a nine-year maturity is less than nine years. For example， the duration of a 6% coupon par bond with nine-year maturity is only seven years.
　　3.A
　　Form 13F tillings rcvealed that the portfolio with primarily in cash, with some smaIl positions in smallcr stocks. This is ìnconsistent with the split-strike conversion strategy. Madoff said he converted to cash at the end of the quarter because he did not want to make public his investment strategy. This should have been a red flag to regulators and investors.