UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGNCollege of BusinessDEPARTMENT OF FINANCEFirst ExamFinance 432 Name:________________________Spring, 2007 Maximum Number of Points: 30This exam is open book, open note. You may use a calculator, but not a computer, cell phone or any other communication device. Unless otherwise noted, each part of each question is worth 2 points.1. An insurer has agreed to buy 10,000 ounces of gold through the futures market at a price of $650 per ounce. The initial margin required is $100,000 and the maintenance margin is $75,000. Given the following futures prices, fill in the following table, and show how much money is in the insurer’s account at the end of each day. If the insurer has a margin call, assume the insurer adds only the minimum amount required. Round all figures to the nearest dollar.a)Day Price ofGold perounce ContractValueChange inValueMarginAccountAmount Added(if any)0 650 $6,500,000 - $100,000 -1 6522 6473 6434 648b) Explain how marking-to-market works to a Vice President of Claims for a life insurance company who is not familiar with finance.2. The current spot rates are listed below:0r13.5%0r23.9%0r34.2%0r44.5%0r54.7%0r64.9%0r75.1%0r85.2%0r95.3%0r105.3%0r155.3%0r205.3%0r255.1%0r305.0%a) Plot the spot rate curve based on these values. b) Which theory of the term structure could best explain this shape? Support your choice.c) Calculate the implied five year forward rate twenty-five years from now (5f25).3. Calculate the values and draw the risk profiles for the change in value of these instruments with respect to changes in interest rates for each of the following situations. Be sure to label the axes.a) A $1 million 10 year zero coupon bond based on a current interest rate of 6%.b) A Forward Rate Agreement (FRA) for the party paying fixed based on a notional amount of $1 million for a one year period starting on July 1, 2007. The contract rate is 6%. The current interest rate is 6%. c) The next payment on an 8% cap on a notional amount of $1 million. Assume the contract is settled annually. Current interest rates are 6%.4) A stock currently sells for $22.50. The exercise price on a call option with 1 year until expiration is $25. The risk-free rate is 5.0%, the stock has an assumed volatilityof 0.25, and the price of a put option with the same terms is $3.00. What is the price of the call option?5) The ten largest aggregate losses from a set of 100 values of the program you used on assignment 3 are listed below in descending order: 654,560,199 272,768,641 146,039,039 108,034,367 99,019,828 98,590,288 86,426,212 78,824,686 78,676,238 73,729,082 a) What is the 95% VaR based on these values?b) What is the Tail VaR based on the same parameters used in part (a) of this question?c) Explain VaR to a senior actuary who is not familiar with financial risk management.6. What is the limit that portfolio risk approaches as the number of risks increases if the individual risks are independent of each other? Explain.7. Which type of insurance enterprise (property-liability insurers, life insurers or pension plans) is most exposed to liquidity risk? Explain why.8. What is the invoice price for a T-bill future based on a notional amount of $1 million if the index price is 93.0? Assume there are 90 days in the contract