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EC3333 final 2007 Fall - EC3333 NATIONAL UNIVERSITY OF...

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Unformatted text preview: EC3333 NATIONAL UNIVERSITY OF SINGAPORE EC3333 FINANCIAL ECONOMICS I (SEMESTERI : AY2-007-2008) Time Allowed: 2 Hours INSTRUCTIONS TO CANDIDATES 1. This examination paper contains FOUR (04) questions and comprises SIX1061 printed pages. . 2. Candidate must attempt THREE (3) questions. Question 1 is compulsory. It carries 30 marks. Answer any TWO (2) from the remaining THREE (3) questions, each carrying 10 marks. 3. This is a CLOSED BOOK examination. (Note : Students are not allowed to bring any reference materials to the examination hall at all) 4. The statistical tables are provided. 5. Total marks for the paper is 50 2 EC3333 _ Question 1 {Compulsoryl {BO-marks) A. State whether the following statements are True, False or Uncertain. Provide a short justification for your answer. (You are evaluated on your justification) [10 marks, 2 marks each] (a) (b) (C) (d) (E) B. De (8) (b) (c) (d) (e) An asset with a beta smaller than one cannot have a total variance greater than the variance of the market returns. An option (call or put) with less time to expiration will sell at a higher price than an option with more time to maturity. (Assume that the options are on the same. stock and have the same strike price.) ' Let RSG be the annual risk free rate in Singapore, RUK be the risk free rate in the United Kingdom, F be the futures price of S$/BP for a 1—year contract, and E the spot exchange rate of S$/BP. If RSG _ > RUK, then E < F. On September 1, you took a long position on one December Stock futures contract at a futures price of $42. On October 1 the December futures price were 43. If you closed your position on October 1, your loss would be $1. The liquidity preference theory indicates a flat yield curve if anticipated future short—term rates exceed the current short—term rate. scribe the differences between options and futures CML and SML short rate and spot rate hedgers and arbitrageurs straddle and strangle _ [10 marks] 3 EC3333 The spot price of wheat is 550 cents per bushel. The risk—free rate of interest is 5% per annum. (a) Suppose the six—month forward price is 581.1 cents per bushel. The storage cost to be paid at the end of the contract is 17 cents per bushel. Is there an arbitrage opportunity in this market? Explain how you would exploit it. [3 marks] (b) Now suppose that the six—month forward price is equal to 585 cents per bushel. Consider a miller who needs to buy 20,000 bushels of wheat in exactly six months and wishes to hedge his exposure to fluctuations in the price of wheat. If one wheat forward contract obligates the buyer to purchase 5,000 bushels at the forward price, describe how the miller can hedge the commodity price risk using a position in forward contracts. Be sure to specify the position (buy/seli), number of contracts, and the guaranteed doilar cost in six months. {2 marks] (c) Construct the hedge for the miller using options rather than forwards. Specifically, you can buy or sell either put or call options given in the following table: Strike Price Cail Premium Put Premium cents er bushel cents er bushel cents er bushel 585 30 34 Option contracts are per 5,000 bushels. Hence, the table reads as follows: If you buy one put(caii) option contract on wheat for six months with a strike price of 585 cents, you will have a right to seii( buy) 5, 000 bushels at a price of 585 cents per bushel. Today you have to pay 34(30) cents per bushel for this option. Which option do you buy/se-li and how many? What is the maximum cost including the option premiums that the miller guarantees by hedging with options? [3 marks] (cl) A friend of yours wants to create a long futures position on wheat and he asks for your help. Using the information given in (c) for put and call, Can you replicate the cash flows of the futures contract? Explain. (You are free to borrow or lend at risk—free rate.) [2 marks] 4 _ EC3333_ Question 2| 10 marks] A)’ Assume that you can either invest all of your weaith in one of two assets, ABC and XYZ, or some proportion of your wealth in each. The rates of return have the following means and standard deviations: Asset Mean Returns Standard deviations ABC 20% 30% 'XYZ 10% 20% (a) What is the expected return of the global minimum variance - portfolio if the two assets are perfectly negatively correlated? [2 marks] (13.) Suppose you can also invest ina riskfifree asset that has a return of 13%. Is the return on the risk—free asset consistent with market equilibrium? Expiain. [1 mark] B) Consider the portfolios P and Q, with the following characteristics: Portfolio P Portfolio _Q Standard deviation 20% 32% Beta 0.8 1.2 The Portfolios are valued in a market where investors can freely borrow and lend, using T-bills, at risk-free rate of 5% and they require a risk premium of 8% for holding the market portfolio. Assume CAPM hold. (a) Compute Sharpe ratios for portfolios P and Q. [3 marks] (b) Suppose that you can only invest in one of the above portfolios and T—bills to construct the lowest risk portfolio that gives you an expected return of 14.6%. What is the standard dEViation of this portfolio? [2 marks] '(c) Now suppose that you can iend at the risk-free rate of 5% but are forced to borrow at 7% because of credit concerns. Explain how to construct the lowest risk portfolio with an expected return of 14.6%. [2 marks] 5 ' EC3333 uestion 3 10 marks On November 1, you observe that Centrix Corporation stock price is $40. The April call option and put option written on the stock With exercise price $45 will expire in exactly six months. Assume that the interest rate is 10% pa. The volatility (standard deviation). of the underlying stock is estimated to be 0.45. Centrix will not pay dividends over the next six month. or: SON(d,)—Xe“"N(d2) Where (5%l+lr+“%li In of: 1 OJ; d2 :51, 4% (5) Calculate the call price using the Black»Scholes model. [5 marks] (b) Determine the price of the put option using the put—call parity theorem [1 mark] (c) Calculate the time value of the call and put options on November 1. [1.5 marks] (d) Suppose that the call and put described above are trading at the prices you obtained in (a) and (b). You believe that, due to recent economic events, the volatility of the underlying stock will be in excess of 60%. You have no view about whether the stock wili go up or down in next few months. Describe how you might trade on this view. You are free to buy or sell the call/put or both. Plot the payoff of your proposed strategy as a function of the underlying stock price on the maturity date of the options. ' [2.5 marks] 6 EC3333 Question 4|10 marksl Consider the following prices for zero—coupon bonds with face value of $1,000: Maturity Price 1 $952.381 2 $889996 3 $827849 (a) Calculate the yield to maturity of each of the above bonds. [1.5 marks] (b) What is the forward rate for a onenyear loan, two years from today? [1.5 marks] (c) Assume that in addition to the zero coupon bonds described above, there is a three—year coupon bond with a face value of $1,000 and an coupon rate of 20%, however, the bond does not begin making payments until two years from today. That is, if you purchase the bond today, you will receive the first coupon payment two years from today and the next coupon payment plus principal three years from today. What is the duration of this coupon bond? [3 marks] (d) If you expect to sell the above coupon bond after receiving its first coupon payment, what is the market expectation of the price that the bond will sell for two—years from now? (Assume expectation theory of the yield curve is correct.) [2 marks] (e) Two years from today, you intend to begin an MBA program. As a result, you have been offered a contract that will cost you $19,500 today, but will give you $10,800 for each of your two years spent at business school. More specifically, you will receive two payments of $10,800: onein two years from today and another in three years from today. Should you take advantage of this contract? Why? [2 marks] - END OF PAPER - ...
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