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EC3333 Final 2006 Spring - EC3333 NATIONAL UNIVERSITY OF...

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Unformatted text preview: EC3333 NATIONAL UNIVERSITY OF SINGAPORE EC3333 FINANCIAL ECONOMICS I (SEMESTER 11 : AY2006-2007) Time Allowed: 2 Hours INSTRUCTIONS TO CANDIDATES 1. This examination paper contains FOUR (04) questions and comprises Seven (07) printed pages. 2. Candidateimust attempt THREE (03) questions. Question 1 is compulsory. It carries 30 marks. Answer any TWO (2) from the remaining THREE (3) questions, each carrying 10 marks. 3. Total marks for the paper is 50. 4. This is a CLOSED BOOK examination. EC3333 Question 1 ICompulsory] (30 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.) (i) Suppose that a share of DBS now sells for $22.80. Then a call option written on the DBS stock that expires in November 01, 2007, with a strike price of $26.50, is worthless today. (ii) The “efficient frontier” relates all the combination of risk and return that represent the same level of satisfaction. (iii) Modified duration of a coupon bond is always less than the duration of a zero coupon bond with the same maturity and face value. (iv) The hedge ratio, A, that is used in the binomial option pricing model will be lower. the more in~the money the call option is. (v) Suppose that the spot price of the euro is currently 93 cents (USS). The one-year futures price is 90 cents (USS). The interest rate is higher in euro zone. (B) [5 marks] You are a manager in a brokerage firm which makes markets in a variety of securities including stock, bonds and options. The firm assumes that the CAPM holds in the market. The expected return and the standard deviation of the XYZ stock 8.72% and 40% respectively. The expected return of the market portfolio is 10% and its standard deviation is 15%. The correlation between stock and the market return is 0.2. (a) What is the beta of XYZ stock? [1 mark] (b) Find the risk-free interest rate. [1.Smarks] (c) XYZ stock is currently selling at $50. Suppose the firm expects to write a six-month European call option on XYZ with an exercise price of $48. It is given that dl20.56, d220.27 and c : SON(d, ) — Xe”’N(d2) What would be the theoretical price of the call option? [2.Smarks] EC 3333 (C) Briefly Explain. [5 marks] (a) Optimal risky portfolio (b) Duration of a bond (c) Preferred Habitat theory (d) Diversification (e) Protective put (D) [10 marks] (a) Hedgers, speculators, and arbitrageurs are all desirable participants in the derivatives market. Explain the role of each. [3 marks] (bl A futures contract is available on a company whose stock is currently priced at $200. Each futures contract calls for delivery of 1,000 shares of stock six months, daily marking to market, an initial margin of $20,000 and a maintenance margin of $10,000. Current futures price is $208. (i) Suppose the futures price drop to $193. Will an investor that has a long position in one futures contract of this company realize a gain or a loss? Why? What will be the amount of this gain or loss? [1.5 marks] (ii) Following the price drop in (1), what will be, if any, the change in the margin account? Will the investor need to top up the margin account? If yes, by how much and why? [2.0 marks] (iii) Given the price drop in (1), what is the percentage return on the investor’s position? [1.5 marks] (iv) Suppose the minimum price change is $0.50. At what price an investor who has a long position in the futures contract get a margin call? [2.0 marks] EC 3333 Question 2| 10 marks] John has just inherited $100,000 that he is going to use for remodelling his house. He needs to invest the money until the plans are done and the construction begins. This may take one or two years. Since he has a short horizon and he is risk averse, he decides to invest in safe government bonds. He contacts a broker and is told that a one year zero-coupon bond with face value $1,000 sells for $952.38 and a two-year zero—coupon bond with face value $1,000 sells for $898.45. (a) What are the current one-year and two-year spot interest rates? [2 marks] (b) What is the forward rate? [1 mark] His broker also points out the possibility of buying two-year bonds with 10% coupons, paid annually, in case the planning stage lasts for two years but John needs to pay some expenses after one year. (c) What is the maximum price that John will accept to pay for this coupon bond? [1 mark] (d) Find the duration of this bond [2 marks] John is really tempted by the low price of the twowyear zero-coupon bond but, as his broker points out, if he buys two-year bonds he is not sure of how much money he will have to spend 011 the remodel. Thus, for the first time in his life, John reads the fnancial and economic pages of his newspaper and forms his expectations about the likely values of the interest rate next year. He estimates that there is a 50% chance that in one year the one-year interest rate wil] be 6%, that there is 30% chance that it will be 5.5% and 20% chance that it will be 5%. (e) What is John’s expected value for the interest rate next year? [1 mark] (f) Is his estimate consistent with the expectations hypothesis on the term structure of the interest rates? Explain the content of the expectations hypothesis, under which conditions it is likely to be satisfied, and discuss whether these conditions are likely to be met. [1.5 marks] (g) 13 his estimate consistent with the liquidity preference hypothesis? Explain the content of the liquidity preference hypothesis, under which conditions it is likely to be satisfied, and discuss whether these conditions are likely to be met. [1.5 marks] EC3333 Question 3| 10 marks] Consider two stocks "B“ and "C" with following properties: E(rB)=8% E(rc):20% GB=IS% ocz-zscyo Correlation =ch = —0.2 The risk free rate is 5% (a) You are advising a client who has 331 million invested entirely in stock C. Your job is to come up with a better portfolio than the one currently chosen by your client. Design a portfolio R (using B, C and the risk—free security) that has the same expected return as your client's current portfolio but has the lowest standard deviation possible. (i) What investment is in each of B, C and the risk-free security? [3 marks] (ii) What is the standard deviation of the portfolio R? [1 mark] (iii) Draw the CAL on the risk-return diagram. Show the efficient frontier, Optimal risky portfolio. portfolio R, Stock B and Stock C [1 mark] (h) Suppose that your client want to achieve the highest possible expected return while keeping standard deviation of her portfolio below 18%. What investment portfolio would you recommend? How high the associated expected return? [2 marks] (c) You figure out that your client’s risk aversion coefficient is A=4, would you advise your client to change her investment strategy in part (b)? [1 mark] (d) Now suppose you meet another client, who would like to achieve an expected return of 12% at the lowest risk possible. What is your recommended portfolio? What if borrowing and lending rates differ? Explain briefly. [2 marks] EC3333 Question 4 110 marksl (A) Jo Fullerton is evaluating option strategies that will allow him to profit from large moves in a stock's price either up or down. He believes that a combination of a long put and a long call option with the same expiration and exercise price would meet his objectives. Jo gathers the AOB stock and option pricing data shown in the following table: Price Exercise Price Expiry AOB call option $5 $50 3 months from now AOB put option $4.20 $50 3 months from now Current price of the A013 stock is $50 Risk-free interest rate 25% (i) Suppose Jo buys the put and the call option (given) on AOB stock to achieve his objectives. Draw a payoff/profit diagram at expiration and answer the following: maximum possible loss per share. maximum possible gain per share and the break even prices. 12 marks] (ii) Jo has some background in option pricing. He anticipates the AOB stock to go up or down by 20% in next three months. What would be the theoretical price of the A013 call option and put option on the stock. [3.5 marks] (B) Side Porch Games, Inc. is a USA based company that develops and manufactures games for people of all ages. On the manufacturing side, Side Porch contracts out much of its work to a company located in Thailand, which charges Side Porch in the Thai currency, bahts. The current spot exchange rate is 40.75 bahts per U.S. dollar and the six-month forward rate is 41.05 bahts per dollar. The current six-month interest rate in USA is 2.4%, and in Thailand it is 3.0%. The Thai manufacturer is scheduled to ship a large order to Side Porch. The bill is for 320,000 bahts. due in six months. (i) Does interest rate parity hold? [1.5 marks] (ii) Suppose you would like to hedge your liability to the Thai manufacturer completely. How would you construct the hedge? Explain. {3 marks] EC3333 Formulas: When two risky assets (B and. C) and a risk-free asset (n) are available, weights of optimal risky portfolio : Rama?- —R,,(C)cov(r,,,1;.) Ramos + Rama: — (RAB) + RMCDCOVO' a) Bit ‘WB where 13,13) : E(?}:)“T} and RP(C) = E(r(.) v 1'] WV : I — WE For a utility function U : E(r)-0.005Aa- Optimal allocation in the risky asset # _ E(rl')_r,l w — —2 0.0!A0' -End of paper- ...
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