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

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Unformatted text preview: EC3333 NATIONAL UNIVERSITY OF SINGAPORE EC3333 FINANCIAL ECONOMICS I (SEMESTERI : AY2006-2007) Time Allowed : 2 Hours INSTRUCTIONS TO CANDIDATES 1. This examination paper contains FOUR (04) questions and comprises Seven (07) 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. Total marks for the paper is 50. 4. This is a CLOSED BOOK examination. 2 EC3333 Question 1 |Comgulsory| [30 marks} (A) State whether the following statements are True, False or Uncertain. Provide a short justification for your answer. (10 marks 2 marks each.) (i) (ii) (iii) (M (V) The duration of a zero—coupon bond is increasing in the bond’s maturity T. When an investor buys a large number of shares of a stock, the firm specific risk of the stock would be mostly diversified away. A strategy that involves writing a put and writing a call (both with the same exercise price that equals the current stock price) ' is a bet that the price of the underlying stock will not change significantly before the expiration of the options. The current spot price of gold is $600 per ounce and the one- year futures price is $660 per ounce. These numbers tell us that the market is expecting at most a 10% increase in the price of gold over the next year. It is possible for a bond to have a positive yield to maturity (ytm> 0) and a price that is higher than the face value. (B) Suppose that a stock is priced at $30 and has standard deviation of 0.45. You buy a call option with an exercise price of 25 that expires in three months. A one—year zero—coupon bond with face value of $1000 sells at $952.38 Determine the theoretical value of the call. [4 marks] State the effect, if any, of each of the following two variables on the value of a call option. (a) a decrease in stock price volatility [1 mark] (b) an increase in exercise price [1 mark] (C) (D) (b) EC3333 Briefly explain. (6 marks) (1] (ii) (iii) (iv) (v) {vi} Market segmentation theory Convexity Optimal risky portfolio Market price of risk Yield curve Security Market Line Identify the fundamental distinction between a futures contract and an option contract, and briefly discuss difference between a futures contract and a forward contract. [3 marks] The spot price of Malaysian Ringgit (MR) is currently S$0.4278. The one-year futures price of MR is S$0.4164. Is the interest rate higher in Singapore or Malaysia? Why? [2 marks] You are a coffee dealer anticipating the purchase of 82,000 pounds of coffee in three months. You are concerned that the price of coffee will rise, so you take a long position in coffee futures. Each contract covers 37,500 pounds, and so, rounding to the nearest contract, you decide to go long in two contracts and buy the rest on the Spot in three months. The futures price at the time you initiate your hedge is 55.95 cents per pound. Three months later, the actual spot price of coffee turns out to be 58.56 cents per pound and the futures price is 59.20 cents per pound. Determine the effective price at which you purchased your coffee. [3 marks] 4 EC3333 Question 2 (10 marks! You are assigned to evaluate some option strategies that will allow your client to profit from certain moves in price of ABC stock and options written on ABC stock. ABC stock currently sells at $35. Risk— free rate is 4%. You have collected the following information: Strike Price Call option Put 0 tion All options mature in one—year from now. Some option prices were not available. (a) Calculate the price of ABC put option with X=3O and the price of ABC call option with X=50. [2 marks] (b) Construct a protective put strategy which guaranteed a minimum value of $30 at the maturity. Draw payoff /prof1t diagram. [2 marks] (c) Briefly explain how you construct a collar strategy using a share of ABC, a put option, and a call option. Use the given information to illustrate payoff and profit. [3 marks] (d) Which of the above portfolios (refer to (b) and (0)) is a better investment if you think that ABC has considerable upside potential, but there is also a chance that the share price might fall substantially? Why? [1.5 marks] (e) Which strategy {(b) or ((3)) is better if you think that the share price might increase by some but not too much, and it might fall substantially? Why? [1.5 marks] 5 EC3333 Question 3 [10 marks] John, a friend of yours, recently studied the Treynor—Black model to learn how to improve his current portfolio which consists of the market portfolio and T—bills. As he understands from the model it could be done by investing in a portfolio of mispriced securities (active portfolio) and a diversified portfolio (market portfolio). John has collected the following information: Market Potfolio M 16.0% 23% Active Portfolio A 22.8% 34% Riskwfree Rate (a) Find the Jensen’s alpha for the active portfolio. [1 mark] (‘0) Compute Sharpe measure for active and market portfolios. [1 mark] (c) After some tedious work, John came up with the composition of the optimal risky portfolio. According to his findings, he should allocate 60% in the market portfolio and rest in the active portfolio. What are the expected return, variance, and beta of the optimal risky portfolio? [3 marks] (d) Suppose John’s degree of risk aversion is A=2.8. What proportion, w, of the total investment Should be invested in the optimal risky portfolio? What would be the expected return and standard deviation of John’s complete (overall) portfolio? [3 marks] (e) Draw the CAL to represent his complete portfolio (refers to ((21)) on an expected return—standard deviation diagram. Show also the position of active and passive portfolios. [2 marks] 6 EC3333' Question 4 (10 marl-Isl A. Discuss how expectations (unbiased) theory for the term structure of interest rates could explain an upward slope of the yield curve. [2 marks] B. You are considering investing in a bond for the next twelve months. You limit your choice of bond to one of the following: Maturity Annual Yield to Face I Coupon maturity (0/0) Value($) rate (0/01 _ 0 7.6 1000 O “P 1000 8 8.5 1000 (a) (b) (d) Calculate the prices of bond A and C. [2 marks] What will the yield to maturity on bond B be? [1.5 marks} If the expectation theory of the yield curve is correct, what is the market expectation of the price that the bond 13 will sell for next year? [1.5 marks] Calculate the modified duration of the bond C. [2 marks] Estimate, using duration, the expected change in price of bond C for a 0.2% change in yield to maturity. [1 mark] 7 EC3333 Black—Scholes 0 tion ricin formulas with usual notation : c = S N(dl ) — Xe"”N(d2) where For the utility function U = E(r) — 0.005Ao-2 The optimal position for risk averse investors in the risky asset, w*, is given by * H E(r)—rf w __ 0.01Ao'2 — END OF PAPER — ...
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This note was uploaded on 10/30/2011 for the course ECON EC3333 taught by Professor Lu during the Spring '11 term at National University of Singapore.

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

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