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Unformatted text preview: EC3333 NATIONAL UNIVERSITY OF SINGAPORE EC3333 FINANCIAL ECONOMICS I (SEMESTER II : AY20052006) Time Allowed : 2 Hours INSTRUCTIONS TO CANDIDATES 1. This examination paper contains FOUR (4) questions and
comprises SEVEN (7) printed pages. 2. Candidates must attempt THREE (3) questions. Question 1 is
compulsory and it carries 31 marks. Answer any TWO (2) from
remaining THREE (3) questions, each carrying 12 marks. 3. This is a CLOSED BOOK examination. 5. The total marks for the paper is FIFTY FIVE (55). 2 EC3333 Question 1 lCompulsoryl [31 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) (15 marks 3 marks each.) (i) (ii) (iii) {iv} (B) If two assets are negatively correlated, then there is a portfolio of two
assets with a variance of zero. In order for investors to be willing to invest their money for the long run, the yield to maturity on a 15 year bond must always be greater than the
yield to maturity on a 5 year bond. The stock of ABC is currently trading for $5 and won't pay any dividends
in the next three months. Call options on ABC with strike price of $1 and expiration in three months are currently trading for $5.50. There is an
arbitrage opportunity. In a CAPM equilibrium, no risky asset will have a lower expected return
than the risk free asset. A speculator who expects that the interest rates will go up in the future
should invest in a bond portfolio with a long duration. (i) ”There is no real difference between options and futures. Both are hedging tools and both are derivative products. It’s just that with options you have
to pay an option premium, while futures require no upfront payment except for a ’good faith’ margin. I can’t understand why anyone would use
options.” Do you agree with this statement? Explain. [2 marks] Suppose that you enter into a short futures contract to sell July silver for
$5.20 per ounce on the SICOM exchange. The minimum price change is $0.05. The size of the contract is 5000 ounces. Initial margin is $4000, and
maintenance margin is $3000. (a) At what price will you get a margin call? [2 marks] (b) How much more will you have to deposit? [1 mark] 3 EC3333 (C) Fresh out of school with your degree, you are considering a position as a head
of marketing for XYZ Corporation, a biotech firm. As a new firm, the salary is not that great. But your package will include call options on 10,000 shares of
XYZ stock. XYZ stock currently is selling for $10 per share. The options you will be
granted if you accept the job have an exercise price of $10 and expire in three
years. They cannot be exercised early. The standard deviation of stock return
is 28%, and the current yield to maturity on three—year bonds is 3.6%. (a) What is the value of the options on all 10,000 shares?
[5 marks] (b) State the effect, if any, of each of the following three variables on the
value of a call option: (i) an increase in exercise price,(ii) an increase in
stock price volatility, and (iii) a decrease in time to option expiration. [1.5 marks] (D) You have the following information about the prices of a oneyear zero coupon
bond A and a twoyear coupon bond B. 0 Bond A pays $1000 in one year and sells for a current price of $960 0 Bond B has a face value of $1000 and an annual coupon of $60. Bond B
currently sells at $1050. (a) What are the 1—year and 2year spot rates? [2 marks] (b) Consider a 2~year annuity with annual payments of $500. What is the
duration of this annuity? [2.5 marks] 4 EC3333 Question 2 (12 marks] Consider the following information: Asset Expected return Std. deviation Corr. with the market
Stock A ? 20% 0.4 Stock B ? 30% 0.7 Market 10% 15% 1.0 Riskfree 5% (a) According to the Capital Asset Pricing Model (CAPM), what should be
the expected return of stock A and stock B? [2 marks] (b) Suppose the correlation between the return of stock A and stock B is
0.5. What is the expected return and standard deviation of the return of
a portfolio (say, P) that has 40% investment in stock A and 60%
investment in stock B? {3 marks] (c) What is the beta of the portfolio P in part (b)?
[1 mark] (d) Assume that the CAPM is valid. How could you construct a new
portfolio (say, Q) using the market and risk free asset that has the same
expected return as the portfolio P you considered in part (b) but has
the lowest standard deviation possible? What is the standard deviation
of the return of this portfolio? [3 marks] (e) Consider an investment that is made up of a combination of the
portfolio P and riskfree asset What is the Sharpe ratio of this
investment portfolio? Does it outperform the portfolio Q in part (d)?
Why? [3 marks] 5 EC3333 Question 3 [12 marks] On Jan 02, 2006 ABC’s stock price closed at $28. The following option prices
were quoted in Business Times. Exercise Expiration Call Price Put Price
Price 25 June 4.35 1.00 30 March 100 2.69 35 June 0.58 ?? Based on historical returns, standard deviation of returns is 30%. (a) Assuming that there are no dividends paid on the stock and no arbitrage
opportunity, compute the price of the 6—months put option (June, 35) with
exercise price of 35. The riskfree interest rate is 4% per annum. [2 marks] (b) Compute the intrinsic value and time value of these options.
[3 marks] Linda Morgan, an investor, is evaluating option strategies that will allow her to
profit from large moves in a stock’s price, either up or down. You believe that the
price of ABC could move in either direction from its current price in reaction to expected court decision involving company in the coming months. Linda currently owns no ABC shares and but ask you for advice about implementing a
strategy to capitalize on the possible stock price movement. (c) Recommend whether Linda should choose a long straddle or a short
straddle strategy to achieve her objective. Justify your recommendation.
[2 marks] ((1) Suppose you have recommended her to use options with exercise price
of 30. Indicate, at expiration for the appropriate straddle strategy in part
(a) the : maximum possible loss per share, maximum possible gain per
share and breakeven stock price(s). [3 marks] (e) The delta (hedge ratio) of the call option is 0.625. Calculate the
appropriate change in price for the call option if ABC’s stock price
immediately increases to $38. [2 marks] 6 EC3333 Question 4 (12 marks] (A) Briefly discuss the difference between futures and forwards.
[ 2 marks] (B) Stock in the Sunset Corporation (SSC) currently trades for $100. Since it is a relatively new company, it does not pay any dividends. The risk—free rate is
5% per annum. (a) Find the equilibrium futures price, the price that two parties can agree
on today for a sale of one share of SSC that will take place oneyear
from today. [1.5 marks] (b) Suppose that the futures price in the market currently is $106. Is there
any arbitrage opportunity? Show all the steps and determine the
arbitrage profit. [25 marks] (C) Currently the spot exchange rate is S$1.60/ US$ and the threemonth forward
exchange rate is S$1.55/ USS Assume that the interest rate in Singapore is 1.5% per annum and 2.5% per annum in the US. Assume that you can borrow
as much as S$160,000 or US$100,000. (a) Define covered interest rate parity (CIRP). Determine whether it is
holding in the above situation. [3 marks] (1')) If CIRP is not holding, how would you carry out covered interest
arbitrage? Show all the steps and determine the arbitrage profit. [3 marks] 7 EC3333 Black Scholes formula: c = SON(d,) — Xe“”N(d2) “where
[%%;]+(r+%:)r
(N? m
$2 @2ﬂ—ar — END OF PAPER — ...
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 Spring '11
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 Economics

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