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Unformatted text preview: EC3333
NATIONAL UNIVERSITY OF SINGAPORE EC3333 FINANCIAL ECONOMICS I (SEMESTERI : AY20062007) 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 oneyear 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 marlIsl 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) — 0.005Ao2 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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 Spring '11
 Lu
 Economics, Derivative

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