BEEM 6047
UNIVERSITY OF EXETER
SCHOOL OF BUSINESS
MAY/JUNE 2009
ADVANCED FINANCE THEORY
Duration: THREE HOURS
Answer THREE out of EIGHT questions
Calculators permitted
Statistical tables are provided
1.
How can option contracts assist the attainment of efficiency in an economy
that would otherwise be inefficient? Does this observation justify the
introduction of increasingly complex financial instruments?
[33 marks]
2.
Consider an economy with one risk-free asset and one risky asset. The riskfree asset has a price of 1 at time zero and a price of 1  r , r  1 10 , in either
of the two possible states at time 1. The risky asset has a price of 6 at time
zero and future state-contingent prices of 8 and 4.
a. Assess whether these prices satisfy the no-arbitrage condition by computing
a state price vector and risk neutral probabilities.
[8 marks]
b. Is the market complete?
[6 marks]
c. Consider a contingent claim that pays 6 in state 1 and 3 in state 2. Find the
value of this claim in the initial period using risk neutral valuation and by
constructing a replicating portfolio.
[12 marks]
d. Do these valuations techniques provide a practical methodology? [7 marks]
3.
An investor has the utility function
U  ln W  ,
where W is wealth in period 1. Initial wealth W0 is invested in two risky
assets. Asset 1 has returns (2, 1) and asset 2 has returns (1, 2) in the two
possible future states.
(i) Characterize the optimal portfolio if the investor aims to maximize
expected utility.
[6 marks]
(ii) When is investment in asset 1 negative? Explain why this occurs.
[6 marks]
(iii) Define an equilibrium for this economy. If the economy is composed of
many investors with the preferences above, can the assets returns given
constitute an equilibrium?
[13 marks]
(iv) Now let the assets have returns (2, 1) and (3, 2). Show there is no optimal
portfolio with finite holdings of the assets. Explain why not.
[8 marks]
4.
(i) Explain the distinction between forwards and futures.
[5 marks]
(ii) What are “hedging” and “speculation” in futures markets? Explain their
role in normal backwardation and normal contango.
[8 marks]
(iii) Assume you hold a portfolio of 80 stocks that are traded on the London
Stock Exchange. How would you use stock index futures to hedge this
portfolio?
[8 marks]
(iv) A forward contract is written on No. 10 Red Wheat on 1 February 2009
for delivery on 2 June 2009. The spot price for Red Wheat on 1 February is
$100 per tonne. What is the forward price in the contract? The spot price on 2
April is $105. What is the value of the contract? Which side of the contract is
in profit?
[12 marks]
5.
(i) Describe assumptions and conclusions of the Capital Asset Pricing Model
and Arbitrage Pricing Theory.
[10 marks]
(ii) What are the testable implications of the theories?
[10marks]
(iii) Does the empirical evidence provide confirmation or rejection of either
theory?
[13 marks]
6.
(i) A European call option on a stock is currently trading for £1.20. The
underlying stock is trading for £10 and over the course of the year until expiry
may rise to £12 or fall to £9. The exercise price is £10. Using the single-period
binomial model what risk-free rate of return justifies the option value?
[8 marks]
(ii) Assume that both the price rise and the price fall occur with probability
1/2. Find the variance of return for the stock.
[6 marks]
(iii) Using the solution to (ii) value the option described in (i) using the BlackScholes equation.
[14 marks]
(iv) Discuss the differences between the two valuations.
[5 marks]
7.
"Valuation relies on the absence of arbitrage opportunities. If there is no
arbitrage all asset prices are in equilibrium. We therefore do not need to
value." Explain the first two statements, and discuss whether the third
statement is justified.
[33 marks]
8.
a. Determine the value of a call option with 9 months to go before expiration
when the stock currently sells for £105, has an instantaneous standard
deviation of 1.4, the exercise price is £100 and the continuously compounded
risk-free rate of return is 6%.
[11 marks]
b. For the same data as in (a), value a call option that pays a continuous flow
of dividends at the rate of 2%. Contrast the result with that from (a) and
explain.
[15 marks]
c. Can the Black-Scholes equation be used to increase an investor’s wealth?
[7 marks]