Paper Code: ECON 308 Page 1 of 4

Paper Code: ECON 308 Department: ULMS
Examiner: Ruijun Bu Tel. No: 50573


JANUARY EXAMINATIONS 20XX

ECON 308 Quantitative Financial Economics


TIME ALLOWED: Two Hours

INSTRUCTIONS TO CANDIDATES

The use of pre-programmable calculators is not permitted during this exam.

You must complete ALL THREE questions.
Paper Code: ECON 308 Page 2 of 4

JANUARY EXAMINATIONS 20XX

ECON 308 Quantitative Financial Economics

QUESTION 1 (30 Marks)
a) Graphically demonstrate the Fisher separation theorem for an individual whose optimal investment
and consumption decisions require him to borrow money from the capital market, and clearly label
the following quantities on your graph:
i. The initial endowment,  10 , yy ;
ii. The capital market line and its slope when the market determined rate of interest is r ;
iii. The initial wealth, 0W ;
iv. The optimal investment, I ;
v. The optimal consumption,   10 ,CC ;
vi. The present value of final wealth, 
0W .
(9 Marks)
b) Graphically illustrate the effects of an exogenous decrease of the interest rate on the borrower’s
optimal investment level, present value of final wealth, and optimal level of utility. Explain these
effects intuitively.
(12 Marks)
c) Consider two 2-year projects with the following cash flow schemes:

t = 0 t = 1 t = 2
Project 1 -5000 6000 650
Project 2 -5000 8000 -1650

Assuming that the opportunity cost of capital is k = 10%, calculate the internal rate of return (IRR),
the economic interpretation of the rate of return on investment (ROI) and the geometric average rate
of return (GAR) of the two projects. If the two projects are mutually exclusive, comment on which
project should be selected if the objective is to maximize the shareholders’ wealth.
(9 Marks)


TOTAL [30 Marks]
Paper Code: ECON 308 Page 3 of 4


QUESTION 2 (35 Marks)
On January 1, a one-year forward contract maturing on December 31 written on a non-dividend-paying
stock was entered when the stock price was £40. Meanwhile, the one-year risk-free interest rate on the
same day was 5% per annum with continuous compounding.
a) On January 1, what should be the no arbitrage delivery price for this forward contract and what was
the value of this forward contract?
(5 Marks)
b) On July 1 (six months later), the price of the same stock has gone up to £60 and the six-month risk-
free interest rate is now 4% per annum with continuous compounding. On July 1, what is the forward
price for the same stock with delivery date on December 31 and what is the value of the forward
contract entered on January 1?
(5 Marks)

A stock price is currently £50. Over each of the next two three-month periods it is expected to either go
up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding.
c) Using a binomial tree to evaluate a six-month European call option with a strike price of £51?
(10 Marks)

d) Using a binomial tree to evaluate a six-month European put option with the same strike price?
(10 Marks)

e) If the put option were American, would it ever be optimal to exercise it early at any of the nodes of
the tree?
(5 Marks)


TOTAL [35 Marks]





Paper Code: ECON 308 Page 4 of 4


QUESTION 3 (35 Marks)
Suppose that the daily returns of two risky assets 1 and 2 are normally distributed with the two means
denoted by  1RE and  2RE , the two variances denoted by  1RVar and  2RVar , and their correlation
coefficient denoted by 12 . Suppose that an individual’s utility function is given by
   bWWU  exp1 , where 0b and W denotes wealth.
a) Calculate the individual’s absolute risk aversion (ARA) and relative risk aversion (RRA), and describe
their relations to the individual’s wealth level W .
(10 Marks)
b) Write down the mean,  PRE , and variance,  pRVar , of the daily return of a portfolio consisting of
proportion  of wealth invested in asset 1 and 1 invested in asset 2, and find the minimum
variance portfolio allocation.
(10 Marks)

c) Suppose that at time T the individual wants to invest in the minimum variance portfolio consisting
of asset 1 and 2 for just 1 day, that is, between T and 1T . He has established that the daily returns
of the two assets can be modelled sufficiently by the following two AR(1) models, respectively:

Asset 1: ttt RR ,11,1,1 10.005.0   where  21,1 ,0~  IIDt
Asset 2: ttt RR ,21,2,2 08.002.0   where  22,2 ,0~  IIDt
In addition, it is observed that 03.0,1 TR , 05.0,2 TR , and it has also been estimated that
09.021  , 04.0
2
2  , and 20.012  . Forecast the mean return,  1, TPRE , of the individual’s
minimum variance portfolio conditional on time T .
(15 Marks)


TOTAL [35 Marks]