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A31021 Any Calculator
Department of Economics
Economics of Financial Markets
Time Allowed: 1 Hour plus 30 minutes for uploading of answers
Answer TWO questions
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Answer Two Questions. Each question has 25 marks allocated. The
marks awarded for each section of a question are shown in bracket.
In order to gain full marks you must explain fully the steps you take in solving the
problems. Since this is an online exam, if you use formulae from the lectures or class
exercises, you will not get credit for stating these formulae without an explanation of
what the formulae mean and why you are using them to answer the question.
1. You observe that a consumer with a power utility function in consumption
U=400C0.5 and a subjective discount factor of value 5/6, chooses to consume
400 today and a distribution of consumption next period such that the
expected value of marginal utility is 12 and a standard deviation of marginal
utility is 0.1. There is a single financial asset with an expected net return of x
and this asset has a standard deviation of return of y and a correlation of -0.8
with the individual’s marginal utility of future consumption.
What is the relationship between x and y if the individual is maximising utility?
(10 marks)
Explain how the Consumption-based CAPM provides an understanding of the
risk of an asset and discuss how this is illustrated in terms of the relationship
between x and y
(15 marks)
2. The consumer has a utility function given by U(C)=ln(C-H) where H is the
habit level of consumption. Her subjective discount factor is given by 0.8.
There are two states of the world next period. Given contingent claim prices
the individual chooses a level of consumption 15 today and 16 in state 1 and
17 in state 2. State 1 occurs with probability 0.6.
Use this information to calculate the value of the two contingent claim prices
(7 marks).
Discuss how incorporating Habit in the utility function delivers time-varying
risk aversion (8 marks)
Discuss, briefly, how time-varying risk aversion provides an explanation for
the predictability of stock returns. (10 marks)
3. An individual with current wealth of 10 at time t, investing over a single
period, has a utility function U=100Wt+1-0.5Wt+12 where Wt+1 is wealth at t+1.
She can hold either cash which pays zero interest or a share which has a
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price today of P and will have a price next period of 90 in state 1 with
probability 0.5 and 120 in state 2 with probability 0.5 (the price includes any
dividend owing).
What is the optimal portfolio for this individual to hold?
(15 marks)
Use you solution in the problem above to explain the optimal portfolio
selection when an individual’s labour income varies across the two states of
the world in the second period
(10 marks)
4. (a) Consider the share of a new company that is expected to pay no dividend
for n periods and then a dividend D* which grows at rate g after that. The
expected return on the asset is R*. Show that the price (P) of such an asset is
P=D*
(1+g)
(1+R*)
n
(R*-g)
(10 marks)
(b) Use the analysis above to consider how the share price of a company
displaying this dividend behaviour could develop a bubble. (7 marks)
(c) examine how the price equation above could be used to explain the impact
of the covid-19 pandemic on share prices (8 marks)