ECM171 - ASSET PRICING
Deadline: March 30/2022 at 4 pm

Instruction and the Rules:

1) Please answer all questions.

2) Answers should be typed in MS Word (.docx) if possible. If this is not possible, I will accept
pictures of handwriting, conditional on the picture being readable. If the picture is not clear and
readable, your answer will be considered null and void.

3) This work is individual: this means that you must work on the assignment by yourself, with
no copying or help from other students or any other source.

4) I will check for plagiarism and for similarity among different submissions. If copying or
plagiarism is detected, both students’ exam will be nullified and they will be reported to the
Academic Misconduct Committee.

5) The deadline for the submission of this assignment is the March 30/2022 at 4 pm London
Time.

6) The assignment must be submitted via Moodle on the “Written Assignment Submission
Point”.

7) Late submissions will be penalized with a reduction in your grade.

8) My advice is to aim to submit in advance of the deadline. My suggestion is to aim to submit
1 hour before the deadline. I will not accept excuses such as “My internet wasn’t working” or
“My laptop crashed”.

9) Please check Moodle and your City e-mail address as I might post corrections or clarify any
doubts raised by students about this assignment. It is your responsibility to check.










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Question 1
In your own words, explain the concept of no arbitrage and discuss its relevance for the
methodology of Asset Pricing.
[20 marks]
Question 2
In your own words, briefly describe the Capital Asset Pricing Model, in terms of its assumptions
and main results. Discuss the theoretical and empirical advantages or problems it may have.
[20 marks]
Question 3
Consider an individual with standard expected utility preferences. In your own words, describe
graphically and algebraically the concepts of risk-aversion and risk-loving, risk premium and
certainty equivalent.
[20 marks]
Question 4
Explain graphically and algebraically how the Capital Market Line is derived in the Capital
Asset Pricing Model.
[20 marks]
Question 5
Consider an agent with the following utility function: () =
1−
1−
. Y is an uncertain outcome:
it can be either 16,000 with probability 1/4 or 54,000 with probability 3/4,
(a) Compute the certainty equivalent and the risk premium in the cases of = 0 and =
2.
[10 marks]
(b) What is the effect of the level of risk-aversion (parameter ) on the maximum amount
an agent is willing to pay for the investment opportunity?
[10 marks]

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Question 6
A portfolio consists of the following three stocks, whose performance depends on the
economic environment.

Assuming that the good economic environment is twice as likely as the bad one, compute the
expected return and variance of the portfolio. What if $1,000 of stock 4, which has mean return
of 4%, a variance of 0.02, and is uncorrelated with the preceding portfolio, is added to the
portfolio? How will this change the expected return and variance of the total investment?
Question 7
Consider an individual with concave utility function given by () = ln (). He has an initial
wealth of W0 = 10. Let a lottery offer a payoff of 26 with probability = 1/2 and 6 with
probability 1- = 1/2.
(a) If the individual already owns the lottery, calculate the certainty equivalent price he
would sell it for.
[10 marks]
(b) If he does not own it, calculate the certainty equivalent price he would be willing to pay
for it.
[10 marks]
Question 8
At time 0, a stock sells for 75 pounds. At time 1, the stock will sell for either 50, 75, or 100
pounds. You can purchase (or sell) the following two options:
(1) Option to buy the stock at time 1 for 50 pounds;
(2) Option to buy the stock at time 1 for 60 pounds.
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The price of the first option is 10 pounds. The price of the second option is 55 pounds.
Is there an arbitrage opportunity in this market? If there is an arbitrage opportunity, construct
two portfolios that generate arbitrage.
[20 marks]
Question 9
There are three assets, A, B and C, where A is the market portfolio and C is the risk-free asset.
The return on the market has a mean of 12% and a standard deviation of 20%. The risk-free
asset yields a return of 4%. Asset B is a risky asset whose return has a standard deviation of
40% and a market beta of 3/2.

(1) Calculate the expected return of asset B and its covariances with asset A and asset C
[10 marks]
(2) Consider a portfolio of the two risky assets, A and B, with weight w in asset A (the market
portfolio) and 1−w in asset B. Calculate the expected return and return standard deviation of
the portfolio with w being 1/2, 3/4, and 1.
[10 marks]

(3) Consider the following portfolio: equal weights in assets B and C. Denote this portfolio as
asset D. Compute the return standard deviation and expected return of asset D.
[10 marks]

(4) Consider a portfolio of asset A (the market portfolio) and C. Find the portfolio weight such
that its return and standard deviation is the same as that of asset D in Question (3).
[10 marks]