Department of Economics
Course name: Financial Economics
Course code: EC2206
Type of exam: Retake exam
Examiner: Roine Vestman
Number of credits: 7.5
Date of exam: 2019-12-03
Examination time: 4 hours (9:00-13:00)
Aids: Pocket calculator (not programmable)
Write your identification number on each answer sheet (the number stated in the upper
right hand corner on your exam cover).
Start each new question on a new answer sheet.
Explain notions/concepts and symbols. If you think that a question is vaguely
formulated, specify the conditions used for solving it. Only legible exams will be
marked.
There are 100 points in total, including the credit question. The credit question is meant
for students who did not hand in the problem set and for students who received less than
10 points and wish to improve. For students who handed in the problem set, the credit
question only counts if it improves the total score. For the grade E a total of 45 points
are required, for D 50 points, C 60 points, B 75 points and A 85 points.
Your results will be made available on your Ladok account (www.student.ladok.se)
within 15 working days from the date of the examination.
Good luck!
, Exam December 3, 2019 (Financial Economics, EC2206)
See formula sheet at the back. A pocket calculator is allowed as long as it is not connected
to the internet or is programmable. Upon request, the memory of the calculator should be
erased.
Question 1: Smaller questions (25 points)
These questions (a. to e.) can be answered independently.
a. Suppose that you have returns at monthly frequency on a portfolio and compute the
portfolio’s Sharpe ratio to 0.100 when using these returns. Assume that monthly re-
turns are identically and independently distributed (i.i.d.). Compute the Sharpe ratio at
quarterly frequency. (5 points)
b. We watched a discussion between Eugene Fama and Richard Thaler. Fama mentions that
one particular risk factor (among Small-Minus-Big, High-Minus-Low, and Momentum) is
particularly hard to reconcile with market efficiency. Which factor and why? (5 points)
c. In empirical sciences it is common to test a null hypothesis such as H0 : α = 0 where α
can be, among other things, the effect of some medical treatment or the effect of some
action.
i. In this kind of hypothesis testing, what does a “false positive result” mean? (2
points)
ii. Suppose that a researcher tests the null hypothesis multiple times, that is, H0 :
α1 = 0, H0 : α2 = 0,...,H0 : αN = 0. How does this affect the likelihood of obtaining
a false positive result? You may find it helpful to draw analogies to the “lucky event
issue” or to other empirical sciences. (2 points)
iii. What kind of bearing does the insight from part (ii.) have on evaluations of actively
managed mutual funds? (1 points)
d. Suppose that you have found an optimal portfolio P of risky assets which will have a
stochastic return rp . It has an expected return denoted by E[rp ] and a volatility denoted
by σp . You form your complete portfolio C by deciding on the portfolio weight y invested
into P and the weight 1 − y invested into the risk-free asset which has a deterministic
return rf .
i. Write down an expression for the return on the complete portfolio, rc . (1 point)
ii. Suppose you have preferences given by U (y) = E[rc ] − 21 Aσc2 where A is a parameter
that determines risk aversion, E[rc ] is the expected return on the complete portfolio
and σc2 is the variance of the complete portfolio. Solve for the optimal weight in P
as a function of E[rp ], rf ,A, and σp . (4 points)
1
Course name: Financial Economics
Course code: EC2206
Type of exam: Retake exam
Examiner: Roine Vestman
Number of credits: 7.5
Date of exam: 2019-12-03
Examination time: 4 hours (9:00-13:00)
Aids: Pocket calculator (not programmable)
Write your identification number on each answer sheet (the number stated in the upper
right hand corner on your exam cover).
Start each new question on a new answer sheet.
Explain notions/concepts and symbols. If you think that a question is vaguely
formulated, specify the conditions used for solving it. Only legible exams will be
marked.
There are 100 points in total, including the credit question. The credit question is meant
for students who did not hand in the problem set and for students who received less than
10 points and wish to improve. For students who handed in the problem set, the credit
question only counts if it improves the total score. For the grade E a total of 45 points
are required, for D 50 points, C 60 points, B 75 points and A 85 points.
Your results will be made available on your Ladok account (www.student.ladok.se)
within 15 working days from the date of the examination.
Good luck!
, Exam December 3, 2019 (Financial Economics, EC2206)
See formula sheet at the back. A pocket calculator is allowed as long as it is not connected
to the internet or is programmable. Upon request, the memory of the calculator should be
erased.
Question 1: Smaller questions (25 points)
These questions (a. to e.) can be answered independently.
a. Suppose that you have returns at monthly frequency on a portfolio and compute the
portfolio’s Sharpe ratio to 0.100 when using these returns. Assume that monthly re-
turns are identically and independently distributed (i.i.d.). Compute the Sharpe ratio at
quarterly frequency. (5 points)
b. We watched a discussion between Eugene Fama and Richard Thaler. Fama mentions that
one particular risk factor (among Small-Minus-Big, High-Minus-Low, and Momentum) is
particularly hard to reconcile with market efficiency. Which factor and why? (5 points)
c. In empirical sciences it is common to test a null hypothesis such as H0 : α = 0 where α
can be, among other things, the effect of some medical treatment or the effect of some
action.
i. In this kind of hypothesis testing, what does a “false positive result” mean? (2
points)
ii. Suppose that a researcher tests the null hypothesis multiple times, that is, H0 :
α1 = 0, H0 : α2 = 0,...,H0 : αN = 0. How does this affect the likelihood of obtaining
a false positive result? You may find it helpful to draw analogies to the “lucky event
issue” or to other empirical sciences. (2 points)
iii. What kind of bearing does the insight from part (ii.) have on evaluations of actively
managed mutual funds? (1 points)
d. Suppose that you have found an optimal portfolio P of risky assets which will have a
stochastic return rp . It has an expected return denoted by E[rp ] and a volatility denoted
by σp . You form your complete portfolio C by deciding on the portfolio weight y invested
into P and the weight 1 − y invested into the risk-free asset which has a deterministic
return rf .
i. Write down an expression for the return on the complete portfolio, rc . (1 point)
ii. Suppose you have preferences given by U (y) = E[rc ] − 21 Aσc2 where A is a parameter
that determines risk aversion, E[rc ] is the expected return on the complete portfolio
and σc2 is the variance of the complete portfolio. Solve for the optimal weight in P
as a function of E[rp ], rf ,A, and σp . (4 points)
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