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Department of Economics
Course name: Financial Economics Course code: EC
Type of exam: Retake exam Examiner: Roine Vestman Number of credits: 7. Date of exam: 2019 - 12 - 03 Examination time:
Aids:
4 hours (9:00-13:00)
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 H 0 : 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? ( points) ii. Suppose that a researcher tests the null hypothesis multiple times, that is, H 0 : α 1 = 0, H 0 : α 2 = 0,...,H 0 : 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] − 12 Aσ^2 c where A is a parameter that determines risk aversion, E[rc] is the expected return on the complete portfolio and σ^2 c 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)
i. Compute the fund’s covariance with the market portfolio, cov(Ri, RM ). (2 points) ii. Use the formula for the slope coefficient in a bivariate regression: βi = cov var(R(iR,RMM ) ). (2 points)
d. Compute the fund’s alpha (αi) by proceeding in two steps:
i. Express the fund’s expected excess return, E[Ri], as function of the fee and the expected market excess return. (2 points) ii. To solve for the fund’s alpha, use the formula for the intercept coefficient in a bivariate regression: αi = E[Ri] − βiE[RM ]. (2 points)
e. Draw a graph with the expected return-beta relationship and position the index fund relative to the axes and to the security market line (SML). (2 points)
Question 4: Arbitrage pricing theory (7 points)
a. Assume that arbitrage pricing theory works. The figure above is taken from Bodie et al., chapter 10. Describe a portfolio consisting of A and B such that an arbitrage is earned. (4 points)
b. Describe the Fama-French 3-factor model, including its factor structure (and the positions in each factor) and its pricing equation. (3 points)
Question 5: Financial Crises (15 points)
This is an essay question. Nevertheless, please be brief and to the point. Your total answer should not exceed 2 pages.
a. Describe how traditional securitization of mortgage backed securities worked in, say, the 1990s. (Who were the main players? What kind of mortgages were securitized? Illustrate with a value chain.) Then contrast to how securitization evolved in the early 2000s in the boom phase of the financial crisis. Describe the main differences and the appearing moral hazards. (5 points)
b. Why are central banks the natural lender of last resort? Under which three conditions can it lend to a financial entity? (5 points)
c. In chapter 20 of Mankiw’s text book, six common features of a financial crisis are listed. Describe these features very briefly without necessarily making references to any specific crisis. (5 points)
Question 6: Questions for credit score (10 points)
Credit question. These questions should only be answered by students who either did not hand in the problem set or by students who received a score below 10 on the problem set and wish to try to improve. In the latter case, the best of the two scores will be counted.
a. Bond pricing. A stream of pay-outs c in the next T periods is called an annuity. Derive the following expression for its value: cr
[
1 − (^) (1+^1 r)T
]
where r is the market interest rate. For a full score (5 points), start by deriving the value of a perpetuity. For a partial score (2 points), take the value of a perpetuity as a given from the formula sheet. (5 points)
b. Consider two random variables, x and y. Show that var(x + y) = var(x) + var(y) + 2 · cov(x, y), starting from the definition of variance in the formula sheet. (5 points)
