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Unformatted text preview: Second Midterm Examination, Fall 2009
Fin 580 FEl / FE2 Financial Economics Instructions: You have 80 minutes to complete the following examination. The exam consists
of 10 multiple choice questions and 4 additional questions. The multiple choice questions are
contained in a separate packet. The answers to the multiple choice questions must be recorded
on the scantron answer sheet using a pencil. For the other four questions, write your answers
in the spaces provided in this packet. You may use the back pages if you need extra space for
calculations or explanations. Answer all parts of all questions. If you believe that the question is ambiguous, explain why and
state what assumption you are making to resolve the ambiguity, and then answer the question
given that assumption. When explanations are required, the explanation will count for most of
the answer. Numerical answers are not necessarily whole numbers. The exam has 80 points. As a guide, you should spend no more than 1 minute on a question for
every point that it is worth: 10 points 9 10 minutes. Numbers in square brackets at the start of
each question tell how many points that question (or part of a question) is worth. You may use a calculator. However, it should be used for simple arithmetic only. No other
materials are allowed. Please write your name and your University ID # in the space below. NAME: University ID: Do not open this packet until the exam begins. NAME: University ID: Question Multiple Choice Questions 1 — 10 are multiple choice questions. Each question is worth 3 points. The
questions are in a separate packet. Please write your responses on the scantron answer
sheet using a pencil. You will receive credit only for responses on the scantron sheet. Computational/Short Answer Questions: Please write your answers in the space provided.
Partial credit will be awarded for partially correct work. So, write legibly and show your
work. Full credit will not be given for a correct answer without showing supporting work. 11. Consider a consumer who lives for two periods, 0 and 1, with utility function: 111(01) UC,C =lnC
(01) (mm; where 8 > 0. The consumer receives income 100 in each period and can borrow or save as
much as desired at real interest rate r = O. a. What is the consumer’s intertemporal budget constraint? [6 points] C0 +C é b. Suppose 8 =0.1. If the consumer maximizes utility, what are the optimal values of C0 and
C1? [9 points] NV 2 J— MU : _._I,_.
0 C0 1' U‘HDC;
Po=Pt1 i 12. Consider a decision maker with utility function u(x) = l/x, and assume that this decision
maker maximizes expected utility. This decision maker is given the opportunity to draw a ball
out of an urn containing 100 balls. Some of the balls are red, and some are black. If the decision
maker draws a red ball, he wins $50,000. If the decision maker draws a black ball, he loses
$50,000. Let R be the number of red balls he believes are in the urn. If the decision maker’s
initial wealth is $500,000, and he is willing to accept this opportunity, what must be true about
how many red balls (R) he believes are in the urn? Be as accurate as possible. [15 points] Vitae oi RED 3 E P [00 H 8.5.0 000
P r >
xv 8 001000 + __
S—@ 000 ‘1 (Salem) $10,000
P + 0—?) é __L
[I @' ‘é‘? lo [0
[lo LOE’ .4. Cl“?
«1013.4: "Ll P 2 “/w 4.27/23 2 5‘? Write your answer in this space KS: 55’ 13. A Decision Maker has utility function U(w) = ln(w) and initial wealth 100. The decision
maker faces the choice of investing in a safe asset or a risky asset. $1 invested in the safe asset
returns $1 with certainty. With probability 1/2, the state is “good,” and $1 invested in the risky
asset returns $1.25. Otherwise, (i.e., with probability 1/2), the state isnbadﬂand $1 invested in the
risky asset returns $0.80. Let y denote the amount of money DM invests in the risky asset. a. In terms of y, what is the decision maker’s ﬁnal wealth in each (i.e., good and bad) state.
[7 paints] Scuff % [00 — «j
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Final Wealth in Good State Final Wealth in Bad State: Mo — ,a
b. What is the optimal investment in the risky asset? [8 points]
1
ELF ill/1000 +1833 + {£14 (100"be
PD *7 \ 0:95 __ I (,1) _ O
. ZS‘ _ (2..
(00+.‘LS‘3 [coo—.13 25‘ 151.233: 20 +15 (.233 5:.13
we 14. Suppose the government implements a policy where they pay people to get vaccinated
against the H1N1 ﬂu virus. Using ideas from the course, in two or three sentences explain
why such a program might be justiﬁed as improving efﬁciency. [5 points] Shine e/‘H'a U Mei/tka
lecM/fil 0 ~ S.
axle/maxi} / AA, 0 ’H‘Q “ ﬁlm/(€71 "
(w: H lea/we Jr) (kgdggg {QQ m U4 Cdﬂgé‘wta
a ? (Q 01:) a 'n #11
(Meat MM  (Q J0 (/4 00,4 219 “ﬁg: Qayﬂmi cam/X mlgqﬂﬂzsL/w ~C3~ Va ' W END OF EXAM First Midterm Examination, Fall 2009 FIN 580 FEl / FE2
Financial Economics Multiple Choice. [3 points each] Select the best answer to each question. Write the
letter corresponding to your answer on the scantron answer sheet using a #2 pencil. If
you do not write your answer on the scantron answer sheet using a #2 pencil, if you
select more than one answer, or if it is ambiguous which answer you have selected, you
will not receive credit. 1. A utilitymaximizing consumer has initial wealth w and no additional income, and
lives for two periods, 0 and 1. If the real interest rate increases this consumer will: a. Increase his savings in period 0.
b. Decrease his savings in period 0. c. Not change his savings in period 0. The effect on savings cannot be determined without more information. 2. According to the Fisher Separation Theorem: a. All consumers should choose the same consumption bundle, regardless of
their income stream. All consumers should choose the same income stream, regardless of their
preferences. c. All consumers should choose to save the same amount, regardless of the
interest rate. d. All consumers should borrow the same amount, regardless of their utility
functions. 3. According to the Lifecycle Model of consumption over time: @ consumer’s current consumption should depend more on permanent income
than on current income. b. A consumer should consume the same amount (in real terms) each period. c. A consumer should choose the income stream that maximizes the present
value of lifetime consumption. (1. A consumer’s current consumption should only depend on current income. 4. Which of the following is true of a risk averse decision maker: a. The expected utility of any lottery is equal to its expected value.
b. The expected utility of any lottery is less than its certainty equivalent.
0. The certainty equivalent of any lottery is greater than its expected value. The expected utility of any lottery is less than the utility of the lottery’s
expected value. 5. Consider a decision maker with utility function u(w) = w“2 and initial wealth w =
100. This consumer’s coefﬁcient of relative risk aversion is: a. 1/200 c. 2
d. 50 6. Prospect theory incorporates all of the following except: Aversion to ambiguity about probabilities. .b. Different risk attitudes toward gains and losses.
c. Reference Points. (1. Nonlinear weighting of probabilities. 7. The stochastic discount factor is: a. The expected value of the rate of time preference. he intertemporal marginal rate of substitution. c. The slope of the capital markets line. d. The ratio of state prices. 8. According to the Consumption CAPM model, an asset should have a high expected
rate of return when: a. Its returns are positively correlated with market’s returns.
b. Its returns are more variable than the market’s returns.
@Its returns are negatively correlated with the stochastic discount factor. (1. Its return is near zero in absolute value. 9. Consider a model with two consumers, C1 and C2. C1 undertakes an activity x
which also affects C2. The level of X is chosen by C1. Let Cl ’s utility be given by
U1(x,m1) = 50X — x2 + m1, where m is the amount of money C1 has, and C2’s utility
be given by U2(x,m2) = 500 — x + m2. Suppose that activity x is free. If the
government wants to induce the Pareto Optimal choice of x, it should: @mpose a tax on C1 of $1 per unit of x consumed.
b. Impose a tax on C1 of $2x per unit of x consumed.
c. Impose a subsidy on C1 of $1 per unit of x consumed. d. Impose a tax on C1 equal to U2(x,m2). 10. Suppose that there are three states of the world, a, b, and c. The probabilities of the
three states are 1:1 = 0.25, it; = 0.5, and M = 0.25. Let A, B, and C denote the Arrow Debreu securities that pay $1 in states a, b, and c, respectively. That is, A = (1,0,0), B
= (0,1,0) and C = (0,0,1). Let pA = 0.4, p3 = 0.5 and pc = 0.2 denote the prices ofA,
B, and C. Consider a security X which is worth $2 in state a, $3 in state b, and $1 in state c. If
there are liquid markets for A, B, C and X, what is the price of X? ...
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This note was uploaded on 01/18/2011 for the course FIN fin580 taught by Professor Miller during the Spring '10 term at University of Illinois, Urbana Champaign.
 Spring '10
 Miller

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