Assignment 1
1. Expected Utility (15 = 5 × 3 points).
(a) Suppose that a person maximizes his expected utility, with the utility function given
by u(w) = w0.5 and engages in a risky venture which leaves him with either $81 or $25
with equal probability. Answer the following questions. Show the calculation
(i) What is the certainty equivalent of this business venture?
(ii) What is the risk premium?
(b) What’s the implication of noise trader risk when the fund managers want to exploit one
arbitrage opportunities to correct mispricing?
(c) Which one of the following assumptions about neoclassical economics is incorrect? How
would you modify it?
(A) People have rational preferences across possible outcomes or states of nature.
(B) People maximize utility.
(C) People have difficulties in acquiring and assessing all relevant information.
(D) People’s preferences are complete and transitive.
(d) Which one of the following statements about anomalies is correct? How would you
modify the other statements?
(A) Momentum exists when returns are negatively correlated with past returns.
(B) Value investing is the tendency to overweight stocks that the market anticipates
high future growth.
(C) The small-firm effect is the tendency for firms with low levels of market capitalization to earn excess returns after accounting for market risk.
(D) The earnings announcement drift is consistent with market efficiency.
2. Market Efficiency and challenges(15 = 5 × 3 points).
(a) Which one of the following statements is correct concerning market efficiency?
(A) Real estate markets are more efficient than financial markets
(B) If a market is efficient, arbitrage opportunities should be common
(C) In an efficient market, some market participants will have an advantage over
others.
(D) A firm will generally receive a fair price when it sells shares of stock.
(E) New information will gradually be reflected in a stock’s price to avoid any sudden
change in the price of the stock.
(b) According to the efficient market hypothesis, why would financial markets fluctuate
daily?
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(c) If you excel in analyzing the future outlook of firms, which form of market efficiency
you would prefer so that you can have an advantage in the marketplace.
(A) weak
(B) semi-weak
(C) semi-strong
(D) strong
(E) perfect
(d) Differentiate the following terms/concepts?
(A) Momentum and reversal
(B) Fundamental risk and noise trader risk
(C) Value and growth stocks
(e) For the example of 3Com and Palm in the lecture, if you are a sophisticated arbitrageur,
how will you trade to make profits? What will prevent you from implementing this
arbitrage? .
3. Preference-dependent(12 = 4 × 3 points).
(a) Under the prospect theory, what features the probability weighting function?
(b) In sporting competitions, we often observe that the team in the lead plays more conservatively (takes fewer risks) than the team that is behind. Can we use prospect theory
to explain this result?
(c) One experiment on trading gave chimpanzees the choice between peanut butter and
juice. When peanut butter was given first, 80% refused to exchange it for the juice.
The opposite was also true when juice was given first. Which of the following can be
an explanation?
(A) Endowment effect.
(B) Salience bias.
(C) Anchoring.
(D) Base rate neglect.
(d) Try to describe the plot on Page 83 (Reference-dependent Preference Slides) and explain
what you can observe.
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4. CAPM (Capital Asset Pricing Model) (8 points).
Stock A has a beta of 1.35 and an expected return of 16%. A risk-free asset currently earns
4.8%.
(a) What is the expected return on a portfolio that is equally invested in the two assets?
(2 points)
(b) If a portfolio of the two assets has an expected return of 8%, what is its beta (3 points)?
(c) If a portfolio of the two assets has a beta of 2.70, what are the portfolio weights? (3
points)
5. Prospect Theory (15 points)
Consider a person with the following value function under prospect theory where z is the
gain or loss:
(
v(z) =
z .85
when z ≥ 0
−3(−z)
.85
when z < 0
The individual has the following probability decision weighting function where γ has been
set at 0.6:
pγ
π(p) =
1
(pγ + (1 − p)γ ) γ
(a) Is this individual loss averse? Explain. (2 points)
(b) Which of the following two prospects (A and B) would he choose using objective probabilities rather than decision weights? (5 points)
A (0.001,–$5,000) (a probability of 0.001 of losing $5,000 and a probability of 0.999
of losing nothing), or
B (–$5) (a certain loss of $5).
(c) Which prospect would he prefer using decision weights rather than probabilities? Explain what these results illustrate about people’s preferences. (8 points)
6. Reference-Dependent Preference (20 points)
Suppose Jenny’s utility function of pairs of shoes (cs ) and money (cm ) takes the following
form:
u(cs − rs ) + v(cm − rm )
where rs is Jenny’s reference point for pairs of shoes and rm is her reference point for money.
The function u() is defined by
(
u(x) =
√
when x ≥ 0
10 x
p
−20 |x| when x < 0
and the function v() is defined by
( √
x
when x ≥ 0
p
v(x) =
−2 |x| when x < 0
Jenny currently has 7 pairs of shoes (1 pair for each day of the week) and $100 in cash.
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(a) Provide a brief interpretation of Jenny’s preferences, i.e., what’s her risk preference in
the gain domain (for cs ≥ rs and cm ≥ rm ) and loss domain (for cs < rs and cm < rm ).
Does she exhibit increasing or diminishing sensitivity? (4 points)
(b) Suppose first that her reference points reflect the status quo (rs = 7 and rm = 100).
She sees an ad for a pair of Zalora shoes priced at p = $20. Is Jenny willing to buy the
pair of shoes at this price? (5 points)
(c) Jenny runs into her friend Cathy. They begin discussing shoes, and Jenny learns that
Cathy only owns 6 pairs of shoes (1 pair for each weekday and 1 pair for the weekend).
Now self-conscious about how many shoes she owns, Jenny updates her shoe reference
point to rs = 6. Is Jenny still willing to buy the advertised shoes at p = $20? (5 points)
(d) Compare your answers to questions (b) and (c). If your answers to questions (2) and
(3) differ, explain why Jenny’s decision about shoe buying changed. (6 points)
7. More Questions (15 points)
(a) Consider the following prospect choices:
Question 1
Prospect A
Prospect B
$2,500
33%
$2,400
66%
0
1%
$2,400
100%
Question 2
Prospect C
Prospect D
$2,500
33%
$2,400
34%
0
67%
0
66%
It has been shown that more people choose B when presented with problem 1 and when
presented with problem 2, most people choose C. Do these choices violate expected
utility theory? Why? (5 points)
(b) What are the three supports on which market efficiency rests? Markets can be efficient
if any one of them is satisfied. True or False? Explain. (5 points)
(c) Consider the following two descriptions of Mary:
(i) Mary loves to play tennis.
(ii) Mary loves to play tennis and, during the summer, averages at least a game a
week.
Someone believes that description 2 has a higher probability. Do you agree? Explain.
(5 points)
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