Fin 3322
Arbitrage Homework
The following information should be used for problems #1 - 4:
Suppose that we have identified three important systematic risk factors given by
exports, inflation, and industrial production. In the beginning of the year, growth in
these three factors is estimated at -1%, 2.5%, and 3.5% respectively. However,
actual growth in these factors turn out to be 1%, -2%, and 2%. The factor betas are
given by EX = 1.8, I = 0.7, and  IP = 1.0.
1.
If the expected return on the stock is 6%, and no unexpected news concerning the
stock surfaces, calculate the stock's total return.
R = 6% + 1.8(0.01--0.01) + 0.7(-0.02-0.025) + 1(0.02-0.035) + 0 = 0.0495
R = 6% + 1.8(0.02) + 0.7(-0.045) + 1(-0.015) + 0 = 0.0495
2.
Calculate the stock's total return if the company announces that an important patent
filing has been granted sooner than expected and will earn the company 5% more in
return.
R = 6% + 1.8(0.01--0.01) + 0.7(-0.02-0.025) + 1(0.02-0.035) + 0.05 = 0.0995
R = 6% + 1.8(0.02) + 0.7(-0.045) + 1(-0.015) + 0.05 = 0.0995
OR
R = 4.95% + 5% = 9.95%.
3.
Calculate the stock's total return if the company instead announces that they had an
industrial accident and the operating facilities will closed down for some time thus
resulting in a loss by the company of 7% in return.
R = 6% + 1.8(0.01--0.01) + 0.7(-0.02-0.025) + 1(0.02-0.035) - 0.07 = -0.0205
R = 6% + 1.8(0.02) + 0.7(-0.045) + 1(-0.015) - 0.07 = -0.0205
OR
R = 4.95% - 7% = -2.05%.
4.
What would the stock's total return be if the actual growth in each of the facts was
equal to growth expected? Assume no unexpected news on the patent.
.
R = 6%, the expected return on the stock.
Market Efficiency Homework
1.
Define the three forms of market efficiency.
Weak form efficiency: we cannot make excess return based on historical price
or volume information
Semi-Strong form efficiency: we cannot use any publicly available information
to earn excess return
Strong form efficiency: we cannot use any private (insider) information to earn
excess return
2.
Explain why it is that in an efficient market, investments have an expected NPV of
zero.
In an efficient market, prices are “fair” so that the cost of an investment is
neither higher nor lower than the investments expected NPV. Thus, on
average, investments in an efficient market will yield a zero NPV. Investors get
exactly what they pay for when they buy a security in an efficient market and
firms get exactly what their stocks and bonds are worth when they sell them.
3.
Do you think the lessons from capital market history will hold for each year in the
future? An example, if you buy small stocks will your investment always
outperform U.S. Treasury bonds?
While on average small stocks should outperform U.S. Treasury bonds, this
need not be the case every year. As the return on small company stocks is
riskier, its year to year return is highly variable, some years it will be high and
others it will be low. While the return on the U.S. Treasury bonds less variable.
4.
Suppose your cousin invests in the stock market, creating a portfolio with a beta of 1,
and doubles her money in a single year while the market, on average, earned a
return of only about 15%. Is your cousin’s
performance a violation of market
efficiency? Why?
No, market efficiency does not preclude investors from “beating the market.” It
is entirely possible to earn higher returns than the market at times. However, if
your cousin is able to do so consistently, then there would certainly be some
doubt cast upon market efficiency.
5.
Aerotech, an aerospace-technology research firm, announced this morning that it
has hired the world’s most knowledgeable and prolific space researcher. Before
today, Aerotech’s stock had been selling for $100.
a. What do you expect will happen to Aerotech’s stock?
b. Consider the following scenarios:
i. The stock price jumps to $118 on the day of the announcement. In
subsequent day it floats up to $123 then falls back to $116.
ii. The stock price jumps to $116 and remains there
iii. The stock price gradually climbs to $116 over the next week
Which scenario(s) indicate market efficiency? Which do not? Why?
a) Aerotech’s stock price should rise immediately after the announcement of
the positive news.
b) Only scenario (ii) indicates market efficiency. In that case, the price of
the stock rises immediately to the level that reflects the new information,
eliminating all possibility of abnormal returns.
In the other two scenarios, there are periods of time during which an
investor could trade on the information and earn abnormal returns.
Scenario (i) indicates over-reaction
Scenario (iii) indicates under-reaction