ECON 4751 Midterm – Given the same maturity and face value

Subject: Economics    / General Economics
Question
ECON 4751
Fall 2016
Midterm

Time Limit: 1 Hour Name (Print):
Instructor: Student ID: This exam contains 12 pages (including this cover page) and 4 problems. Check to see if any pages
are missing. Enter all requested information on the top of this page, and put your initials on the
top of every page, in case the pages become separated.
You may not use your books, notes, or any graphing calculator on this exam. Using non-graphing,
non-programmable calculator is allowed. During the exam you may not communicate with anyone
in or outside the exam room except for your instructor. You may not share your calculator with
other students taking the exam
You must show your work for all questions. In doing so, please follow the rules given below: • Refer only to results from Slides, Lecture
Notes and Textbook. Citing results from Homework will result in reduced credit. Problem Points 1 25 2 25 3 25 • Label all graphs. This includes curves, intercepts, and intersection points. 4 25 • Mysterious or unsupported answers will not
receive full credit. A correct answer, unsupported by calculations, explanation, or algebraic
work will receive no credit; an incorrect answer
supported by substantially correct calculations and
explanations might still receive partial credit. Total: 100 • Organize your work, in a reasonably neat and
coherent way, in the space provided. Work scattered all over the page without a clear ordering
will receive very little credit. • Illegible answers will not be graded. There is
a lot of space on the exam to allow you to produce
legible graphs and answers.
Do not write in the table to the right. Score ECON 4751 Midterm – Page 2 of 12 10/22/2016

1. True or False questions. To receive full credit you must explain your answer, regardless of whether the statement is true or false.

(a) (5 points) True or False: Given the same maturity and face value, it is likely that a
callable bond will have the same price as a convertible bond. (b) (5 points) True or False: If stock X has a beta of 1.2 and stock Y has a beta of 0.6,
then stock X will have a higher expected return and a higher exposure to risk than stock Y. (c) (5 points) True or False: The expected return of a security with ? = 0 and ? = 0 is 0%,
but the actual return can take on any value (positive or negative). ECON 4751 Midterm – Page 3 of 12 10/22/2016 (d) (5 points) True or False: The payoff of a call option is zero whenever the price of the
underlying asset is lower than the exercise price. (e) (5 points) What type of investment plan was Dr. Winkelmann’s lecture focused on? Depending on the source of funding and the investment decision, what were the two classifications of this investment plan? Briefly describe the difference between the two. What
type was his example? ECON 4751 Midterm – Page 4 of 12 10/22/2016 2. This question is a mix of questions off of the homework. Please answer all three. Remember
to show and explain all work.
(a) (10 points) Homework 1:
Data on five different stocks is given in the following table:
Stock Initial Price Final Price Shares (million)
XYZ
25
15
40
UVW
35
75
20
RST
60
30
30
OPQ
50
80
10
LMN
20
15
50
A: Suppose that both the DJIA and the S&P 500 are composed of only these five stocks.
– Find both the initial and final index values as well as the percentage change (to
the nearest whole percent) in the DJIA index using the initial and final prices
given in the table.
– Find both the initial and final index values as well as the percentage change (to
the nearest whole percent) in the S&P 500 index using the initial and final prices
given in the table.
B: Now, suppose at the beginning of the initial period, stock RST splits two for one, so
now the initial share price of RST is $30. Assume that the price of RST falls by half
just as suggested in the initial table.
– Find the new index values and the percentage change (to the nearest whole percent) of the DJIA index.
– Find the new index values and the percentage change (to the nearest whole percent) of the S&P 500 index. ECON 4751 Midterm – Page 5 of 12 10/22/2016 (b) (5 points) Homework 2: There are four possible states of the world tomorrow. Assume
all states are equally likely. The price of three different stocks in each of the states are
given by the table. Recall that options give you the right not the obligation to buy or sell
at the exercise price.
State of the World 1
2
3
4
Stock Price 1
$6 $2 $1 $3
Stock Price 2
$9 $2 $1 $6
Stock Price 3
$7 $4 $8 $1
A. Find what a call option on stock 1 with a strike price of $3 pays the investor in each
of the four states.
B. Find what a put option on stock 2 with a strike price of $4 pays the investor in each
of the four states.
C. A risk neutral investor wants to buy on option on stock 3. Should they buy a call
option with strike price of $6 or a put option with a strike price of $5? (c) (10 points) Homework 3: Suppose there are many stocks in the security market and
that the characteristics of stocks A and B are given by E(rA ) = 0.02, E(rB ) = 0.05,
?(rA ) = 0.9, ?(rB ) = 0.11 and Corr(rA , rB ) = ?1. Here ? represents standard deviation.
Investors are not constrained to invest their wealth in only one security but they can invest
it across different securities. Is it possible in this economy to invest at a risk-free rate? If
yes, what will be the risk free rate? Explain. ECON 4751 Midterm – Page 6 of 12 10/22/2016 3. This question will ask you to apply concepts from the Markowitz portfolio theory. Make sure
to explain all your work.
Drew has invested $300,000 in a fully diversified portfolio of debt securities. He inherits a Small
Firm ETF worth $50,000 and a Large Firm ETF worth $150,000. His financial adviser provides
Drew with the following estimates on his current portfolio and his inheritance. Original Portfolio
Small Firm ETF
Large Firm ETF Expected Monthly Return
0.50 percent
4 percent
2 percent Standard Deviation of Monthly Return
2.4 percent
10 percent
4 percent The returns of the ETFs are uncorrelated among each other and uncorrelated with Drew’s
original portfolio.
(a) (2 points) Do the ETFs and Drew’s original portfolio satisfy the no-free-lunch principle
of financial assets? Explain why or why not. (b) (3 points) The inheritance changes Drew’s overall portfolio and he is deciding whether he
wants to keep the two ETFs or not. Assuming he does keep the inheritance, calculate the
expected return and standard deviation of the new portfolio. ECON 4751 Midterm – Page 7 of 12 10/22/2016 (c) (3 points) If Drew sells the inheritance and invests the proceeds in risk-free government
bonds yielding 0.2 percent monthly return, calculate the expected return and standard deviation of his portfolio. What does it mean for Treasury Bills to be risk free? Write down
an explanation that includes both an intuitive interpretation of risk and a mathematical
characterization. (d) (2 points) Will the systematic risk of his new portfolio, which includes government securities, be higher or lower than that of his original portfolio (before inheritance)? (e) (3 points) Drew’s friend, Ryan is the manager of a mutual fund that specializes in energy
stocks. His mutual fund has the same expected return and standard deviation as the
Small Firm ETF. Ryan tries to convince Drew to invest in his mutual fund. He says ’It
doesn’t matter whether you keep your $150,000 worth of Small Firm ETF you inherited
or you replace it with $150,000 in the mutual fund that I manage. Its not going to change
anything in your portfolio.’ Is Ryan’s comment correct? Why or why not? ECON 4751 Midterm – Page 8 of 12 10/22/2016 (f) (3 points) Drew is now trying to figure out whether he should buy more or less of each
ETF in order to obtain his optimal risky portfolio. Write down a problem, whose solution
characterizes the set of all expected return-standard deviation pairs he can construct. (g) (3 points) Write down a problem whose solution characterizes the optimal risky portfolio. (h) (3 points) Suppose that in the solution to the problem above, Drew finds that his inheritance is just right. He doesn’t need to buy or sell any more of any of the ETFs. If Drew’s
risk aversion coefficient is 4 and he has the standard mean-variance utility function, write
down a problem whose solution characterizes the optimal complete portfolio. ECON 4751 Midterm – Page 9 of 12 10/22/2016 (i) (3 points) Suppose that the three assets are perfectly correlated and that no shorts sales
are allowed. What optimal risky asset will Drew select in this case? Explain. ECON 4751 Midterm – Page 10 of 12 10/22/2016 4. This question will ask you to apply concepts from single index models and the CAPM. Make
sure to explain all your work.
The following image shows the security characteristic line (SCL) for two different
stocks, A and B. Stock A’s SCL is given on the left, while B’s is given on the right.
Use this image to help you answer parts (a)-(e). (a) (1 point) Which stock has greater firm specific risk? Why? (b) (1 point) Which stock has greater systematic (market) risk? Why? (c) (1 point) Which stock has the higher R2 ? Why? (d) (2 points) Which stock has the higher ?? Why? (e) (2 points) Which stock has the higher ?? Why? ECON 4751 Midterm – Page 11 of 12 10/22/2016 (f) (2 points) Which stock would you likely include in an active portfolio? Why? For the remainder of the question assume that the risk free rate of return in
the economy is 4%, and that the expected rate of return on the market is 10%.
Investors use CAPM to fairly price securities.
(g) (4 points) A share of stock C sells for $20 today. If its beta is 1.25, what do investors
expect the stock to sell for at the end of the year? (h) (4 points) Stock D has an expected rate of return of 2%. What is its beta? What does
this beta mean? (i) (4 points) Suppose you want to buy a firm with an expected perpetual cash flow of $1000.
You believe the firm’s beta to be 1.15, when in fact the beta is really 1.30. Supposing you
buy the firm, will you pay more or less than fair price for it? ECON 4751 Midterm – Page 12 of 12 10/22/2016 The last part of this question is related to Dr. Winkelmann’s lecture
(j) (4 points) What did Dr. Winkelmann’s analysis conclude about the target rate and the
funding ratio? (Note: You can answer this qualitatively, meaning you do not need to
reproduce specific numbers). Why is this important? (k) (0 points) Extra Credit: For 2.5 points each, what were the last two pieces of advice
Dr. Winkelmann gave?