FNCE401 assignment 1

Assignment 1

Instructions
Assignment 1 should be submitted after you
have completed Unit 2. This assignment is worth
15 percent of your final grade.
Assignment 1 contains five problems. The
maximum mark for each problem is noted at the beginning of the problem. This
assignment has a total of 100 marks.
Read the requirements for each problem and
plan your responses carefully. Although your responses should be concise,
ensure that you answer each of the required components as completely as
possible. If supporting calculations are required, present them in good form.
When you receive your graded assignment,
carefully review the comments the marker has made. This review component is an
important step in your learning process. If you have any questions or concerns
about the evaluation, please contact the Student Support Centre.

Problem 1 (15 marks)
You have $30,000 in your margin account, and you want to invest in
BMO stock. The minimum margin requirement for BMO is 30%. You just got a quote
on BMO as follows:
Bid: 55.25
Ask: 55.26
The interest rate on the margin
loan is 6% per annum.
1)
If you want to buy BMO in
margin, what is the maximum number of shares can you buy?

2)
Suppose you want to buy 1200
shares of BMO in margin. Answer the following questions:
a.
What is the initial margin
ratio?
b.
Suppose you are going to hold
the shares for one year. At what price at the end of next year will your
investment break even? (assuming no margin calls in the year)
c.
How far could the stock price
fall before getting a margin call?
d.
If the stock price falls to
$40, you would get a margin call. If this happens, how much new fund would you
need to add to your account to respond the margin call?

Problem 2 (15
marks)
Assume you sell short 100
shares of common stock at $70 per share, with initial margin at 55%. The
minimum margin requirement is 30%. The stock will pay no dividends during the
period, and you will not remove any money from the account before making the
offsetting transaction.
1)
At what price would you face a
margin call?

2)
If the price is $86 at the end
of the period, what is your margin at that point?

3) What would be your profit if you repurchase the
stock at $63/share?

Problem 3 (15 marks)
Use the following expectations on stocks X and Y to answer the questions
below:

Bear Market

Normal Market

Bull Market

Probability

0.2

0.5

0.3

Stock X

-20%

18%

50%

Stock Y

-15%

20%

10%

The correlation between stock X and Y is 0.4.
1)
What is the expected return for
each stock?

2)
What is the standard deviation
for each stock?

3)
Assume you invest your $100,000
in a portfolio with $90,000 in stock X and $10,000 in stock Y. What are the expected return and standard
deviation of your portfolio?

Problem 4 (15 marks)
You have $800,000 invested in a complete
portfolio that consists of a portfolio of risky assets (P) and T-Bills. The
information below refers to these assets.

E(rp)=12.00%
?p =7.00%
T-Bill rate=3.6%
Proportion
of T-Bill in the complete portfolio: 20%
Proportion
of risky portfolio P in the complete portfolio: 80%
Composition of P:
Stock A 40%
Stock B 25%
Stock C 35%
Total
100%
1)
What is the
expected return on your complete portfolio?

2)
What is the
standard deviation of your complete portfolio?

3)
What are
the dollar amounts of Stocks A, B, and C, respectively, in your complete
portfolio?

4)
If your
degree of risk aversion is A=4, is your complete portfolio optimal? (assuming P
is the optimal risky portfolio)

Problem 5 (40 marks)
SPY and XIU are ETFs tracking the S&P 500 and S&P/TSX 60
index, which are often used as proxies for the US and Canadian stock markets,
respectively. From a set of their historical data, the annual expected returns
and standard deviations of those two ETFs and their covariance are estimated as
follows:
SPY:
E(r) =
0.36

0.26

XIU:
E(r) =
0.44

0.28

Covariance
between= 0.0568

Suppose that you have $5 million to invest for one year and you want
to invest this money into SPY, XIU and the Canadian one-year T-bill. Assume
that the interest rate of the one-year T-Bill is 6% per annum.

Suppose that
you have the following utility function:
U=E(r) – ?2

Answer
following questions using EXCEL:

1)
Draw the opportunity set
offered by these two securities (with an increment of 0.01 in weight).

2)
What is the optimal portfolio
of SPY and XIU?

3)
Determine your optimal asset
allocation among SPY, XIU, and T-Bill, in percentage and in dollar
amounts.