Homework 1

1. Homework #1
Finc 335
Due: Thursday, Feb. 4, 2021
Instruction: Use closing prices on Jan. 28 of relevant stocks to do Problems 5,
6, and 7.
1. A T-bill has an annual percentage rate (APR) of 1.92% based on the ask
price. The maturity of the bill is 30 days.
(a) Find the ask price (for $100 face value) of the T-bill.
(b) If you wish to invest a par value (or face value) of $75,000, how much
do you have to pay?
2. Consider the following two T-bills (both prices are for $10,000 face value)?
(1) A 3-month bill selling at $9,901
(2) A 6-month bill selling at $9,804
(a) Calculate the annual percentage rate (APR) for each T-bill above.
(b) Which security o¤ers a higher e¤ective annual rate (EAR) and why?
3. Banks o¤er CDs (certi…cates of deposit) for their customers. Conventional
CDs are time deposits that promise a …xed interest rate. However if a
customer cashes out her CD before the CD matures, then the bank imposes
a penalty on the customer. Suppose you have $20,000. You are considering
buying a 3-month CD with this $20,000. Bank A is o¤ering a 3% APR
on its 3-month CD and Bank B is o¤ering a 3% EAR on its 3-month CD.
Suppose all other aspects of these two banks are the same with regard to
their 3-month CDs, which bank would you buy your CD from? Why? By
the time your CD matures, how much money would you get back when you
cash out your CD when it matures.
4. Four years ago, you invested $50,000 in stock ABC. For the four years you
have invested in this stock, you did not adjust your position. The following

2. table represents the actual annual returns of the stock over the past four
years.
Years Actual Annual Return
2017 20%
2018 -50%
2019 -20%
2020 10%
(a) Compute both the arithmetic average annual return and the geometric
average annual return of ABC stock over the past four years.
(b) How much is your ABC stock holding worth at the end of 2020?
(c) Which average annual return (arithmetic or geometric) better re‡
ects
your actual performance over the past four years?
(d) Use a spreadsheet to compute your actual portfolio value at the end of
each year and a hypothetical portfolio value (also starting at $50,000 in
the beginning of 2017) at the end of each year when its annual return
is a constant and it is equal to ABC’
s geometric average return over
the past four years. Chart both paths on the same graph.
5. Where is Intel common stock listed? What is its listing symbol? Assume
that the closing price for Intel stock lies halfway between its best bid and
ask prices. Assume also that the bid/ask spread is 0.02 point.
(a) If you submit a market buy order, at what price is your order likely
executed?
(b) If you submit a market sell order, at what price is your order likely
executed?
(c) Suppose you submit a limit order to sell at $56.30. What will happen
most likely?
(d) Suppose you submit a limit order to buy at $56.10. What will happen
most likely?
6. You are bullish on MSFT. You purchase 100 shares of MSFT stock at the
market price using $14,000 of your own money and some additional funds,
which you borrow from your broker at an interest rate of 6% per year.
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3. (a) What is the holding period return of this buy on margin if the price of
MSFT stock increased by 15% over the next year?
(b) What if MSFT stock price increased by 2%?
(c) If the maintenance margin requirement is 35%, how far can the price of
MSFT stock fall before you get a margin call?
(d) Your friend is also bullish on MSFT stock and she purchases 100 shares
of MSFT stock at the market price by using $20,000 of her own money
and borrow the rest from her broker at an interest rate of 6% per year
also. Answer (a), (b) and (c) above for your friend.
(e) Compare your answers to all the questions above and relate to the
amount of money borrowed in your and your friend’
s investment.
7. You are bearish on Tesla. You short sell 200 shares of Tesla stock at the
market price.
(a) If your broker’
s initial margin requirement is 50% of the value of the
short position, how much in cash or securities must you put into your
brokerage account?
(b) If the maintenance margin requirement is 30% of the value of the short
position, how high can the price of Tesla stock rise before you get a
margin call?
(c) Suppose also that at the time you close your short position in Tesla in a
year, its price is at $900 per share. What is your holding period return
of this particular short sale? (Assuming that you never get a margin
call during that time period.)
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