Midterm Exam Long Answer Questions
Investments (FINA 3720)
Instructor: Dr. Ligang Zhong
Oct 22, 1:00 pm-3:30 pm (150 minutes, including the time for finishing multiple choice questions on blackboard), 2021
(Total: 80 Marks)
Student Name____________
Student ID_______________
There are 3 long answer questions.
Provide you solutions for the long answer questions after the corresponding questions. Partial marks will be credited for long answer questions if you provide the right process without getting the right answer.
This is an open book exam.
There is another portion of the exam, the multiple-choice questions, on blackboard website.
Maintaining academic integrity and fairness is always the top priority in this class. Consequently, you should finish the exam by yourself. No discussion should be allowed among students. Originality of the work will be carefully checked.
The long answer questions are organized in an assignment format, you should first download the files containing the questions and then work offline. You should submit your solution files before the due time. Only electronic submission on the Blackboard website is allowed
Students bring their own calculators to exams. Calculators may not be shared.
I will not answer any content related questions so to be fair to all students.
The due time for the entire exam (including the multiple-choice questions) is 3:30pm on Oct 22nd. However, in accordance with UWSA’s request, to allow for any possible technical difficulties, there will be a 15-minute grace period at the end of the exam during which late exams will still be accepted for grading. Any exams received after this 15-minute period expires will not be graded. Hence, any exams submitted after 3:45pm will receive a mark of zero.
Long Answer Questions
(20 Marks) 1. Assume you have $1 million Cash and are trying to choose among three securities to invest. All are default free fixed income securities.
a. Security A is a Treasury bill with 180 days to maturity with face value of $1,000. It is traded at the price $960 per share.
b. Security B is a U.S. Treasury bill with 90-day maturity and face value of $1,000 per share. It sells at a bond equivalent yield of 3%.
c. Security C is a 20-year maturity bond with par value of $1,000 and the bond makes semi-annual coupon payments at a coupon rate of 10%. The bond is selling at price of $1,100 per share.
Given the above choices, calculate and answer:
i). What is the bank discount yield and bond equivalent yield for security A? (5 Marks)
ii). How many shares of security B you can buy with your $1 million cash? (4 Marks)
iii). What is the Bond Equivalent Yield and Current Yield of Security C? (5 Marks)
iv). Without Considering the risk, Given the above conditions, which one delivers the highest effective yield among the three choices? (You need to show the calculation process to get the full marks) (6 Marks)
(30 Marks) 2. Assume the current yield curve for default-free zero-coupon bonds is as follows:
Maturity (Years)
YTM (%)
1
5
2
6
3
7
4
8
Starting from year 4, the yield curve is flat at 8% for all the longer (longer than 4 years) maturities.
Based on the above yield curve, calculate & Answer
i). If you invest $100 today, what is the final wealth in the end of year 1, year 2, and year 3, respectively? (6 Marks)
ii). What is the implied one-year forward rate starting at the beginning of year 1, year 2, and year 3, respectively? (6 Marks)
iii). A default free bond with 8.5% coupon making annual payment, $1000 par value that matures in 4 years is newly issued to the market, what should the bond price be if it is correctly priced? What is the yield to maturity for the bond? (6 marks)
iv) Suppose the above yield curve perfectly predicts the future interest rates (Future interest rates are certain in this world), a 5-year-maturity default free bond with a par value of $1,000 currently sells for $960, the bond pays 7% annual coupon rate (coupons are paid annually). What is the realized compound yield for an investor investing in this 5-year bond but with a 4-year holding period? (12 Marks) (Assuming the investor can buy the bond at the current price and will liquidate the position at the end of year 4. In year 4, the bond is correctly priced according to the yield curve. Hints: under certainty)
(30 marks) 3. Suppose that Tesla Inc stock (TSLA) currently is selling at $799.5 per share. You have $1,380,000 cash in your account. You are bullish on the stock and decided to take a position using all your money. Your financial advisor at TD Bank provided you with two options to invest:
Option one: Open a TFSA account, where you can invest only all your cash to buy the shares.
Option two: Open a margin account, where you can invest with all your cash and also borrow additional amount from your broker to buy the shares. The initial margin requirement is 50%, and the minimum margin requirement is 30%. The interest rate charged on the margin loan will be 9% per year.
With both options, the commission is 50 cents per share for each transaction.
Calculate and answer:
i) With option one, how many shares maximum you can buy with the cash you have in the account? (2 marks)
ii) With option two, how much maximum you can borrow? How many shares maximum you can buy in the margin account? (4 marks)
iii) Suppose in one year, Tesla stock is traded at $1,000 per share and you decide to sell it to realize the profit, after you sell all the shares, what is the Equity value of your account with option one and option two, respectively; what is the rate of return under option one and option two, respectively? (8 marks)
iv) Suppose your prediction is not correct, in one year, Tesla stock declined to $500 per share, what is the margin level in your account with option two? If you do not have sufficient cash in your position, your broker decided to liquidate the position for you with the price of $500 per share, what is the rate of return with option two? (7 marks). What is the rate of return with option one if you liquidate the stock at $500 per share by yourself? (3 marks)
v) Assume two years has passed, how far can Tesla stock to fall for you to get a margin call with option two? (4 marks)
vi) Given the above calculation, briefly state the advantage and disadvantage of trading with margin (2 marks)
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