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Com4FE3 Continuous Compounding Assignment

Instructions

• This assignment is to be done individually or with one partner.
• Please show all your works and use 4 decimal points in your answers.
• All interest rates herein are expressed with continuous compounding.
• In case you need to make assumptions, please clearly state them. Only reasonable assumptions are acceptable.  Assumptions that violate finance principles are not to be made.
• For numerical questions, simply calculating the numbers out will not be sufficient. Please also provide me with the reasons for your calculations.  Correct thinking processes are much more important than correct numbers.  Therefore, regardless of whether or not your numbers are correct, no marks will be given if (a) no explanation of your calculations is provided; or (b) the explanation provided is incorrect.  On the other hand, even if your numbers are incorrect, partial marks will be given if your thinking process is correct.
• Please note that marks can only be given based on what you write. Therefore, I request that you attempt to convey your ideas to me as clearly as possible.  I will not make a guess as to what you intend to mean if you do not make it obvious and clear.
• When your answers involve taking positions in securities or lending/borrowing, please mention all the relevant details such as the timing of the transactions, the side of the contracts (e.g., long or short forward), the length of the contracts (e.g., 6-month futures), the exercise prices (in case of options) and the interest rates (in case of lending or borrowing).
• Every question in this assignment is taken (or is adapted) from questions from past exams. Therefore, it is important that you try to do every question on your own (even though you’re working with a partner).  Please take this opportunity to familiarize yourself with what the exams will be like.
• The bank that you work for was just contacted by a customer. The customer wants to long a 1-year gold forward contract and wants a quote of the forward price.  To come up with the price, you observe the following information:

Current gold price = $1,700 per ounce.

Current 1-year risk-free interest rate = 3% p.a.

Current storage cost = 0.15% p.a.

• (3 points) What price will you quote to the customer so that the bank will profit by $5 per ounce?
• (2 points) The customer will compare your quote with the synthetic forward price that he/she can create. Suppose that his/her borrowing rate is 3.50%, while his/her lending rate is 2.75%.  Do you think the customer will accept the bank’s contract?
• (3 points) TD Canada Trust currently offers a “Market Growth” Guaranteed Investment Certificate (GIC). This GIC has a 3-year term, and provides the following returns:
• The minimum return is 2% (Note that this is 2% per 3 years, not 2% p.a.).
• The return is linked to the performance of the S&P/TSX60 index over the 3year term, with the maximum return of 15% (per 3 years).

Suppose that the current level of the S&P/TSX60 index is 1,200.  Please describe how you would replicate the payoff of this GIC (assuming an initial investment of $100).

• (3 points) You work for a bank. Your bank was just contacted by a customer.  The customer is a gold-mining company.  It wants to borrow money.  But it wants to repay in gold instead of in cash.  It offers to pay your bank 1,000 ounces of gold each year for 5 years, with the first payment starting one year from now.  The current price of gold is $1,700 per ounce and the current risk-free rate is 2% p.a. for all terms.  Suppose the storage cost for gold, expressed in percentage term, is 0.15% p.a.  How much money should your bank give to the customer now in exchange for the offered stream of gold payments, provided that your bank wants to make a profit of $100,000 (in today’s dollars) on the loan.

Hint: The repayments are done in gold, and so they are risky because you do not know what gold price will be in the future.  Is there a way to hedge this risk?

• (3 points) Consider the following gold futures prices:

Assume that the current risk-free rate is 2% p.a. for all terms.  What is the storage cost (in percentage terms) for gold?

(3 points) A friend of yours believes that Tesla is the best car in the world and that Tesla stock is now undervalued.  As a result, she expects that its stock price, now at $775 per share, will continue to go up.  She is prepared to back up her conviction by offering you the following bet.  If in exactly one year from now Tesla stock price is lower than $775/share, she will give you one hundred times the amount of the difference (e.g., suppose the price in one year is $700 per share, you will get $7,500).  On the other hand, if the price in one year ends up above $775/share, you will have to give her one hundred times the amount of the difference (e.g., suppose the price in one year is $800 per share, you will have to give her $2,500).  Suppose that the expected return on Tesla stock is 10% p.a.  Suppose also that the current risk-free rate is 2% p.a. and Tesla does not plan to pay dividends in the next year.  What is the value of this bet to you? [Hint: Write out the payoff of the bet.  What does the payoff look li