Homework 1 due Feb 10 Thursday K Foster, Options & Futures, Eco 275, CCNY, Spring 2010

 

You are encouraged to form study groups to work on these problems.  However each student must hand in a separate assignment: the group can work together to discuss the papers and comment on drafts, but each study group member must write it up herself/himself.  When emailing assignments, please include your name and the assignment number as part of the filename.

Please write the names of your study group members at the beginning of your homework to acknowledge their contributions.

1. Complete Assignment Question 1.26 in Hull.
2. Complete Assignment Question 1.27 in Hull.
3. Complete Assignment Question 2.27 in Hull.
4. Complete Assignment Question 2.28 in Hull.
5. Leverage is at the heart of the popularity of options and futures.   Consider if you have $10,000 equity to invest.  You can put money into an investment that will return 10% in a year on the funds invested.  What is your return on equity if you can't borrow?  Now consider if you can borrow at 6% per year for up to half of the value of the investment.  How much can you now invest?  How much is left over, after you repay the loan?  What is now your return on equity(ROE)?  What if you can borrow up to 80% of the value of the investment?  What if (this is the real estate case) you can put just 2% down and borrow the rest?
6. Imagine that you had $5000 available to invest in futures contracts.  Go online and carefully look at the requirements (for margin, fixed cost, etc) for entering into a contract.  Describe a position that you would take (in any commodity, currency, index or bond that is traded standardly) using this imaginary $5000.  Under what circumstances would you make a profit?  How much?  A loss?  How much?  (Each person in a study group should choose a different portfolio since next week we'll look to see who made the most money!)
7. In the market for widgets, suppose that the current price is $30.  You can enter into a forward contract to buy/sell widgets at $31.25 in one year and $31 in six months.  The interest rate (at which you can borrow or save) is 4%.  Assume that storage is costless.  Consider an investment of $1m.
1. If you bought widgets today and entered into a contract to sell them forward in a year, what would your portfolio be worth in 1 year?
2. If you bought widgets today and entered into a contract to sell them forward in six months, then at six months took the money and saved it (assume interest rates are unchanged), how much would your portfolio be worth in one year?
3. If, instead of saving the money for the second half of the year, you could buy/sell widgets at $31 and then sell after a year, how much would the portfolio be worth?
4. If you put your $1m into the bank (saved it) how much would it be worth in a year?
5. Now suppose that the margin is 50%
   
    what are the possible payoffs now?
6. Now what if transactions cost $0.10 per widget
   
    what are the possible payoffs now?