Rules for Question:

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).

Question:

1. (3 points) You want to short a 6-month forward contract on a stock. You contacted your bank and were offered a forward price of $39.85 [Note: This forward price is available only to customers who want to take a short position. Customers who want to take a long position will get a different quote.]. You also observe the following information:

-Current price of the stock = $40

-Expected dividend on the stock = $0.50, payable 3 months from now

-Your spot 3-month lending rate = 2.50% p.a. [i.e., This is the rate that you will get if you lend money for 3 months, starting now.]

-Your spot 3-month borrowing rate = 4.00% p.a. [i.e., This is the rate that you will have to pay if you borrow money for 3 months, starting now.]

-Your transaction cost in buying one stock in the spot market = $0.10, payable at the time of the transaction.

-Your transaction cost in short selling one stock in the spot market = $0.20, payable at the time of the transaction (This already includes the transaction cost for closing out the short-sale transaction).

What is the minimum 6-month spot lending rate that you need to get in order for you to reject the bank's offer?