Assignment: Problem Set
Please show all work. Please use four decimal places for all calculations.
1. What is the difference between open interest and trading volume?
2. What does it mean to say someone has a long position in a futures contract?
3. A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price would lead to a margin call? Under what circumstances could $1,500 be withdrawn from the margin account. Note:The size of the wheat futures contract is 5,000 bushels.
4. Assume the interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding? Comment on your answers for problem a, b and c and explain why they make sense.
5. Use the data in the following table, determine the zero rates for maturities of 6 months, 1 year, and 18 months expressed in terms of continuous compounding. Bond 2 and 3 have semiannual coupon payments.
|
Bond Number
|
Bond Principal
|
Time to maturity (years)
|
Annual Coupon
|
Bond Price
|
|
1
|
100
|
0.5
|
0
|
97
|
|
2
|
100
|
1.0
|
7
|
102
|
|
3
|
100
|
1.5
|
9
|
103
|
Please fill in the following table and show your work.
|
Time (years)
|
Annual Zero Rate
(continuous compounding)
|
|
0.5
|
|
|
1
|
|
|
1.5
|
|
6. Find the cash price for a 1.5 year bond with a 5% coupon rate. Assume payments are semiannual and the next payment is in 6 months. Zero rates (expressed with continuous compounding) are 5%, 6%, and 7% for 6 months, 12 months, and 18 months respectively. Assume the bond has a face value of 100.
7. A deposit account pays 10% per annum with continuous compounding, but interest is actually paid semiannually. How much interest will be paid in the first six months on a $100,000 deposit?