Assignment:
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 Under what circumstances could $1,500 be withdrawn from the margin account.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?