Question

1. Assume all positions are held to the delivery date, ignoring margin issues, transaction costs, delivery issues and assuming stable markets for futures and spot markets for oil. In the real world you would have to include all issues and be precise in your calculations. Let S bet the spot price and F be the futures price at delivery. There are 360 days in a year. e.g. Suppose the spot price for oil is $20 and the futures price for oil is $25 for delivery in 180 days. The cost to carry is 7% per year and the risk-free rate of interest is 1% per year. Today’s date is time zero or t = 0. S = 20 dollars at time 0. F = 25 dollars or Futures Price. rf = .01 or 1% per year. s = .07 or 7% storage cost per year. T = delivery date is 180 days. t = todays date is 0. a) What is the Implied futures price? b) If the Implied futures price is different from the futures price what should your strategy be? c) If there is a profit opportunity, find the profit. d) Show all cash flows.

2. Using the data from problem one, now assume the cash price for oil is -$40 (the spot price). Answer the following questions again. In this one you will have to think. a. What is the Implied futures price? b. If the Implied futures price is different from the futures price what should your strategy be? c. If there is a profit opportunity, find the profit. d. Show all cash flows. e. What would be the major problems with undertaking this strategy?

Answer 1

( Please note that you have posted 2 questions, each with multiple subparts. The first question with all its subparts is answered below. Please post the 2nd question in a separate post.)

Part 1a)

Part 1.b)

As the implied price is lower from the market price, the strategy should be to short sell the futures as they are overpriced in the market, long positions should be taken on physical oil as it is underpriced with respect to futures.

Part 1.c)

The profit opportunity in such situations is the difference between the market price of futures and their implied calculated price.

So it will be $25 - $20.78 = $4.22

Part 1.d)

The cash flows for executing the above trade are as shown below:

Time	Trade	Cash flow
t= 0	Short sell oil future at t=0	0
t= 0	Borrow $20 at t=0 at 1% Rf	20
t= 0	Buy oil in spot market	-20
T= 180	Payback borrowed amount and also Pay 1% interest & 7% storage costs at end of 6 months	-20.78
T= 180	Deliver physical oil to futures conterparty at $25	25
	Net cash flows (Profit)	$       4.22