# Backwardation or Contango of a Market

Question

The United States Oil Fund (ticker: USO) is a popular exchange-traded security that is designed to track changes in the price of oil (specifically, West Texas Intermediate or WTI). Since spot oil is expensive to store, the fund uses futures contacts to generate its returns. In simplified form the fund uses the following strategy: At the beginning of each month, the fund enters into long positions in one-month futures contracts, and rolls them over at maturity (i.e., it closes out the contracts at the end of the month and takes positions in new one-month futures).

Note that at maturity, the futures contract has become a contract for immediate delivery, so has essentially become a spot contract. Thus, at maturity, the price of the expiring futures contract must equal the spot price. Now, the strategy involves taking a long position in a futures contract at the beginning of each month and closing it out--i.e., taking an offsetting short position in the same futures contract--at the end of the month. Since at month's end the contract is at maturity, this means we buy at the futures price at the beginning of the month and sell at the spot price at the end of the month.

The purpose of this question is to see if the fund's returns are affected by whether the market is in backwardation or contango. A futures market is in backwardation if the futures price is less than the spot price. It is in contango if the futures price is greater than the spot price.

1. First suppose the market is in contango (i.e., futures prices are greater than spot prices). Specifically, suppose the following is the series of realized spot and one-month futures prices that prevailed at the beginning of each month over a three month horizon:
 Beginning of Month 1 2 3 4 One-month Future Price 52 59 60 62 Spot price 50 57 59 60

What is the fund's total profit (or loss) from futures trading over this three month horizon? [Note: The three-month horizon means that the fund enters into long futures positions at the beginning of months 1, 2, and 3 and closes them out respectively at the beginning of months 2, 3, and 4.] Do these returns exceed or lag the actual change in the spot price of oil over these three months?

1. Now suppose the market is instead in backwardation (futures prices are less than spot prices). Specifically suppose that the following is the series of realized spot and one-month futures prices that prevailed at the beginning of each month over a three month horizon:

 Beginning of Month 1 2 3 4 One-month Future Price 48 55 58 58 Spot price 50 57 59 60

(Note that the spot prices are unchanged from the previous table.) What is the fund's total profit (or loss) from futures trading over this three month horizon? Is this greater or less than the actual spot price change in oil over these three months?

Summary: This question belongs to finance and discusses about discusses about United States Oil Fund which is a exchange-traded security that is designed to track changes in the price of oil and to find the fund's total profit (or loss) from futures trading.

Answer is in Excel format

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