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# Contango and backwardation review

Review of the difference uses of the words contango, backwardation, contango theory and theory of normal backwardation. Created by Sal Khan.

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• Why would a seller want to lock in a lower price if generally the expected price would tend to be closer to the spot price? And a related question is, does volatility benefit a seller more than a consumer?
• If you are the leader of a huge corporation you are responsible for paying thousands of people. Their wages won't go up or down depending on the market price, so the price of the commodity changing a lot can ruin your business. So if you are able to guarantee that you will sell in the future the security is worth the loss in profit.
• how accurate are futures prices at predicting prices? which direction is more common for converging?
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• The point of the futures market is not to predict prices, but to allow for people buying and selling the underlying to hedge against future price volatility.

For example, look at stock and bond futures. The price 6 months from now is in no way a prediction of where the index will be in 6 months. It is merely the price of the next future to expire, adjusted for the risk free rate of return. It cannot be anything else or else someone would be able to make a risk free profit.

Things get a little more tricky with physical commodities because you have to factor in storage and delivery costs. But still, they are not a prediction of future prices, they are merely a tool for people who buy and sell commodities to lock in prices and avoid volatility.
• Let's use the notation E(X_t,s) for the market price at time s, where t is the time the expectation is calculated. Does the "expected price" in the video mean E(X_8,8) or E(X_0,8) ?
• If I am reading your notation/question correctly, the "expected price" in the video is E(X_0,8). As time goes on, the expected price tends to get closer to the spot price, so that E(X_4,8) is going to be closer to the spot price at time 4 than E(X_0,8) was at time 0. If everything is working properly, E(X_8,8) is equal to the spot price at time 8.
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• so if downward convergence of futures prices to spot price is evidence of contango, defined by futures price > E(future prices), are we implicitly saying that the spot price representative of E(future prices)? This makes sense to me if we assume that prices move in random walk, making the spot price the best estimate of future prices.
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• Why would futures price be decreasing in backwardation if backwardation is when the futures price is below the current spot and should increase to converge to the spot price at maturity.
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• Can a situation occur where you have a 'contango' shaped futures curve wherby the future price is still less than the "expected" future price? Ie the futures price movement may track flat over time and then move higher?
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• So is there always arbitrage opportunity in both contango and backwardation. In contango couldn't you just buy the security for spot price and short it in the future and vice versa for backwardation? Or does storage and delivery prices offset most arbitrage opportunity?
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• is there any circumstance that future's price move down towards the spot price in backwadation? means the spot price keep going down?
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• Is it fair for me to assess deep ITM Call LEAPs as being in backwardation when the market is bullish?

This week I bought some deep ITM WMT (Walmart) LEAPs for very little premium against today's prices. If the bull market continues and thus the expected price is about \$10 more than today's price, then my options should converge with the higher price making capital gains while forgoing dividends. Is this an example of backwardation?
• The terms contango and normal backwardation are generally used in reference to commodity futures/forward markets only.

The LEAP is an option that gives you the right, but not the obligation to purchase the Walmart shares whereas in the futures market for oil, wheat etc, there is an obligation to buy or sell that commodity at that price. This "option" without obligation reflects a totally different risk level which is more associated with how much the asset moves (it's implied volatility) rather than the expected price of that asset X years from now. This is different than the futures market which is more based on the expected demand for the commodity and the opportunity cost of storing that asset (I could use that oil to run a tractor that would yield harvest rather than have the oil sit in storage -- thus there is some value in consuming the asset now rather than just purchasing it and storing it). The expected price is where demand and supply intersect for a commodity at some point in the future.

Interesting that you mention dividends as dividends play an important role in options as they reduce the value of an option. If you compare a 1 year option price to a 1 year share price of an asset with dividends, the option price will vary greatly even if the volatility is the same (you are foregoing all the dividends when you lock up your money in the premium when you could have instead bought the stock -- especially important in LEAPs as the money is stuck for a longer term).
• How can i get a contango percentage?