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Contango is commonly defined as "The situation where the price of a commodity for future delivery is higher than the expected spot price". But how is this "expected" spot price determined? My understanding is that such a measure is highly subjective, as each investor would have their own opinion regarding how the price will change in the future. How then can the futures price converge on the expected spot price, when it is not known?

My second question, which follows from the first, is what shape does the contango curve take? Is it increasing or decreasing? My understanding is that if the futures price is higher than the expected spot price, and the two must converge at expiration, the curve should be decreasing (see image 1). However, when googling contango and backwardation curves, I get conflicting results, with some images showing the contango curve as increasing and others as decreasing (see image 2). Why is that?

Image 1

Image 2

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Both charts are right in their own way.

The second chart shows the shape of the Curve of Futures Prices at a point in time (for ex: today at 10am). In Contango far away futures contracts are priced higher than nearby. It has nothing to do with expectations or subjective factors and can be displayed easily using the Bloomberg CCRV command. If Bloomberg shows that the Sep Fute price is higher than the Aug Futures price then we can say that "as of 10:00am these two contracts are in contango".

The first chart is theoretical and conceptual, it shows how prices will unfold on average as time progresses towards delivery (for ex: what will happen to Dec futes over the next 6 months), the contango premium gradually dwindles down until delivery. The so-called convegence to spot phenomenon. Naturally this this is only true in expectation over many cycles (prices are extremely volatile, they don't behave smoothly like this) and the Expected Spot Price is not known in advance. This theory involving expectations is due to Keynes in the 1940s, it has been difficult to confirm empirically as expectations are not directly observed. It has little to do with the definition of contango/backwardation, which is the second chart and is extremely objective and established.

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The statement is correct,

"Contango is commonly defined as "The situation where the price of a commodity for future delivery is higher than the expected spot price". But how is this "expected" spot price determined? My understanding is that such a measure is highly subjective, as each investor would have their own opinion regarding how the price will change in the future. How then can the futures price converge on the expected spot price, when it is not known?"

Contango occurs when the spot price, when the first expiration futures of the whole futures curve has the highest demand, hence the highest price. Please note I am referring to FUTURES CONTRACTS which REQUIRE CASH DELIVERY if one is short the Futures to one WHO IS LONG futures. Hence a situation can occur during shortages, that the LONGs dont sell and the zero sum game of futures means there is a short being squeezed so the contango is the first chart. A contango would occur in crude oil during say a opec squeeze and there is an unnatural or natural need for spot oil. Backwardation best example is when spot expiring crude fell to -40 dollars on april 20,2020 during the pandemic ALL CAPS FOR A REASON--NO ONE WANTED OIL AND THE LONGS HAD TO PAY SOMEONE 40 BUCKS TO TAKE THEIR BARREL OF TOXIC OIL. THAT CURVE WAS FLAT TO BACKWARDS.

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