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My understanding is that "contango", when describing the forward curve, describes forward prices that are above the current spot price, i.e. $F_{t+1} > F_{t} > S$. This is directly observable at the current time.

"Normal backwardation" is the phenomenon that the current forward price is below the expected spot price at expiry. I understand this can happen when speculators go net long and expect a profit (i.e. expect a premium to take on the risk by the hedger).

However, my understanding is these two can happen simultaneously. Due to carrying costs, etc. a forward curve is often in contango. I expect this when the convenience yield is less than the cost of carry.

I would also expect that simultaneously, most futures would exhibit "normal backwardation". due to the above reasoning regarding risk premium for speculators.

My question is: how can both be true simultaneously? A forward curve in contango seems to imply to me that the future has negative theta, i.e. decays to expiry. However, normal backwardation seems to imply to me that it is positive theta, i.e. will rise to meet the spot at its (higher) expected value.

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I think these are just words. Contango means forwards are higher than spot. Backwardation means forwards are lower than spot. The only way they can both be true is if the forward curve has a complex shape so that for some forward dates , the forward is higher than spot and for others, lower.

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    $\begingroup$ Normal backwardation is not the same thing as backwardation: en.wikipedia.org/wiki/… When I say "contango but in normal backwardation" I mean that forward are higher than the current spot, but the expected spot price is higher than the forwards. $\endgroup$
    – rb612
    Commented Sep 4, 2023 at 0:18
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    $\begingroup$ That definition does not seem useful - how does anyone know what is the expected spot price at expiration ? $\endgroup$
    – dm63
    Commented Sep 4, 2023 at 4:07
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    $\begingroup$ "Normal Backwardation" is a theoretical concept by Keynes (1930) that is difficult to verify empirically, because the expectation is not observable. At best NB might hold on average over a long period of time. It would not contradict occcasional observations of contango. $\endgroup$
    – nbbo2
    Commented Sep 4, 2023 at 5:26
  • $\begingroup$ @nbbo2 can you provide a hypothetical example of how, if the forward curve stayed in contango, it would be possible to still observe NB? That’s the root of my question—if the forwards decay to the spot (in contango) but rise to the present expected value of the spot (which is higher due to NB) how can both be true? $\endgroup$
    – rb612
    Commented Sep 4, 2023 at 20:56
  • $\begingroup$ @dm63 agreed that it would be impossible to know the spot price at expiration, but under Keynes’ assumption, hedgers are typically net short and thus speculators are net long, and hence require a positive “risk premium” in exchange for taking on the risk from the hedger. This implies that their expectation of the spot at expiry is higher than the forward price. If speculators didn’t see any positive EV in entering into a long position, why would they take on the risk for no gain? $\endgroup$
    – rb612
    Commented Sep 4, 2023 at 20:59
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Yes. Especially on a stock futures/commodities market.

https://www.cmegroup.com/education/whitepapers/trading-the-curve-in-energies.html

Simply speaking, cost of money/storage causes contango and supply cycles and limit storage can cause backwardation.

A good example - negative prices on oil futures.

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