# Someone please explain backwardation (as seen in wiki)

#### donny

Hey Quantnet forum,

So, I'm trying to wrap my head around this idea of backwardation. The wiki for "Normal backwardation", which they claim is the same as backwardation, quotes this:

"A backwardation starts when the difference between the forward price and the spot price is less than the cost of carry, or when there can be no delivery arbitrage because the asset is not currently available for purchase."

I thought it through and I still don't get it.

So, firstly, I'm guessing they are referring to backwardation starting from contango. This implicity assumes that forward prices are above spot prices. If the difference between forward and spot is less than the cost of carry, people rather long the forward contracts than buy and store.

Say spot at $10, contract at$14 and cost of carry at $5. It benefits someone to long the contract paying$14 on delivery than $15 ($10 + $5) for buy and storing. This is what I don't get. 1. Wouldn't longing these forward contracts bid up the price from$14 to possibly \$15?
2. The normal sloping forward curve (contango) will then shift upwards AND still remain normal sloping. How does backwardation even occur, which I'm guessing is defined in most areas as invert sloping?
3. Backwardation is when forward prices are below spot prices. I don't see how the above scenario would lead to that.

Any help will be greatly appreciated. Thank you.

Donny

#### donny

Added: A backwardation, again which is defined as forward price less than spot, would result if either one of these two happens:

1. Spot price increases.
2. Forward price decreases.

It just can't piece how does the cost of carry result in either 1 or 2.

#### diegosanaz

##### BU MSMF
I think it would happen when there is a shortage of supply, making the spot price to rise a lot.

For example, this season crops were spoiled by some storm or whatever. So the spot price will increase, but futures prices won't since those crops might be fine.

#### Yike Lu

##### Finder of biased coins.
This arbitrage is not realizable because you cannot short the spot commodity. Yes, buying the futures/forward is cheaper than storing and carrying, but the inventory risk is high and the benefit is limited to those who actually use the commodity so not as much capital can flow into the trade.

As such, there are various theories as to why backwardation exists.

#### diegosanaz

##### BU MSMF
I think it can be explained like this:
$$F_t=S_t e^((r-q)(T-t))$$ So, then $$F_t < S_t \iff q>r$$

In the case of futures, q would be the convenience yield and r is the cost of storage. So backwardation occurs when the opportunity of having it now surpasses the cost of storage? Still need to understand it further, but I think this is more less the direction.

#### Yike Lu

##### Finder of biased coins.
Also, strictly speaking, "backwardation" is futures below spot. "Contango" is futures above spot. "Full carry" is futures at the cash and carry arbitrage price. Futures should almost never trade above "full carry" because of the arbitrage, so long as there is sufficient storage.

C S

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