Basis weakening / strengthening

[hsuwang]

Hello David,
On M&P notes pg.29, it says:
"When the spot price increases by more than the futures price, the basis increases and this is said to be a “strengthening of the basis".

I'm curious if this is true only if the market is in backwardation (future price lower than spot), so when spot price increases by more than the futures price, the basis strengthens (and weakens when futures price increase by more than the spot price). In the case of a market that's in contango, it would be another way around?

Thanks!

 

[David Harper CFA FRM]

Hi Jack,

Great idea to connect the two ... but it's the other way around (and with a caveat):

basis = spot - futures price, so for example if we go back about a year (mid 2008) and (just estimating):
oil spot = $ 110 and oil forward = $100
oil was in backwardation and basis = 110 - 100 = $10
under the *assumption* of no shift in the forward curve (i.e., the curve holds steady as time marches forward) and under the assumption of convergence:
the forward price increases to converge with the spot: the basis *weakens* from 10 and converges to 0.
So, "steady" backwardation with convergence implies basis will weaken

conversely, more recently more like oil spot $60 and forward at $80. Basis -$20. Assume convergence and basis will "strengthen" from -20 to 0; i.e., contango implies basis will strengthen

so, i would say, if we can assume convergence, a backwardation must weaken (i.e., expect positive current basis will go to zero) and a contango (expect negative basis will go to zero) must stengthen.

the caveat is, from Hull, pretty sure it's in the notes: it's the *unexpected* basis that creates problem for the hedger. So, in the case of current oil contango, a hedge assumes convergence if held to maturity plans for a strengthening from -20 to 0. But say the forward doesn't converge to spot, e.g., spot goes + 10 to $70 and forward is unchanged at $80. The future (realized) basis will then be (70-80 = -10). Now, we *anticipated* strengthening to 0 but realized basis was -10, so Hull calls the *unanticipated weakening* (vis a vis our 0 expected basis). Note oil forward still in contango, so his point is that what challenges the hedger is the unanticipated portion of the basis change (I am using convergence here for convenience, but more realistically, we can be referring to futures contracts not held to maturity but rollover over prior to maturity).

David

 

[hmehrotra]

David,

Great explanation. Can you please expand this example to the rollover hedge that you mentioned in your last line?

Thanks,
Hanu