Basis strengthening or weakening

[brian.field]

I find this a little unintuitive, although I do have it stored in memory.

Let spot at time 1 = 100 and futures at
time 1 = 80 and spot at time 2 = 120 and futures at time 2 = 110.

Clearly, basis at time 1 = 20 and the basis at time 2 = 10, so the basis has weakened.

The magnitude of the basis is the "risk" or the degree of mismatch - I think we all agree on this.

Then let spot at time 1 = 100 and futures at time 1 = 150 and spot at time 2 = 100 and futures at time 2 = 200.

Clearly, basis at time 1 = -50 and the basis at time 2 = -100, so the basis has weakened.....???

Weakened? This is not intuitive to me.

The basis (or mismatch) has worsened!!!! So it seems more natural to describe this as a strengthening of the basis but that doesn't appear to be the approach used in practice.

 

[jairamjana]

Hi @brian.field ,
I will put this in table form

Short Hedge Strengthening Basis
[b(t) - b(0)]

Spot price rises more than futures price rises
or
Spot price falls less than futures price falls
or
Spot price rises and futures price falls​

Long Hedge Weakening Basis
[b(0) - b(t)]

Spot price rises less than futures price rises
or
Spot price falls more than futures price falls
or
Spot price falls and futures price rises​

Now for some equations..
b(0) = S(0) - f(0) (todays basis)
b(t) = S(t) - f(t) (basis at time t)
b(t) - b(0) = S(t) - f(t) - (S(0) - f(0))

b(0) - b(t) = [f(t) - f(0)] - [S(t) - S(0)]
or
b(t) - b(0) = [S(t) - S(0)] - [f(t) - f(0)]

In general If the spot price increases by more than the futures price, the basis will increase [b(t) - b(0) > 0]. This is said to be a strengthening basis, and it improves (reduces) the performance of the short (long) hedge.
If the futures price increases by more than the spot price, the basis will decrease [b(0) - b(t) > 0], reducing (improving) the performance on the short (long) hedge. In that case, the basis is said to be weakening.

In your example
basis at time 1 = 20 and the basis at time 2 = 10 [b(0) - b(t) = 10] Weakening

basis at time 1 = -50 and the basis at time 2 = -100 [b(0) - b(t) = 50] Weakening


Hope that's clear

 

[ShaktiRathore]

Hi Brian,
Its the direction that matters in terms of determining whether the basis is Strengthening or Weakening,Not the magnitude or the sign as per the Hull. Strengthening of basis is an increase in basis from -ve to +ve direction that is basis moves towards positive direction while Weakening of basis is an decrease in basis from +ve to -ve direction that is basis moves towards negative direction.
In your example the basis has moved from -50 towards negative direction to -100 thus its Weakening.
I referred: https://forum.bionicturtle.com/threads/basis-risk-strengthening-weakening-in-notes.7074/#post-25342
Thanks