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# Basis Risk Strengthening & Weakening in Notes

#### mga

##### New Member
Hello,

I would like to ask a question regarding P1.T3 Page 39. In the example for strengthening on May, basis is ($0,10), then there are two scenarios discussed in columns, weakening and strengthening scenario. Under Basis Weakening Scenario, Basis is stated as ($0,05) and Basis Strengthening scenario, it is $0,05. What I understood from notes and my search in internet is, if basis is getting more positive then it is a strengthening. But here the basis on May was ($0,10), and in both two scenarios Basis is getting more positive;
($0,10) < ($0,05) & $0,05 , so basically in both scenarios it is strengthening compared to May Basis. But in notes scenario with ($0,05) basis is stated as basis weakening, is there a mistake here or did I understand the topic wrong ?

#### chiyui

##### Member
People tend to say the term "strengthening" or "weakening" in terms of sign, not in terms of movement.
In your case, -0.1 going to -0.05 means that the basis is still negative. So people call it a weakening.
However, -0.1 going to +0.05 means that the basis changes to positive. So people call it a strengthening.
The sign matters, not the moving direction.

This is what I think.

#### chiyui

##### Member
Actually, I don't like to say that basis is strengthening (or weaking) in terms of sign nor in terms of direction of movement, but in terms of magnitude.
The sign and the direction does not matter, only the magnitude matters.
And this is what I really see in most textbooks or in the internet.

So:

If a +0.2 basis changes to +0.3, I will call it a strengthening.
If a +0.2 basis changes to +0.1, I will call it a weakening.

If a -0.4 basis changes to -0.5, I will call it a strengthening.
If a -0.4 basis changes to -0.3, I will call it a weakening.

If a +0.2 basis changes to -0.3, I will call it a strengthening.
If a +0.2 basis changes to -0.1, I will call it a weakening.

If a -0.4 basis changes to +0.5, I will call it a strengthening.
If a -0.4 basis changes to +0.3, I will call it a weakening.

Therefore I don't know why Schweser notes don't interpret in this way.

#### mga

##### New Member
Hi,

I searched net a bit more about topic and found the manual below. If you go to page 3 of the manual you will see that if it is getting more negative it is weakening and if it is getting more positive it is strengthening as per my understand. The second link below also handles the issue in same way.

http://www.gofutures.com/pdfs/Understanding-Basis.pdf
http://www.theoptionsguide.com/futures-basis.aspx

For instance
If a -0.4 basis changes to +0.3, I will call it a weakening. -> this is a strengthening according to manual in the first link.

I think it is not only magnitude but also sign is important, as you know basis is S-F, because in example above, if it is negative it means a contango but if positive then this is backwardation

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
The FRM follows the assigned Hull, where basis (B) = S(0) - F(0) and a strengthening of basis is an increase (+) and a weakening is a decrease (-), so with respect to "strengthening" or "weakening," it is only the direction that matters, not the magnitude and not the sign.

mga in regard to the example on page 39, the table should be better labeled to accompany the text, but the point of the example is to make John Hull's point: the unexpected basis strengthening or weakening interferes with the hedge. Specifically:

We start with an initial basis, B(0) = -$0.10 The hedger expects the basis to converge to zero, E[B(T)] = 0; i.e., the expectation is for a strengthening of the basis, from -$0.10 to zero. This is an expected strengthening because it's an increase (regardless of magnitude, regardless of sign).

In the first scenario, B(T) = -$0.05. This is referred to as an unexpected weakening, relative to the E[B(T)] = 0 • So, the basis did strengthen, because it increased from -$0.10 to -$0.05 • But, at the same time, as the hedge trade was put on against expected B(T) = 0, there was also an unexpected weakening relative B(T) = 0 Again, the unexpected component is the emphasized on the assumption that the hedge trade hedges based on the expected basis, such that if the expected basis is realized, then the hedge trade will be "perfect." I hope that explains (paraphrases) Hull, which is the basis (pun intended) of the FRM, thanks, #### mga ##### New Member Hi, I am really confused with that, which is our reference point to decide for strengthening/weakening of basis, B(0) or B(T)? Because as in the example above based on reference point the answer changes. Thanks in advance for answer #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber The references are B(T) and E[B(T)], if we want to complicate matters. First, if you want to thing of the simple case "without any hedge," then basis strengthening or weakening is simply a matter of an increase (strengthening) or decrease (weakening) of basis over some time period. This is simply B(T) - B(0). If B(T) - B(0) > 0, the basis strengthened between Time (0) and Time (T). We may think of this simple case as before any hedge trade, where the "reference" is B(0). Second is Hull's point about a hedge trade: the hedge trade is based on an expectation of E[B(t)]; e.g., often the hedge trades expects convergence to B(t) = 0, which may be an weakening or strengthening. Quite aside from the simple (absolute) strengthening/weakening, there may be an UNEXPECTED realization of B(t) versus E[B(t)]. Hull's point is that (eg) a short hedge profits (loses) due to the unexpected weakening. We may think of this as after the hedge trade (i.e., the net position = underlying exposure plus the hedge trade) where the reference is E[B(t)] which informed the hedge. I think the numerical examples may be easier to follow. Thanks, #### chiyui ##### Member OIC.......unexpected basis. Thanks for David's information #### bpdulog ##### Active Member The FRM follows the assigned Hull, where basis (B) = S(0) - F(0) and a strengthening of basis is an increase (+) and a weakening is a decrease (-), so with respect to "strengthening" or "weakening," it is only the direction that matters, not the magnitude and not the sign. mga in regard to the example on page 39, the table should be better labeled to accompany the text, but the point of the example is to make John Hull's point: the unexpected basis strengthening or weakening interferes with the hedge. Specifically: We start with an initial basis, B(0) = -$0.10
The hedger expects the basis to converge to zero, E[B(T)] = 0; i.e., the expectation is for a strengthening of the basis, from -$0.10 to zero. This is an expected strengthening because it's an increase (regardless of magnitude, regardless of sign). In the first scenario, B(T) = -$0.05.
This is referred to as an unexpected weakening, relative to the E[B(T)] = 0
• So, the basis did strengthen, because it increased from -$0.10 to -$0.05
• But, at the same time, as the hedge trade was put on against expected B(T) = 0, there was also an unexpected weakening relative B(T) = 0
Again, the unexpected component is the emphasized on the assumption that the hedge trade hedges based on the expected basis, such that if the expected basis is realized, then the hedge trade will be "perfect." I hope that explains (paraphrases) Hull, which is the basis (pun intended) of the FRM, thanks,
From what I gather based on this is that:

1. Expected basis is always expected to converge to 0
2. Unexpected basis or weakening should be compared to 0, and not the initial basis at t=0

Is that correct?

#### ShaktiRathore

##### Well-Known Member
Subscriber
Hi,
1. Expected basis is not always expected to converge to 0,the asset to hedge might not have futures available so hedge with the futures of nearly correlated asset therefore this results in imperfect hedge that is the basis do not necessarily converge to 0 or that the basis is always present.
2. Unexpected basis strengthening or weakening occurs when basis is becoming more positive or more negative. Yes whether the basis is strengthening or weakening depends on the basis value relative to the value 0.
Thanks

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @bpdulog I agree with @ShaktiRathore . The basis is expected to converge to zero as the futures contract expires (i.e., as maturity tends to zero) because at expiration we expect the forward price to equal the spot price (or technically, but in the zone around the spot price); this is NOT the same as saying the expected basis is zero. Say it is currently February and hedger uses a December contract to hedge an October commodity sale; the expected basis in October will not be zero. But the hedger's trade will be setup for October. If the hedger were hedging a December sale, probably E[B(T)] = 0, but if the hedger does not have the luxury of matching the delivery date/month to the underlying exposure, then E[B(T)] <> 0. Unexpected strengthening or weakening of the basis might be relative to zero ("compared to 0") in many "clean" hedging scenarios where the contract maturity coincides with exposure, but the meaning of "unexpected" is relative to the hedge trade conducted by the speculator/hedger. Thanks,

#### chirania

##### New Member
Subscriber
To summarize
1. For "clean" hedge scenario SIGN determines strength or weakness. + sign (i.e. > 0) means 'strengthening' '-' sign ( < 0 ) means "weakening".
2. For non-hedge scenario the DIRECTION matters.i.e. if B(T) > B(0) means 'strengthening' else "weakening".
3. For un-clean scenario use the expected basis value instead of zero in #1 to get desired result.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @chirania
• I like (and agree with) your numbers (1) and (2): As B = S-F, strengthening of basis is just an increase in B; i.e., B+. Unexpected strengthening is unplanned (unhedged) positive (B), so the basis can decline but unexpectedly strengthen.
And a "clean" hedge scenario here refers simply to a hedge that anticipates a zero basis.
• But I am not sure what you mean by a non-hedge scenario? Basis risk, by definition, implies two positions, the underlying (eg, spot) and the hedge (eg, futures). Thanks,

#### chirania

##### New Member
Subscriber
By non-hedge I meant the simple case "without any hedge".

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @chirania Okay but--I do not mean to nitpick--but if there is no hedge, then there is no basis (nor basis risk), so I don't see "non hedge" as a scenario. I like to say that "basis risk" requires two positions, an underlying exposure and a hedge position (and further, once you have two positions, basis risk is unavoidable).