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#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Basis = Spot price - Futures price; i.e., b(0) = S(0) - F(0, t). Unexpected weakening (strengthening) of the basis helps (hurts) the long hedger.

David's XLS is here: http://trtl.bz/2trHMzs

#### valenski

##### New Member

Hello David

I watched this video very carefully but was confused about why you minus 0.1 from the cell I highlited. I did not get the reason behind it.....

Besides, what do you mean by "unchanged term structure", "unexcpected" and "expected". I could not find these definition in the textbook....

Thanks very much.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @valenski The first sheet ("baseline") contains the baseline assumption of an unchanged (forward) term structure which unrealistically means that as we go forward in time, the term structure does not change:
• The initial term structure, as of March, is a contango where S(0) = $3.60, F(+ 1 month) =$3.65, F(+2 months) = $3.70, ... F(+ 8 mos) =$4.00, F(+ 9 months) = $4.05. • Unchanged term structure is illustrated by going forward in time all the way to November and, at that time, it remains the case that S(0) =$3.60, F(+ 1 month) = $3.65 etc. Your highlight above refers to the sheet = "unexpected strengthening" where the term structure does change. So instead of L39 + 0.05 which would reflect an unchanged term structure (i.e., one month forward is +0.05), I manually forced an unexpected strengthening by forcing the forward month's contract price to be less than the spot by$0.10 (so I actually forced a backwardation). This illustrates a challenge to the hedge: if the term structure is unchanged, we can anticipate the basis. But my forced backwardation illustrates an unexpected strengthening (the term discussed in Hull) in the basis, which renders some volatility (imperfection) in the hedge. I hope that helps, thanks,

#### valenski

##### New Member
Thanks very much!
You actually "create" a "unexpected strengthening" mannually. Can I understand it in this way?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
HI @valenski The XLS is illustrating a commodity forward term structure (i.e., set of forward prices) over time; there is nothing really automatic about any of it, there is no necessary curve. It can start in flat/contango/backwardation and shift to something else. The only automatic dynamic we might require is that, as maturity approaches, the futures price should converge toward the spot. For a December contract, when we get to November, the contract only has one month until maturity, so the forward price should be pretty close to the spot. Admittedly, my manual input to minus $0.10 is overly dramatic, but it was chosen to illustrate the unexpected basis strengthening; I could have used -$0.05 or -\$0.03.

I would revert to the principle being illustrated. If we use the futures contract to hedge spot price exposure and, if we maintain the hedge until exactly the point of contract expiration (delivery), the futures price will approach the zone of convergence such that we can expect a zero basis. (albeit, even when timing is perfect, there are other frictions such that in theory the forward converges to the spot price but in practice due to frictions the forward price converges to a zone around the spot price). In this pristine scenario, there should be neither expected strengthening/weakening of the basis and the hedge should perform almost perfectly.

But we are illustrating a realistic scenario where the contract is closed or rolled prior to maturity, such that there might be unexpected weakening or strengthening of the basis, which itself introduces volatility into the net outcome (i.e., an imperfect hedge). I hope that's helpful!

#### valenski

##### New Member
Thanks! This explanation is really helpful!

#### Harshit Chawla

##### New Member
Hi, can you help me understand how does a hedger know what to expect about the basis in the future? Is that because of the underlying assumption that futures curve will follow the linearity of the spot curve? Also, does this mean that every hedger will have a different exposure to basis because of their own assumptions about the direction of the future prices (both spot and futures)?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Harshit Chawla As basis risk cannot be eliminated, I do not think the hedger can be certain to expect a future basis. Put another way, basis risk is the fact that there always exists the possibility of unexpected basis strengthening/weakening, which is the deviation of realized basis from the expected basis.

However, I think the most typical (if academic) assumption is simply that the future price must converge to the spot price as the contract matures. This is tantamount to expecting a future basis of zero. A key reason this is often unrealistic is that a hedger often does not want to select maturity exactly on same date/month as the exposure because this may risk an obligation to deliver. So as Hull suggests, a good strategy is the use a contract maturity month after the hedged exposure; e.g., if commodity producer knows she will sell her stuff in May, maybe her short futures contract matures in June, so that she will be closing out that contract with < 1 month remaining.

The other approach, short of convergence, to your point, is to make an assumption about the behavior of the forward (price) term structure. One assumption is to assume it will remain static as an Unchanged Term Structure. Another (extreme) is to assume Realized Forwards: that the forward prices are predictive of future spot prices and the spot price shifts with a dynamically adjusting forward price curve. With in-between variations. I hope that's helpful!

#### danghara

##### Member
Subscriber
Hello David
in video you explained Unexpected weakening (strengthening) of basis risk in the scenario of contango.
could you help me to understand what will happen in the scenario of backwardation?

Last edited:

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @danghara I just added thee sheets to the XLS above (http://trtl.bz/2trHMzs): backward-baseline, backward-unexp strengthen, and backward-unexp weakening. Of course, outcome is the same: under unexpected strengthening, the net cost increases; under unexpected weakening, the net cost decreases. Maybe you can take a look at the updated XLS? My written description would be time-consuming and I need to get to other work (including outstanding forum questions) at the moment (Saturday evening!).

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