Nagging question around Basis Risk

[sridhar]

David:

Couple of nagging ones (for me):

1. Does basis risk apply only in a cross-hedge? When the hedging asset (e.g. crude oil) is different from the underlying asset (e.g. jet fuel?)

2. I am a little confused about some of the prices used in the illustration of the basis risk. May I draw your attention to page 11 of the Mkt Risk Study Notes? Take a look at the third graphic titled "Weakening of Basis:"

Here we have 4 prices:

$4.00-- the Spot Price of asset today (e.g. Sep 1, 2008) -- Let's call this price S-1

$3.80-- the future price of asset today, say maturity on March 1, 2009. Let's call this price F-1

Moving on:

$4.20 -- the Spot of price on the maturity date, March 1, 2009 -- Call this S-2

$4.10 -- Future price of the hedge -- call this F-2

From your notes, I do understand that a weakening of the basis has occurred if:

(F-2 - F-1) > (S-2 - S-1), i.e. the futures price has increased at a faster rate than the spot price.

My questions here -- Let's assume I take a short hedge position on Sept 1, 2008.

2.1: I don't really understand what F-2 (the $4.10) price is? What is F-2 the price of? F1 is the price at which I am willing to sell the asset on March 1, 2009.

March 1, 2009 arrives. The "future" has arrived. And now the spot price of the asset is S2, i.e. 4.20. I get this. But what is F-2, $4.10. What "future" does F-2 refer to? We are already at the "future", i.e. March 1, 2009.

Please help me make sense out of this. The only sense I could make out of it is that F-2 is the spot price of the hedged asset -- and it can be different from S-2 only if the hedge is a cross-hedge.


Summary of the above ramble:
Do all the four prices refer to the same underlying asset?

Can you just indulge me and mark-off which price relates to which asset (e.g. underlying or hedge)

What is the difference between F-1 and F-2?

Sorry for this long post...Eagerly awaiting your response.

--sridhar

 

[David Harper CFA FRM]

Hi sridhar,

1. No, basis risk attaches to every hedge; e.g., a CDS carries basis risk, even exchange-traded commodity futures bear basis risk as starkly illustrated by recent lack of convergence in commodities like wheat. It is a matter of degrees; a cross-hedge or futures contract (on standardized exchange) implies high basis risk while an OTC forward (tailored to the need) implies lower basis risk, but it remains nonetheless. The hedging instrument is *always* not identical to the underlying, but in a cross hedge the difference is obvious. The classic (and perhaps most testable) view is:

Exchange-traded future: high basis risk (i.e., you must use standardized features), high liquidity, low/no counterparty risk
OTC forward: low basis risk (i.e., you design your terms), low liquidity (not standardized), high counterparty risk


2. The green are spot prices; e.g., spot price of corn. The blue are forward prices; e.g., forward price of corn.
If today (T0) is September 2008, then spot = $4 and forward (let's just say, for a Sept 2009 delivery) = $4.20

Now go into future, to March 1, 2009:
Spot = $4.20, and
Forward price (for Sept 2009 delivery) = $4.10
(So, the 4.10 is just the latest forward price. Like the spot price, the forward price is changing over time)

So, the green is spot price of the underling over time
The blue is forward price of the hedge instrument over time

And please note, per Hull, it is not the strengthening or weakening per se that hurts hedgers, it is unexpected weakening/strengthening that helps/hurts the hedger.

I hope this explains...

David

 

[sridhar]

Thanks David. Your example -- I understand. If you fast forward to the delivery date -- Sept 2009 -- the maturity date -- will the spot price and the futures prices converge...The "futures" is now -- so even calling it a futures price is awkward. Correct? How should one think about this -- what does the green and blue circles look like on the maturity date. They fuse into one, i.e. the spot price on the maturity date?

--sridhar

 

[ahnnecabiles]

Hi David,

I am also posting a question on this, because same as Sridhar, I also have some confusions on basis risk.

I thought that basis risk is only prevalent on futures. Say you want to hedge the price of corn in a futures exchange. You are buying corn forward, but then before the delivery date you have to close your position so you can buy the corn spot from the market and use whatever you gain or deduct whatever you lose from the exchange to reflect your hedged price of the corn. In this case, if there is an unexpected weakening of the basis (F1-S1>F2-S2), you have gained from that, (instead of a zero gain as the gain from the spot will just offset the loss from the futures if the spreads are just the same), since you will be buying the corn at a lower spot price and thus, your expected "difference" (S1-S2) from buying the corn spot will be lower than your expected gain (F1-F2) from the futures.

Now, in OTC forwards, you cannot be facing these types of unexpected gain/loss because you will be buying the corn directly from your counterparty. Thus, whatever the spot price on the delivery date, you will have nothing to unexpectedly gain or lose because your price is hedged from day zero, no unexpected weakening or strengthening of the basis can affect your transaction. Thus, any convergence or divergence from spot or futures price does not affect your position. Is my understanding correct?

Thanks so much.

 

[David Harper CFA FRM]

Hi Chinquee,

I like your characterization of the unexpected strengthening. Please note I wrote, "Every hedge carries basis risk." In your OTC forward example, there appears to be no hedge. In which case, i agree the idea of basis risk doesn't apply: the counterparties are simply agreeing to a purchase/sale in the future. In your example, the spot price is irrelevant. (although strictly speaking, I'm not even sure basis risk is totally gone to the extent your contract mis-specifies your future need, there may be some basis risk. Arguably, if your futures contract turns out to be incomplete and you need to compensate in the cash market that feels like a basis risk but...)

The basis risk arises when there is an underlying exposure (with a spot price) PLUS a hedging instrument (the forward or futures position). The notion that every hedge carries basis risk is due to the fact that no hedge is perfect; but this depends on both underlying spot exposure and the use of a hedge. We can use the formula, I think: basis = futures - spot (or vice versa), so there must a hedge instrument plus exposure to the cash market.

Let me put another way, assume you expect to buy jet fuel next year (chosen b/c it has no futures contracts). In one approach, you enter an OTC forward with the jet fuel maker to buy the jet fuel next year (analogy to yours, let's agree no hedge = no basis). In another, your jet fuel maker does not trade like this. So, you enter into an OTC forward with some other counterparty to HEDGE. Now you have hedged, now you have some basis risk, albeit less than using heating oil futures but some nonetheless...

All of that said, don't get me wrong, from an exam standpoint, as i wrote above: futures contract: high basis risk, high liquidity; forward contract: low liquidity, low/little basis risk which is nearer to none!

David

 

[ahnnecabiles]

Thanks for your enlightenment David!

 

[nvallabh]

Now that we are on basis risk:

I understand Futures contracts have higher (divergence) basis risk due to difference in the underlying asset but higher liquidity and ability to close out positions earlier.

I understand Fwd contracts have less basis (divergence) risk but lower liquidity and higher counterparty risk

What I am struggling with is understanding if a position necessarily always improves or weakens per se? Is it true that basis (divergence) risk has many different implications: profitable sometimes, losses sometimes, and no gain/loss just lose the premium.

So let’s use this scenario for example:

We enter into a short futures hedge on corn for purposes of hedging an ethanol sale in the future.

If spot prices on ethanol tanks by 50 cents but corn prices tank 80 cents, what happens?

If spot prices on ethanol shoot up 50 cents and spot corn (futures) shoot up 40 cents, then our hedge wasn’t effective or it’s worthless right?

If spot prices on ethanol stays the same and futures corn prices tanks, what happens?

Also can you have negative basis risk in this scenario?

And does the 'divergence risk' I reference in my questions accurately depict the basis risk in your opinion?

Thanks!

 

[David Harper CFA FRM]

nvallabh,

That's a good example, thanks. (Okay if we use ethanol futures contract to hedge?)

Assume spot ethanol = $2.00
Assume futures ethanol = $2.20
Basis (S1 - F1) = $2 - $2.20 = -$0.20

The key is EXPECTED basis. Let's assume, to keep in simple, we expect 100% correlation btwn spot and futures. In other words, we expect an unchanged basis, from -0.20 to -0.20 in the future.

We are short the commodity and hedging with short futures. If there is no unexpected basis strengthening/weakening, we will get paid a total price of $2.00 regardless (i.e., current futures of $2.20 plus future basis of -.20 = $2.00). If our 1:1 assumption holds, we are locking in $2 sale proceeds

"If spot prices on ethanol tanks by 50 cents but corn prices tank 80 cents, what happens?"
Ethanol Spot S2 = $1.50
Ethanol Futures F2 = $1.40
Basis (S2 - F2) = $0.10
In this case, there is an unexpected strengthening of basis (from -.2 to +.1); our position (as short hedger) improves:
Selling at 1.50 but profit on futures +.80 = total $2.30 (we are 0.30 better)

"If spot prices on ethanol shoot up 50 cents and spot corn (futures) shoot up 40 cents, then our hedge wasn’t effective or it’s worthless right? "
Ethanol Spot S2 = $2.50
Ethanol Futures F2 = $2.60
Basis (S2 - F2) = -$0.10
In this case, there is also an unexpected strengthening of basis (from -.2 to -.1); our position (as short hedger) improves:
Selling at 2.50 but loss on futures -.40 = total $2.10 (we are 0.10 better than $2.00)

Now a losing scenario:
Ethanol Spot S2 = $2.50
Ethanol Futures F2 = $3.00
Basis (S2 - F2) = -$.50
Now an UNEXPECTED WEAKENING (from -.2 to -.5) means the short hedger loses:
Selling at $2.50 but a loss on futures of -.80 = $1.70

Hope that helps, I think "divergence risk" is pretty near to what we are talking about with basis risk. To the extent it's about the future basis. For example, if the spot and futures converge to zero, that's a future basis of 0. The hedge can be perfect against that except it requires both (i) convergence in price and (2) perfect timing.

David

 

[nvallabh]

David, thanks for the help on basis risk. That was really the first time I used your Forum and it helped immensely. The other candidates' questions got me thinking, so I posed my own question, and then you were able to help clear up my thinking. Now I can check that box with confidence. Very productive!