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# Basis Risk Strengthening/Weaking

#### BlackSwan

##### New Member
In GARP's FMP book pages 88-89 the basis risk is being explained. It talks about the strengthening (increase) of the basis and weakening (decrease) of the basis. It defines the basis as:
Basis = Spot Price of asset to be hedged - Futures Price of contract used
It later states:
"Note the basis risk can lead to an improvement or a worsening of a hedger's position. Consider a short hedge. If the basis strengthens (increases) unexpectedly, the hedger's position improves; if the basis weakend (decreases) unexpectedly the hedger's position worsens. For a long hedge, the reverse holds"

I am confused on how the hedger's position improves/worsens from my thought process I figured the short hedger's position worsens when the basis strengthens and improves when it weakens.

The book uses as an example S1 = $2.50 F1 =$2.20 and S2=$2.00 and F2=$1.90
Therefore b1=S1-F1=0.30 and b2=S2-F2=0.10

I am thinking if I am in a short hedge, I agree to sell asset X at t2 for $2.20 (F1). So if the basis weakens from 0.30 to 0.10 the spot price at S2 is$2.00. So at t2 I can buy asset X for $2.00 and sell for$2.20 realizing a 0.20 profit. How am I thinking about this wrongly? They mention the effective price for the asset is S2 + F1 - F2 = F1 + b2 and for short hedge the profit is F1-F2 and for long hedge the loss is F1-F2 but I still do not follow how the strengthening/weaking of the basis improves/worsens a short/long hedger's position. Anyone care to explain in a different way? Thank you #### Alex_1 ##### Active Member Hi @BlackSwan , David explains in the following link why "...the unexpected basis strengthening (weakening) that creates a profit (loss)..." https://www.bionicturtle.com/forum/threads/strengthening-of-the-basis.5528/ And in the Practice Question 03.10. (from Hull), the answer is "The basis is the amount by which the spot price exceeds the future price. A short hedger is long the asset and short futures contracts. The value of his or her position therefore improves as the basis increases. Similarly it worsens as the basis decreases." I somehow memorized that if the basis increases ("strengthens") then this has to mean that the spot position increased with a higher amount than the future position did, e.g. spot Jan. = 30 USD, future Jan. = 40 USD; spot Feb. = 40 USD, future Feb. = 48 USD. This means that the basis for Jan. = -10, however the basis for Feb. = -8, so the basis increased ("strengthened") by 2 USD. A "short hedge" = long spot + short futures contract = S - F. For Jan. this would give us a loss of 10 USD, but for February a loss of 8 USD, which means that the position of the short hedger has improved. I am not sure the explanation makes sense, but to my it somehow did. Best regards, Alex #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Thanks @Alex ! ... and once understood, to me, the challenge is storing the concept in the memory bank Here's how I do it, fwiw: • B = S - F (i.e., basis = spot - futures). I remember the "S" comes before the F by noticing BaSis, as a mnemonic. So first I just want to make sure I've got the typical definition, B = S - F. Then it's actually pretty easy: • A short hedge is long the spot and short the futures contract, so the short hedge is +S - F. Therefore, the short hedge profits on anything that increases the basis, B = +(S - F) because the basis, (S-F), "matches" the positions of the short hedge which is long the spot, +S, and short the futures, -F. This also reminds us that basis can increase due to an increase in spot and/or a decrease in futures price, or futures increasing less than spot, or futures decreasing more than spot • The long hedge is short the spot and long the futures, so the long hedge profits on a weakening of the basis, which is -B = -(S - F); i.e., gain on the long futures and/or drop in the spot. So, I use the +/- signs to remember. -(S - F) corresponds to the long hedge's position: short the spot, -S, and long the futures, +F. Maybe that helps. And, the newly assigned IFM chapter 7 (Hedging with futures..) introduces "long the basis" and "short the basis" which is the same way of looking at it: • Short hedger = Long the basis = +B = +(S - F) • Long hedger = short the basis = -B = -(S - F) Last edited: #### BlackSwan ##### New Member Thank you for both of your responses. And I now understand that the basis must converge to zero over time So you will know based on the starting spot/future prices if the basis will be weakening or strengthening for your position #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Yes @BlackSwan exactly as your first version suggested, if you the hedge begins in contango (S < F), then convergence implies a strengthening in basis; and initial inversion/backwardation (S > F) going toward convergence implies weakening. It is a great way to look at it! e.g., contango (backwardation) --> expects strengthening (weakening). However, it's not a "free lunch:" Hull's keyword is unexpected strengthening/weakening as the hedge (i) realistically does not get to stay on exactly until convergence and (ii) it is convergence to a "zone" anyhow due to frictions, not an exact zero. So, the convergence can be parsed into an expected (i.e., toward zero) and unexpected component. Thanks, #### Stuti ##### Member Hi David, Can we also define the basis risk to occur because of location to deliver and the quality of the asset? it then gets termed as location basis risk or quality basis risk? stuti #### gargi.adhikari ##### Active Member Thanks @Alex ! ... and once understood, to me, the challenge is storing the concept in the memory bank Here's how I do it, fwiw: • B = S - F (i.e., basis = spot - futures). I remember the "S" comes before the F by noticing BaSis, as a mnemonic. So first I just want to make sure I've got the typical definition, B = S - F. Then it's actually pretty easy: • A short hedge is long the spot and short the futures contract, so the short hedge is +S - F. Therefore, the short hedge profits on anything that increases the basis, B = +(S - F) because the basis, (S-F), "matches" the positions of the short hedge which is long the spot, +S, and short the futures, -F. This also reminds us that basis can increase due to an increase in spot and/or a decrease in futures price, or futures increasing less than spot, or futures decreasing more than spot • The long hedge is short the spot and long the futures, so the long hedge profits on a weakening of the basis, which is -B = -(S - F); i.e., gain on the long futures and/or drop in the spot. So, I use the +/- signs to remember. -(S - F) corresponds to the long hedge's position: short the spot, -S, and long the futures, +F. Maybe that helps. And, the newly assigned IFM chapter 7 (Hedging with futures..) introduces "long the basis" and "short the basis" which is the same way of looking at it: • Short hedger = Long the basis = +B = +(S - F) • Long hedger = short the basis = -B = -(S - F) @David Harper CFA FRM A Long Hedge = Short Spot + Long Futures ( and vice versa) This however does not seem to align with the example in the Learning Spreadsheet 'T3.a_2012_XLS_bundle_HullCh1-3_"....in the Learning spreadsheet a Long Hedge has been illustrated in both scenarios of a Basis Strengthening and Weakening. And in the example of the Learning spreadsheet, it seems both the Spot and the Futures are Long positions ...am I missing a point..? Much gratitude for all the help.. #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Hi @gargi.adhikari Hello! Below is an instance of the XLS. As labeled, it does intend to illustrate a long hedge because it returns a gain when the futures price increases (ie, long hedge = long the futures contract which is hedging). If this long futures position (which profits on a futures price increase) is indeed a hedge, then (working backwards) it should be hedging against an underlying exposure that experiences losses on a (spot) price increase, and this is reflected in the assumption of a company that plans to purchase copper in the future at the prevailing but currently unknown future spot price. This company will buy buying the spot in the future at an unknown price, but that's actually "short the spot price" because, well, you don't want the price of something you are going to buy to rise! So this is also called a "buying hedge" or its more savvy to say this trade is "short the basis" because this position profits from (unexpected) weakening of the basis. (As illustrated below where the net cost is 48,750 rather than 50,000). I think I see your point: the company will buy buying the copper (spot) in the future, so it's it long the spot. It is interesting; with respect to only the underlying exposure: • If instead this company was purchasing Copper in the future (September) at a predetermined price, say2.00, then what's the risk? The risk is that the spot price drops below $2.00. In this situation, the company is long the spot such that its hedge is short futures position (ie, short hedge; aka, long the basis). That's not our typical "exam assumption" however. Our typical or classic scenario is: • A company that will be purchasing Copper in the future (September at the future (unknown) spot price, in which case the risk is a risk that the spot price increases, and the long hedge is warranted; aka, short the basis. I hope that clarifies. #### gargi.adhikari ##### Active Member @David Harper CFA FRM Much gratitude. Have a follow up question though...i guess ...the point am struggling with .... So a Short Hedge = a Short Position on the Futures Contract and a Long Hedge = a Long Position on the Futures Contract But a Short Hedge can be used with either a Long Spot or a Short Spot right..? or does a Short Hedge is only used with a Long Spot..? Similarly, a Long Hedge can be used with either a Long Spot or a Short Spot right..? or does a Long Hedge is only used with a Short Spot..? #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Hi @gargi.adhikari No worries, this has proven to be a bit confusing. I like to remind folks that basis risk requires two positions. I don't have basis risk if I buy a stock (one position) or plan to purchase a commodity in the future (one exposure to the cash market). I create basis risk when I trade for the purpose of hedging the (underlying or primary) exposure; e.g., when I buy a put option to hedge the stock, or take a long futures position to hedge the spot (cash commodity) exposure. So, hedge and basis risk by definition imply two positions, even if the underlying exposure is more implicit to a risk factor than so explicit as a trade. Given this context .... • A short hedge is also called a selling hedge and is simply a short futures contract position that is performing a hedge. We don't require the underlying exposure to be long/short, but the most obvious exposure (that the short hedge is hedging) is the classic example of a farmer who plans to sell in the future and the then-prevailing (but currently unknown) spot price. • The long hedge is a also called a buying hedge and is any long futures contract position that is performance a hedge. The classic example is an airline who intends to purchase fuel in the future an the future spot price (currently unknown). However, consider Metallgesellschaft (https://en.wikipedia.org/wiki/Metallgesellschaft), a longtime FRM case study. Their underling exposure was long-term written (sold or short) oil contracts to customers. They had promised to sell oil in the future at a predetermined price, such that their underyling price exposure (risk) was to price increases (because then they'd be buying high but selling low to customers per a promise). Because the underyling exposure was to oil spot price increases, the hedge was a long hedge (ie, buying hedge or buying futures contracts). Nevermind the liquid (daily margin-calling) futures contracts were short-term and but the illiquid exposures were long term (basis risk). It was a long hedge because the futures where "long" and they meant to "hedge." I hope that helps! #### gargi.adhikari ##### Active Member @David Harper CFA FRM Thank you Thank you Thank you for the elaborate explanation....clear as the sky now the guess you were referring to the 2 positions in the context of the Weakening and Strengthening of the Basis .... the above clarifies everything.... #### gargi.adhikari ##### Active Member @David Harper CFA FRM Hi David, I have a followup question on this topic :- In the scenario that the Basis strengthens due to an increase in the Spot Price( instead of the Futures Price going down), then in that case how is still favorable for Shorting the Futures and in turn a Short Hedge..? Also, for Basis Risk does the Long and Short positions have to be on the same underlying asset..? or can the hedge be with a different asset..? #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Hi @gargi.adhikari if the basis strenghtens unexpectedly due to a spot price increase the classic short hedger profits because she is long the underlying (aka, cash) commodity so she realizes this gain. It can be understood symbolically with Hull's definition of basis which is (B)asis = +S(pot) - (F)utures; as above, the short hedger is "long the basis" which is buying (+S - F). This quantity increases with an increase in (S) or a decrease in (F). Consider a simple example. Assume today the commodity price is$8.00 with a carry cost of 6% such that expected spot price in one year will be $8.00*exp(6%) ~=$8.50. Assume further that futures price, F(1) = E[S(1)] = $8.50; ie, the one year futures price equals the expected spot price in one year (aka, lack of any normal backwardation). Our classic short hedger is a commodity owner who plans to sell the commodity in one year, and who expects to receive$8.50 in one year for selling (i.e., plans to sell at cost without any profit), but decides to hedge this price risk with a short futures position. Today (T0) the basis = $8.00 - 8.50 = -$0.50, but the hedger expects convergence to basis of zero in one year when she expects spot and futures to both converge to $8.50. There is expected basis strengthening of +0.50. • If the spot price doesn't change over the year, but the spot and futures still converge (as expected), the hedge will work: the commodity will only be sold for$8.00 but the short futures position profits on the futures drop from $8.50 to$8.00. The $0.50 loss on the spot market ($8.50 cost to carry but sold for only $8.00) is hedged by the 0.50 gain on the futures contract • To your scenario, say the spot price jumps unexpectedly to$10.00. But importantly the basis still converges such that expected basis strengthening still happens! Now the commodity is sold for $10.00, which is profit of +$1.50 (over the $8.50 in cumulative cost of carry), but the future returns a loss of$1.50 ($8.50 to$10.00 in a short position).
• Now imagine the basis strengthens as expected by +$0.50 but there is additional unexpected basis strengthening of$0.25. Maybe spot goes to $9.00 but futures price only goes to$8.75. The basis goes from -0.50 (i.e., 8.00 - 8.50 today) to +0.25 (i.e., $9.00 - 8.75). That's a profit on the commodity of$0.50 but only a loss of $.25 on the short futures position for a net profit of$0.25.
Hopefully you can see that "short hedge" is a short futures, as we said above, but classically it is hedging a long underlying (cash or spot) position which, by itself, profits if the spot price increases. There is a key difference here between expected basis strengthening/weakening and unexpected. Re your question about the same asset: no they do not need to be the same asset. If they are different, it is called a cross-hedge by Hull:
"3.4 CROSS HEDGING: In Examples 3.1 and 3.2, the asset underlying the futures contract was the same as the asset whose price is being hedged. Cross hedging occurs when the two assets are different. Consider, for example, an airline that is concerned about the future price of jet fuel. Because jet fuel futures are not actively traded, it might choose to use heating oil futures contracts to hedge its exposure." -- Hull, John C. Options, Futures, and Other Derivatives (9th Edition) (Page 58). Prentice Hall. Kindle Edition.

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