Basis risk

[surbhi.7310]

Hi David

I have a few questions:
Q1. Basis risk of a commodity = b= S0- F0
A farmer who, by taking short position in futures on his corn to hedge (his naturally long position) is benefited by which one from the 2 options below?
1. strengthening of the basis or weakening of the basis?
2. Flat futures curve going to contango or backwardation?


Q2. I have come across synthetic positions in various contexts throughout the FRM coursework. However, the concept is not clear. Can you please clarify how and why the synthetic positions are created in forwards, options, commodities ? Is there any fundamental general concept underlying it which can be recalled every time this crops up?


Q3. I read that option pricing can be calculated from binomial trees as well as BSM model option pricing method. What is the fundamental difference between the two and in which situations are these two used? Is it something to do with real world return expectations?

Also, can you direct me to some thread which summarizes the FRM Level 1 topics as per their testability and importance.

Thank you!
Surbhi

 

[David Harper CFA FRM]

Hi @surbhi.7310 Those are great questions! I will be very brief because they can be deeeeeep

1. b = S(0) - F(0) is the basis; basis risk can be defined as the variance of the basis, σ^(b). The farmer who is using a short hedge (short futures position) symbolically has a hedge portfolio of (+S - F) because (+) is the long exposure to spot market and (-) is the short futures position, and an unexpected strengthening of the basis is an unexpected Δb = Δ(+S - F) which is therefore a gain to the farmer. If a flat curve shifts to contango then increase in F is greater than increase in S (or decrease in F is less than decrease in S), which symbolically is [Δx in S - (Δx+ in F)]; i.e., the subtraction is greater --> weakening of the basis, such that contango will hurt the farmer (and backwardation will profit the farmer). Intuitively, backwardation is inversion in the forward curve with the forward price dropping (which is where the farmer has a short). Also, we can see that contango (backwardation) implies a weakening (strengthening) of the basis. I've often been tempted to define a "shift toward contango" as weakening of the basis, in fact.
2. My favorite resource on this is Neftci https://forum.bionicturtle.com/reso...ancial-engineering-2nd-ed-by-salih-neftci.18/ who defines a synthetic as liquid, replicating portfolio that matches the cash flows of the original instrument. So (because I try not too be too original) I would define a synthetic as a replication, or a portfolio that replicates cash flows. In the FRM, synthetic tends to connote (but not necessarily imply) an unfunded replication. For example, we can synthesize the ownership of equity shares with a portfolio of (long call options funded by written calls) such that the options have a similar payoff profile. In credit, the classic example is writing a CDS instead of investing in the underlying loan; i.e., instead of funding the loan, we invest into a risk-free asset and write a CDS (which is technically incomplete ...)
3. Given the preexisting discussions already on the forum (search is in the upper right), I will be super brief. BSM is the elegant solution to a specific, restrictive set of assumptions including continuous rebalancing (ie., calculus) and a lognormal price distribtuion. So we might think of it as a very elegant but narrow solution to an equation. Binomial is the future. Why would I say that? Because it's a tedious, discrete but intuitive simulation of future possible asset price dynamics (ideal for code!). Binomial is like an erector set: you can build your assumptions to your liking. There is just one flavor (variant) of the binomial called Cox Ross Rubinstein which converges to the BSM solution, because it resembles BSM assumptions. So from the perspective of allowable assumptions, the binomial is (way) super-set. But binomial is what you need when you need to violate the BSM assumptions, which is often. I hope that is a good start, thanks!

 

[surbhi.7310]

Thank you David for the great explanations!

 

[jessicawhite999]

So many thanks, that what I am looking for.

 

[jayan7ec]

Hello @David Harper CFA FRM , I couldn't get a clear picture of the farmer benefitting from a strengthening of basis when she has a short position in futures, because when you say strengthening, spot price increases. Doesn't that mean it is advantageous for a long position in futures (because the farmer will be able to buy at a lower rate and then sell at the higher spot rate). I may be wrong here but it would be really helpful if you could help me with an example using real numbers, like, may be the futures price is $10. Thanks in advance

 

[David Harper CFA FRM]

Hi @jayan7ec I recently recorded a youtube video on this exact topic, please see below. But here is a simple example with $10.00. But please keep in mind that Hull's point is about the unexpected component of basis change. Assume:

• Today: spot, S(March) = $8.00 and F(Dec) $10.00, so basis = 8 - 10 = -$2.00. Farmer plans to sell 5,000 units in November, so employs a short hedge; i.e., short futures contract. Note farmer is hedging November sale with December contract
• Consider scenarios when we get to November
  • Convergence leads to same net result: If spot converges to futures prices, so that S(Nov) = F(Dec) = $10.00, then basis improves to zero but such convergence was expected. There is here no unexpected weakening/strengthening. Farmer sells 5,000 units at $10.00, for $50,000. If spot converges to futures price, so that S(Nov) = F(Dec) = $8.00, farmer only collects $8.00 * 5,000 = $40,000, but gains $2.00 * 5,000 = 10,000 on futures contract, for net receipt of 50,000. If S = F = $12,000, same net result as $60,000 collected on sale of commodity is reduced by $10,000 loss on futures contract. The basis improved from -2.00 to zero but it was expected. Any convergence of spot and futures will lead to same result of net collected = +$50,000
  • Now consider unexpected strengthening: S(Nov) = $10.00 but F(Dec) = $9.00, so that basis is +$1.00 versus zero expected; i.e., unexpected strengthening of +$1.00. Farmer is better off (versus the expected $50.000): $50,000 is collected on sale of commodity plus $5,000 gain on futures = $55.000 (versus 50,000)
  • Similarly, you can imagine an unexpected weakening that will make the farmer worse off; e.g., S(Nov) = $8.00 and F(Dec) = $9.00 --> $45,000

In summary, the short hedger is long the commodity and short the futures contract. An unexpected strengthening implies the spot price increases by more than the futures price, or that the spot price decreases by less than the futures price, relative to expectations. This is favorable to the short hedger.

Here is my video, I hope this helps!

 

[jayan7ec]

Sorry @David Harper CFA FRM , i am still confused. I couldn't understand one piece of information here. If i am the farmer and i have hedged my produce using a short futures position at $10 F(Dec) contract during the month of march, whatever the spot or futures price is in Nov or Dec, i will have to sell my produce at $50,000 (5000*$10) itself, as i have an obligation to fulfill my contract. I couldnt understand the statement "$50,000 is collected on sale of commodity plus $5,000 gain on futures = $55.000" mentioned above, since i believe that you calculated the $50,000 by multiplying S(Nov) with the quantity. Shouldnt it be F(Dec)*Quantity=$10*5000 that I already shorted in March? I also couldnt understand how a change in the futures price in Nov or Dec will affect my profit, as i have already employed a short futures contract in March.

 

[David Harper CFA FRM]

Hi @jayan7ec did you view the video? I ask because it is somewhat detailed, speaks directly to this issue, it may help clarify the confusion. First, can we set aside the Nov/Dec difference: we could alternatively extend the scenario to December. I selected a December futures contract that is closed out in November (one month prior to maturity); most futures contract do not go all to way to maturity (delivery), they are closed out. So let me re-cap the $55,000 scenario but with a focus just on the hedge basics because they hedge basics need to first be understood, or the unexpected strengthening will not make sense:

• Today is March 2018. Say the spot price is $8.00 per unit of the commodity and a December futures contract has a price of $10.00. We are a producer (farmer) with plans to sell 5,000 units of the commodity in November. To put on the hedge, the farmer employs a short hedge by taking a short position in the December futures contract.
• Go forward to November. The spot price has increased to $10.00 (the farmer maybe regrets the hedge, it was not necessary if she knew the spot price would increase!). The farmer sells the commodity at the November spot price.; this is a separate transaction from the future contract. The farmer collects 5,000 * $10.00 = $50,000 for the sale of the commodity at the spot price in November. As a separate transaction, the farmer closes-out the futures contract. It is the same December futures contract, but now it has only one month to maturity (versus 11 months when she entered the contract). If the futures price is $9.00, then her profit is ($10 - 9)* 5,000 = +$5,000; she is better off due to the unexpected strengthening of the basis, where she expected zero basis but basis was +$1.00 when she closed out. If the December futures price, in November, instead is $11.00, her loss is ($10 - 11) * 5,000 = -$5,000; she is worse off due to the unexpected weakening of the basis, where she expected zero basis but basis was +$-1.00 when she closed out.

You can change the November assumptions. But there are two transactions: the commodity will be sold at the then-prevailing (November) spot price; there is no contract with regard to this planned sale at the future spot price. Separately, the short futures contract is entered in March at the Nov (Dec) futures price, then it will produce a gain or loss depending on the futures price at the time of close out (or maturity); the gain/loss on the short futures price is equal to F(March, December) - F(November, December) where F(March) is the futures price in March for the contract with December delivery. Thanks,

 

[jayan7ec]

Hi @jayan7ec did you view the video? I ask because it is somewhat detailed, speaks directly to this issue, it may help clarify the confusion. First, can we set aside the Nov/Dec difference: we could alternatively extend the scenario to December. I selected a December futures contract that is closed out in November (one month prior to maturity); most futures contract do not go all to way to maturity (delivery), they are closed out. So let me re-cap the $55,000 scenario but with a focus just on the hedge basics because they hedge basics need to first be understood, or the unexpected strengthening will not make sense:

• Today is March 2018. Say the spot price is $8.00 per unit of the commodity and a December futures contract has a price of $10.00. We are a producer (farmer) with plans to sell 5,000 units of the commodity in November. To put on the hedge, the farmer employs a short hedge by taking a short position in the December futures contract.
• Go forward to November. The spot price has increased to $10.00 (the farmer maybe regrets the hedge, it was not necessary if she knew the spot price would increase!). The farmer sells the commodity at the November spot price.; this is a separate transaction from the future contract. The farmer collects 5,000 * $10.00 = $50,000 for the sale of the commodity at the spot price in November. As a separate transaction, the farmer closes-out the futures contract. It is the same December futures contract, but now it has only one month to maturity (versus 11 months when she entered the contract). If the futures price is $9.00, then her profit is ($10 - 9)* 5,000 = +$5,000; she is better off due to the unexpected strengthening of the basis, where she expected zero basis but basis was +$1.00 when she closed out. If the December futures price, in November, instead is $11.00, her loss is ($10 - 11) * 5,000 = -$5,000; she is worse off due to the unexpected weakening of the basis, where she expected zero basis but basis was +$-1.00 when she closed out.

You can change the November assumptions. But there are two transactions: the commodity will be sold at the then-prevailing (November) spot price; there is no contract with regard to this planned sale at the future spot price. Separately, the short futures contract is entered in March at the Nov (Dec) futures price, then it will produce a gain or loss depending on the futures price at the time of close out (or maturity); the gain/loss on the short futures price is equal to F(March, December) - F(November, December) where F(March) is the futures price in March for the contract with December delivery. Thanks,

Thanks a ton @David Harper CFA FRM , this cleared all my doubts.