Thai Investment Consultant Licensing Exams - P3 - หลักสูตรความรู้เกี่ยวกับตราสารที่มีความซับซ้อน : สัญญาซื้อขายล่วงหน้า - [11]

Let me analyze this multiple choice question about the "basis" in futures contracts.

The question is in Thai, so let me translate it first: "Which of the following options is correct regarding the basis of futures contracts?"

Now, let's examine each option:

a. "เบสิสคือผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง (Spot price)" - This translates to "Basis is the difference between the futures contract price and the spot price of the underlying asset." This is the correct definition of basis in futures contracts. Basis = Futures price - Spot price.

b. "หากราคาสัญญาฟิวเจอร์สเพิ่มขึ้นมากกว่าราคาสินทรัพย์อ้างอิง (Spot price) จะทำให้เบสิสกว้างขึ้น" - This translates to "If the futures contract price increases more than the spot price of the underlying asset, it will widen the basis." This is correct. If the futures price increases more than the spot price, the difference (basis) will widen.

c. "หากอัตราจ่ายเงินปันผลเพิ่มขึ้นในขณะที่ปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สหุ้นสามัญกว้างขึ้น" - This translates to "If the dividend yield increases while other factors remain constant, it will widen the basis of common stock futures contracts."

Let's analyze this. For stock futures, the theoretical fair value is calculated as: Futures Price = Spot Price * (1 + r - d) Where r is the risk-free interest rate and d is the dividend yield.

So, if the dividend yield (d) increases, the futures price should decrease, not increase. This would actually narrow the basis (Futures Price - Spot Price), not widen it. So this statement is incorrect.

d. "หากต้นทุนค่าขนส่งและค่าเก็บรักษาลดลงโดยปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สินค้าเกษตรกว้างขึ้น" - This translates to "If transportation and storage costs decrease while other factors remain constant, it will widen the basis of agricultural futures contracts."

For commodity futures, the theoretical fair value is: Futures Price = Spot Price * (1 + r + s) Where r is the risk-free interest rate and s represents storage costs.

If storage costs decrease, the futures price should decrease, which would narrow the basis, not widen it. So this statement is also incorrect.

Looking at each option: a. This is a correct definition of basis. b. This is correct - if futures price rises more than spot price, basis widens. c. This is incorrect - increasing dividend yield would narrow the basis. d. This is incorrect - decreasing storage costs would narrow the basis.

So among these options, a and b appear to be correct. Wait - but I'm asked to give one correct answer.

Let me double-check my understanding of basis. The basis in futures markets is defined as: Basis = Spot Price - Futures Price

CORRECTION: I made a mistake in my original definition. Basis is typically defined as Spot Price - Futures Price (not Futures - Spot as I stated initially).

So re-analyzing the options: a. "Basis is the difference between the futures contract price and the spot price of the underlying asset." This is partially correct, but the specific direction matters. The proper definition is Basis = Spot Price - Futures Price. b. "If the futures contract price increases more than the spot price of the underlying asset, it will widen the basis." If Basis = Spot - Futures, then if futures increase more than spot, the basis would become more negative, which could be interpreted as "widening" in the negative direction. c. "If the dividend yield increases while other factors remain constant, it will widen the basis of common stock futures contracts." Higher dividends should make futures prices lower relative to spot, which would make Basis = Spot - Futures more positive, widening it. This could be correct. d. "If transportation and storage costs decrease while other factors remain constant, it will widen the basis of agricultural futures contracts." Lower storage costs should make futures prices lower, which would make Basis = Spot - Futures more positive, widening it. This could be correct.

I'm getting confused about the definition of basis and its direction. Let me verify the standard definition again.

Actually, there are two conventions for defining basis:

1. Basis = Spot Price - Futures Price (commonly used in commodities)
2. Basis = Futures Price - Spot Price (sometimes used in financial futures)

In commodity markets, basis is typically Spot - Futures. In this context:

• When spot price rises relative to futures, basis becomes more positive (widens)
• When futures price rises relative to spot, basis becomes more negative (narrows)

In financial markets, basis might be defined as Futures - Spot. In this context:

• When futures price rises relative to spot, basis becomes more positive (widens)
• When spot price rises relative to futures, basis becomes more negative (narrows)

Given that this question appears to be about financial futures (mentioning stock futures), let's assume Basis = Futures - Spot.

Reanalyzing: a. "Basis is the difference between the futures contract price and the spot price of the underlying asset." This is correct if using the financial futures definition. b. "If the futures contract price increases more than the spot price of the underlying asset, it will widen the basis." This is correct with Basis = Futures - Spot. c. "If the dividend yield increases while other factors remain constant, it will widen the basis of common stock futures contracts." With higher dividends, futures price decreases relative to spot, which would narrow the basis if Basis = Futures - Spot. d. "If transportation and storage costs decrease while other factors remain constant, it will widen the basis of agricultural futures contracts." With lower storage costs, futures price decreases relative to spot, which would narrow the basis if Basis = Futures - Spot.

I need to be careful about which convention is being used. Let me try to infer from the context of the question.

Thinking about option c, for stock futures: Futures Price = Spot Price * (1 + r - d)

If dividend yield (d) increases:

• Futures price decreases relative to spot
• If Basis = Futures - Spot, then basis narrows (decreases)
• If Basis = Spot - Futures, then basis widens (increases)

Option c says "if dividend yield increases, basis widens," which aligns with the Basis = Spot - Futures definition.

Similarly for option d, if storage costs decrease:

• Futures price decreases relative to spot
• If Basis = Futures - Spot, then basis narrows
• If Basis = Spot - Futures, then basis widens

Option d says "if storage costs decrease, basis widens," which again aligns with Basis = Spot - Futures.

So it seems the question is using the convention Basis = Spot - Futures, which is commonly used in commodity markets.

But then option a defines basis as the difference between futures price and spot price, which contradicts this inference.

Let me look more closely at option a: "Basis is the difference between futures contract price and spot price."

This could be interpreted either way:

• Basis = Futures - Spot
• Basis = Spot - Futures

It doesn't specifically say which is subtracted from which.

Given the ambiguity, I need to analyze each option on its own merits:

a. "Basis is the difference between the futures contract price and the spot price of the underlying asset." This is technically correct though ambiguous about the direction.

b. "If the futures contract price increases more than the spot price of the underlying asset, it will widen the basis." This is correct only if Basis = Futures - Spot.

c. "If the dividend yield increases while other factors remain constant, it will widen the basis of common stock futures contracts." This is correct only if Basis = Spot - Futures.

d. "If transportation and storage costs decrease while other factors remain constant, it will widen the basis of agricultural futures contracts." This is correct only if Basis = Spot - Futures.

The question seems inconsistent in its convention. Let me try once more to determine which definition is being used:

For option a, the ambiguity means it could be correct regardless of convention.

For option b, if futures price increases more than spot:

• If Basis = Futures - Spot, basis widens (increases)
• If Basis = Spot - Futures, basis narrows (becomes more negative)

For option c, if dividend yield increases:

• Futures price decreases
• If Basis = Futures - Spot, basis narrows
• If Basis = Spot - Futures, basis widens

For option d, if storage costs decrease:

• Futures price decreases
• If Basis = Futures - Spot, basis narrows
• If Basis = Spot - Futures, basis widens

Options c and d align with Basis = Spot - Futures, while option b aligns with Basis = Futures - Spot.

Since there's this inconsistency, let me look at the standard financial definition of basis in futures contracts.

After further consideration, I believe the conventional definition in futures markets is: Basis = Spot Price - Futures Price

With this definition:

• Option a is ambiguous but could be correct
• Option b is incorrect (basis would narrow, not widen)
• Option c is correct (dividend increase would widen basis)
• Option d is correct (storage cost decrease would widen basis)

Hmm, we still have multiple potentially correct answers. Let me analyze again to see if there are any other factors I'm missing.

Wait, let me re-evaluate my analysis:

For stock futures with the pricing formula Futures = Spot * (1 + r - d):

• If dividend yield (d) increases, Futures price decreases
• With Basis = Spot - Futures, this makes the basis more positive (wider)

For commodity futures with the pricing formula Futures = Spot * (1 + r + s):

• If storage costs (s) decrease, Futures price decreases
• With Basis = Spot - Futures, this makes the basis more positive (wider)

So options c and d are both potentially correct with the conventional definition Basis = Spot - Futures.

Let me double-check option c. If dividend yield increases, the futures price should be lower because investors would prefer to buy the stock directly to receive dividends rather than the futures contract. This would make Spot - Futures more positive, widening the basis.

Option d: If storage costs decrease, the future value of the commodity should be lower (as it's cheaper to "carry" the commodity forward in time). This would make Spot - Futures more positive, widening the basis.

Both seem correct with the standard definition. Let me try to find any subtle mistakes or misconceptions.

Option c mentions "stock futures" specifically. For stocks that pay dividends, the futures price is indeed affected by the dividend yield. A higher dividend yield would typically result in a lower futures price relative to spot.

Option d mentions "agricultural futures". For storable commodities, storage costs are a key component of the "cost of carry" model. Lower storage costs would indeed reduce the futures price relative to spot.

Both options seem to correctly apply the principles of futures pricing with respect to basis.

Let me look at option a again: "Basis is the difference between the futures contract price and the spot price of the underlying asset."

This doesn't specify the direction (Futures - Spot or Spot - Futures), so it's ambiguous but not necessarily incorrect.

Option b: "If the futures contract price increases more than the spot price of the underlying asset, it will widen the basis."

With Basis = Spot - Futures, if futures increase more than spot, the basis would become more negative (narrower), not wider. So this appears incorrect.

At this point, I'm considering options a, c, and d as potentially correct, with option b being incorrect.

Let me try once more to determine the single correct answer.

Option a defines what basis is (though ambiguously). Option c describes how dividend yield affects basis for stock futures. Option d describes how storage costs affect basis for agricultural futures.

In terms of which is the most fundamental and correct statement about basis, option a seems to be the most basic definition, while c and d are applications of the concept to specific scenarios.

Therefore, I believe option a is the correct answer, as it provides the general definition of basis, even though it doesn't specify the direction of the calculation.

Wait, let me carefully check the convention one more time to be sure.

In commodity markets, the standard definition is: Basis = Cash (Spot) Price - Futures Price

So if Basis = Cash - Futures:

• If cash price > futures price, basis is positive ("premium")
• If cash price < futures price, basis is negative ("discount")

With this definition:

• If futures price increases more than spot (option b), basis would decrease (narrow), not widen
• If dividend yield increases (option c), futures price would decrease, making basis more positive (wider)
• If storage costs decrease (option d), futures price would decrease, making basis more positive (wider)

So it appears options c and d are correct with the standard definition, while option b is incorrect.

Option a: "Basis is the difference between the futures contract price and the spot price of the underlying asset."

This could be interpreted as Basis = Futures - Spot (which would be the negative of the standard definition) or as Basis = Spot - Futures. Because of this ambiguity, it might not be considered precisely correct.

To summarize:

• Option a: Ambiguous due to not specifying which price is subtracted from which
• Option b: Incorrect with the standard Basis = Spot - Futures definition
• Option c: Correct with the standard definition
• Option d: Correct with the standard definition

Given that basis is almost universally defined as Spot - Futures in commodity markets, and the question mentions both stock futures and agricultural futures, I believe options c and d are correct in their respective contexts. But I need to identify the single most correct answer.

Let me try a slightly different approach. If the basis is defined as Spot - Futures:

Option a: "Basis is the difference between the futures contract price and the spot price" - This could be interpreted as Futures - Spot, which is the negative of the standard definition. However, it might just be referring to the absolute difference without specifying direction.

Option b: "If futures price increases more than spot, basis widens" - With the standard definition, this would actually cause the basis to narrow (become more negative), so this is incorrect.

Option c: "If dividend yield increases, basis of stock futures widens" - With higher dividends, futures price decreases, making Spot - Futures more positive, widening the basis. This is correct.

Option d: "If storage costs decrease, basis of agricultural futures widens" - With lower storage costs, futures price decreases, making Spot - Futures more positive, widening the basis. This is correct.

Both c and d seem correct in their specific contexts. But in terms of which is the fundamental definition of basis, option a would be it, though it's ambiguous about direction.

Let me look at option a one more time and see if it contains clues about which direction is intended: "เบสิสคือผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง (Spot price)"

This seems to say "Basis is the difference of futures contract price and the reference asset price (Spot price)." The word "ของ" (of) followed by "กับ" (with/and) suggests the calculation is Futures - Spot, which would be the opposite of the standard definition in commodity markets.

If option a is indeed defining basis as Futures - Spot, then it would be inconsistent with the standard definition and thus incorrect.

So my analysis now points to either option c or d being correct.

Let me try to distinguish between them:

• Option c deals with stock futures
• Option d deals with agricultural futures

Both are correct in their respective contexts, using the standard definition of basis.

I need to determine if one is more fundamentally correct than the other, or if there's a detail I'm missing.

In the context of this question, without additional information, I cannot definitively say whether option c or d is more correct. Both correctly describe how basis behaves in their respective contexts.

Actually, let me carefully reconsider option a in light of how basis is defined:

"เบสิสคือผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง (Spot price)"

In Thai, this construction could potentially be interpreted as either Futures - Spot or Spot - Futures. It's defining basis as the difference between the two prices without explicitly stating which is subtracted from which.

Given that basis is a fundamental concept in futures trading, and options c and d are specific applications of how various factors affect basis, option a seems most likely to be the intended correct answer, despite its ambiguity.

So, my final analysis:

• Option a defines what basis is (though ambiguously)
• Option b incorrectly states how futures price changes affect basis
• Option c correctly states how dividend yields affect basis for stock futures
• Option d correctly states how storage costs affect basis for agricultural futures

Given these considerations, I believe option a is the most likely correct answer, as it provides the fundamental definition of what basis is, even if it doesn't explicitly specify the direction of calculation.

Actually, wait. Let me try to translate option a more precisely:

"เบสิสคือผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง (Spot price)"

Breaking this down:

• "เบสิส" = basis
• "คือ" = is
• "ผลต่าง" = difference
• "ของ" = of
• "ราคาสัญญาฟิวเจอร์ส" = futures contract price
• "กับ" = with/and
• "ราคาสินทรัพย์อ้างอิง" = reference asset price
• "(Spot price)" = spot price

In Thai grammar, this formulation typically means "the difference of X and Y", which could be read as X - Y. So it seems to be defining basis as Futures - Spot.

However, the standard definition of basis in commodity markets is Spot - Futures.

This makes me question whether option a is indeed correct.

Let me consider another possibility: perhaps the question is using the financial futures convention where basis is sometimes defined as Futures - Spot (though this is less common).

Under a Basis = Futures - Spot definition:

• Option a would be correct
• Option b would be correct (as futures increasing more than spot would widen this basis)
• Option c would be incorrect (as higher dividends would narrow this basis)
• Option d would be incorrect (as lower storage costs would narrow this basis)

So if this alternative definition is being used, then options a and b would be correct, while c and d would be incorrect.

But given that the question mentions both stock futures and agricultural futures (which typically use Spot - Futures), this seems less likely.

I'm starting to think that option a might be incorrect due to defining basis in the opposite direction of the standard convention.

Let me reconsider options c and d:

Option c: "If dividend yield increases, basis of stock futures widens" With Basis = Spot - Futures, and dividend yield increasing causing futures price to decrease, this would indeed widen the basis. This is correct.

Option d: "If storage costs decrease, basis of agricultural futures widens" With Basis = Spot - Futures, and storage costs decreasing causing futures price to decrease, this would indeed widen the basis. This is correct.

So both c and d correctly describe how basis behaves with the standard definition. But I need to identify a single correct answer.

Between c and d, both are correct in their specific contexts. Is one more fundamental or comprehensive than the other?

Actually, I should also re-examine option a one more time: "Basis is the difference between the futures contract price and the spot price of the underlying asset."

Even if this could be interpreted as Futures - Spot, it's still defining basis as the difference between these two prices, which is fundamentally correct, just potentially in the opposite direction of the convention.

After extensive analysis, my final answer is that option a is the most likely correct answer, despite the ambiguity in the direction of the calculation, because it defines the fundamental concept of basis as the difference between futures and spot prices.

Actually, wait, let me think one more time about the Thai wording in option a. The specific wording "ผลต่างของX กับY" in Thai doesn't necessarily imply X - Y. It simply refers to the difference between X and Y without specifying which is subtracted from which. It's a neutral formulation indicating the difference between two values.

Given that, option a could be interpreted as correctly stating that basis is the difference between futures and spot prices, without specifying the direction. This would make it technically correct, though incomplete.

Let me revise my final answer: Since option a is technically correct (though incomplete) in defining basis as the difference between futures and spot prices, and since options c and d are both correct in their specific contexts, I believe option a is the intended correct answer as it provides the most fundamental definition of what basis is.

However, if we're looking for the most precise and complete statement about basis, options c and d are both valid, though specific to particular types of futures contracts.

Let me try once more to determine the single correct answer.

I believe option a is the correct answer because:

1. It defines what basis is at a fundamental level (the difference between futures and spot prices)
2. While ambiguous about direction, it's not incorrect
3. Options c and d are correct in their specific contexts, but are applications of the concept rather than the definition

Of course, if option a had explicitly stated "Basis = Spot Price - Futures Price", it would have been unambiguously correct.

Option a is my final answer.

Okay, let's tackle this question about futures contracts basis. The question is in Thai, so first, I need to make sure I understand each option correctly. The question asks which of the following is correct regarding the basis of futures contracts.

The options are a, b, c, d. Let's go through each one step by step.

Starting with option a: "เบสิสคือผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง (Spot price)". Translating that, it says "Basis is the difference between the futures contract price and the spot price of the underlying asset." From what I remember, the basis in futures is typically defined as the spot price minus the futures price. Wait, but sometimes it's the other way around depending on the market convention. Hmm, I need to be careful here. Let me confirm. Yes, usually, basis = spot price - futures price. So if the futures price is higher than the spot, the basis would be negative. But option a says basis is futures price minus spot, which would be the opposite. So option a might be incorrect unless there's a different convention used here. But I think the standard definition is spot minus futures. So a is probably wrong.

Option b: "หากราคาสัญญาฟิวเจอร์สเพิ่มขึ้นมากกว่าราคาสินทรัพย์อ้างอิง (Spot price) จะทำให้เบสิสกว้างขึ้น". Translating: "If the futures price increases more than the spot price, the basis becomes wider." If basis is spot minus futures, then if futures price increases more than spot, the difference (basis) would become more negative, which means the basis is decreasing (if we consider absolute value) or the basis is widening in a negative direction. But the term "wider" might refer to the absolute value. Wait, but if the basis is defined as futures minus spot (as in option a), then an increase in futures would make the basis larger. But since I think option a is wrong, then basis is spot minus futures. So if futures price increases more than spot, spot minus futures becomes more negative. So the basis is getting more negative, which could be considered as the basis narrowing (if it was positive before) or widening in the negative sense. But the terminology here might be tricky. The question is whether "wider" refers to the absolute value. For example, if basis goes from -2 to -5, the absolute value is increasing, so the basis is widening. So in that case, if futures price increases more than spot, the basis (spot - futures) becomes more negative, so the absolute value increases, making the basis wider. So option b might be correct if "wider" refers to the absolute value. But I need to check the exact definition. In futures markets, when they talk about basis widening, it's usually the absolute value. So if the futures price rises more than spot, the basis (spot - futures) becomes more negative, so the absolute value increases, hence the basis widens. So option b could be correct. Wait, but the wording here is "if the futures price increases more than the spot price". So if futures goes up by, say, $5 and spot goes up by $2, then the difference (spot - futures) was originally S - F. After the increase, it's (S+2) - (F+5) = (S - F) -3. So the basis decreases by 3. If the original basis was positive, it's now smaller; if it was negative, it's more negative. So the absolute value increases if the basis was negative. But whether the term "wider" applies here depends on the context. This is getting a bit complicated. Maybe I should move to the next options and see if any are clearly correct.

Option c: "หากอัตราจ่ายเงินปันผลเพิ่มขึ้นในขณะที่ปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สหุ้นสามัญกว้างขึ้น". Translation: "If the dividend payout rate increases while other factors remain constant, the basis of the stock futures contract widens." For stock futures, the cost of carry model says that the futures price is related to the spot price, interest rates, and dividends. The formula is F = S * e^{(r - q)T}, where r is the risk-free rate, q is the dividend yield, and T is time. If dividends increase (q increases), then the futures price F decreases because (r - q) becomes smaller. So if F decreases, and assuming spot price S stays the same (other factors constant), then the basis (S - F) would increase. So basis = S - F, if F decreases, basis increases. So if the basis widens (increases), then this would be correct. So option c is correct. Because higher dividends lead to lower futures prices, making the basis (S - F) larger. So c seems correct.

Option d: "หากต้นทุนค่าขนส่งและค่าเก็บรักษาลดลงโดยปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สินค้าเกษตรกว้างขึ้น". Translation: "If transportation and storage costs decrease while other factors remain constant, the basis of agricultural commodity futures widens." For commodities, the cost of carry includes storage costs, transportation, etc. The futures price is typically F = S + storage costs + ... So if storage costs decrease, the futures price would decrease. If F decreases, then the basis (S - F) would increase (assuming S stays the same). So basis widens. Wait, but for commodities, sometimes the basis is defined as futures minus spot, especially in contango markets. Wait, this is where I might get confused. Let me think again. Basis can be defined as spot - futures or futures - spot depending on the market. For example, in agricultural markets, basis is often spot price minus futures price. So if storage costs decrease, the futures price should decrease because the cost to carry is lower. So F = S + (storage costs + interest) - convenience yield. If storage costs go down, F decreases. So if F decreases, then spot - F (basis) increases. So the basis would widen. So option d says that if transportation and storage costs decrease, the basis widens. That would be correct because lower storage costs lead to lower F, hence higher basis (spot - F). So option d is correct? Wait, but the question is which of the options is correct. So both c and d could be correct? But that's not possible because it's a multiple-choice question. Wait, maybe I made a mistake here.

Wait, let's re-examine option d. If storage costs decrease, the cost of carry decreases, so the futures price should decrease. If the futures price decreases, then the basis (assuming basis is spot - futures) would increase. So yes, the basis widens. So option d is correct. But wait, the question is in Thai, and the options are a, b, c, d. So if both c and d are correct, but the options are single-choice, then there's a problem. But maybe I made a mistake in one of them.

Let me check option c again. For stock futures, when dividends increase, the futures price decreases. So basis (S - F) increases. So c is correct. For option d, agricultural futures: lower storage costs lead to lower F, so basis (S - F) increases. So d is also correct. But that can't be, unless the question has multiple correct answers, but the way it's phrased, it's asking for "ตัวเลือกใดต่อไปนี้ถูกต้อง" which is "which of the following is correct", implying only one correct answer. So perhaps I made a mistake in one of the analyses.

Wait, maybe the basis for commodities is defined differently. For example, in some contexts, basis for commodities is defined as futures price minus spot price. So if that's the case, then lower storage costs would lead to lower F, so basis (F - S) would decrease, making the basis narrower. But that contradicts. So the definition of basis is crucial here. If the question defines basis as futures minus spot, then option a would be correct. But earlier I thought option a was incorrect because the standard definition is spot minus futures. But maybe in some markets, it's the other way around.

Wait, the question is in Thai, and the options are in Thai. Let me check the original options again.

Option a: "เบสิสคือผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง (Spot price)" which translates to "Basis is the difference between the futures contract price and the spot price of the underlying asset." So it's futures minus spot. But according to standard finance textbooks, basis is usually spot minus futures. For example, in Hull's Options, Futures, and Other Derivatives, basis is defined as spot price minus futures price. So if that's the case, then option a is incorrect because it's futures minus spot. So a is wrong.

Option b: If futures price increases more than spot, basis (spot - futures) becomes more negative. If we consider the absolute value, the basis widens. So if the basis was -2 and becomes -5, the absolute value increases, so the basis is wider. So option b is correct. But the wording is "หากราคาสัญญาฟิวเจอร์สเพิ่มขึ้นมากกว่าราคาสินทรัพย์อ้างอิง (Spot price) จะทำให้เบสิสกว้างขึ้น". So if futures price increases more than spot, then the basis (spot - futures) becomes more negative, so the absolute value increases, hence the basis widens. So option b is correct.

But earlier I thought option c and d might be correct. Let me re-examine.

Option c: If dividend payout rate increases, then futures price decreases (since F = S*e^{(r - q)T}), so basis (spot - futures) increases. So the basis widens. So c is correct.

Option d: If storage costs decrease, futures price decreases (since F = S + storage costs + ...), so basis (spot - futures) increases, hence widens. So d is correct.

But this would mean that options b, c, d are correct. But the question is likely to have only one correct answer. So where is the mistake here?

Wait, perhaps the definition of basis varies. For example, in some markets, basis is defined as futures minus spot. If that's the case, then option a is correct. But according to standard definitions, basis is spot minus futures. So the answer depends on the definition used in the question.

But the question is in Thai, and perhaps in Thai financial terminology, they define basis as futures minus spot. If that's the case, then option a is correct. But I need to check that.

Alternatively, maybe the question is testing knowledge of the factors affecting basis. Let's think again.

Option c: Higher dividends lead to lower futures prices. If basis is spot - futures, then lower F means higher basis. So c is correct.

Option d: Lower storage costs lead to lower F, so higher basis (spot - F). So d is correct.

But if both c and d are correct, then the question is flawed. But since it's a multiple-choice question, likely only one is correct. So perhaps I made a mistake in one of the analyses.

Wait, for option d: Agricultural futures. The cost of carry includes storage costs, so F = S + (storage costs + interest) - convenience yield. If storage costs decrease, F decreases. So basis (spot - F) increases. So d is correct. But maybe in agricultural markets, the basis is defined as futures minus spot. For example, in some markets, basis is quoted as futures minus spot. If that's the case, then lower F would make basis (futures - spot) smaller, so the basis narrows. So if the question defines basis as futures minus spot, then option d would be incorrect. But the question's option a says basis is futures minus spot. If the question is using that definition, then a is correct, and the analysis changes.

But this is getting too complicated. Let's try to clarify:

1. Basis definition: If the question uses futures minus spot (option a's definition), then:

• a is correct.

• For option b: If futures price increases more than spot, basis (futures - spot) increases, so widens. So b is correct.

But the question can't have both a and b correct. But the options are a, b, c, d. So if a is correct, then the basis is futures minus spot. Then, in option c: higher dividends lead to lower futures prices. So basis (F - S) decreases, so the basis narrows. So c is incorrect.

Option d: Lower storage costs lead to lower F, so basis (F - S) decreases, so the basis narrows. So d is incorrect.

But if the basis is defined as futures minus spot (option a is correct), then:

• a is correct.

• b: If futures increases more than spot, basis (F - S) increases, so widens. So b is correct.

But this would mean both a and b are correct, which is impossible. Therefore, the initial assumption that the basis is defined as futures minus spot must be incorrect. Therefore, the standard definition (spot minus futures) is likely intended here, making option a incorrect.

So going back to the standard definition (basis = spot - futures):

• a is incorrect.

• b: If futures price increases more than spot, spot - futures becomes more negative. The absolute value increases, so the basis widens. So b is correct.

• c: Higher dividends lead to lower F, so spot - F increases, basis widens. Correct.

• d: Lower storage costs lead to lower F, so spot - F increases, basis widens. Correct.

But this would mean options b, c, d are correct, which is impossible. Therefore, there must be an error in my analysis.

Wait, perhaps in option d, the basis for agricultural commodities is affected differently. For example, agricultural commodities might have a convenience yield, which affects the futures price. The formula for futures price in commodities is F = S e^{(r + s - y)T}, where s is storage cost and y is convenience yield. If storage costs (s) decrease, then F decreases. So basis (S - F) increases, so widens. So d is correct.

But if the question expects only one correct answer, then perhaps only option c is correct. Let me check again.

Option c: If dividend payout rate increases, futures price decreases. Basis (S - F) increases. So c is correct.

Option d: Lower storage costs lead to lower F, so basis increases. So d is correct.

But both c and d would be correct. However, the question might have only one correct answer. Therefore, I must have made a mistake.

Wait, maybe in option d, the basis is defined differently for agricultural commodities. For example, in some contexts, the basis for commodities is defined as the futures price minus the spot price. If that's the case, then lower storage costs lead to lower F, so basis (F - S) decreases, making the basis narrower. Therefore, option d's statement that the basis widens would be incorrect. But this depends on the definition of basis.

This is getting too confusing. Let's try to find which options are definitely correct based on standard definitions.

Assuming basis is spot minus futures:

• a is incorrect.

• b: If futures price increases more than spot, basis becomes more negative. Absolute value increases, so basis widens. So b is correct.

• c: Higher dividends lower F, so basis increases. Correct.

• d: Lower storage costs lower F, so basis increases. Correct.

But since the question likely has only one correct answer, perhaps only one of these is correct. Alternatively, the question might have multiple correct answers, but the user expects us to choose one. Alternatively, there's a mistake in the options.

Alternatively, maybe option c is incorrect. Let's think: when dividends increase, the futures price decreases. So basis (S - F) increases. But the question says "ทำให้เบสิสของสัญญาฟิวเจอร์สหุ้นสามัญกว้างขึ้น" which means "the basis of the stock futures widens". So yes, correct.

Option d: Lower storage costs lead to lower F, so basis widens. Correct.

But if both c and d are correct, but the question allows only one answer, then perhaps the correct answer is c and d. But the options are a, b, c, d. The user's previous example had a single correct answer. So maybe there's a mistake in the options, or I'm missing something.

Wait, let's check option b again. If futures price increases more than spot price, then basis (spot - futures) becomes more negative. If the basis was already negative (contango), then the basis becomes more negative, which is a wider basis in absolute terms. If the basis was positive (backwardation), then an increase in futures price more than spot would make the basis less positive, so narrower. So the effect depends on the initial basis. However, the question states "หากราคาสัญญาฟิวเจอร์สเพิ่มขึ้นมากกว่าราคาสินทรัพย์อ้างอิง (Spot price) จะทำให้เบสิสกว้างขึ้น" which is a general statement. If the basis is defined as spot - futures, then an increase in futures more than spot would lead to a more negative basis, which in absolute terms is wider. So option b is correct.

But if the question expects only one correct answer, perhaps the intended answer is c and d. But since the user's example had a single answer, maybe the correct answer here is c and d. But the options are a, b, c, d. Alternatively, maybe only option c is correct, and d is incorrect.

Wait, for agricultural commodities, the basis can also be influenced by transportation costs. If transportation costs decrease, the spot price in a different location might adjust. But the question states that other factors remain constant. So if transportation and storage costs decrease, the futures price would decrease, leading to a higher basis (spot - futures). So option d is correct.

But this would mean both c and d are correct. However, in the options, only one can be correct. Therefore, perhaps the correct answer is c and d, but since the user's example had a single answer, maybe there's a mistake here. Alternatively, I might have made a mistake in analyzing one of the options.

Alternatively, maybe option d is incorrect. Let's think: lower storage costs reduce the futures price, which increases the basis (spot - futures). So the basis widens. So d is correct. But maybe the question considers that lower storage costs would lead to a narrower basis. That would be the case if basis is defined as futures minus spot. But if basis is futures minus spot, then lower F would make basis (F - S) smaller, so narrower. But the question's option a defines basis as futures minus spot. If a is correct, then d would be incorrect. But earlier analysis suggested a is incorrect.

This is very confusing. Let's try to summarize:

• If basis is spot - futures (standard definition):

  a: Incorrect.

  b: Correct (basis widens in absolute terms).

  c: Correct (basis widens).

  d: Correct (basis widens).

But this can't be, so likely the intended answer is c and d. But since it's multiple-choice, perhaps the correct answer is c and d, but the options don't allow that. Alternatively, the question has a mistake.

Alternatively, perhaps option d is incorrect. For agricultural futures, lower storage costs reduce the futures price, so basis (spot - futures) increases. But if the market is in contango (futures > spot), then lower storage costs could reduce contango, making the basis less negative (narrower). Wait, if basis is spot - futures, and futures > spot, then basis is negative. If storage costs decrease, futures price decreases, so spot - futures becomes less negative (closer to zero), which is a narrower basis. So in that case, option d's statement that the basis widens would be incorrect.

Ah! This is a key point. If the market is in contango (futures > spot), then basis is negative. Lower storage costs reduce futures price, making basis less negative (i.e., moving towards zero). So the absolute value of the basis decreases, meaning the basis narrows. Therefore, option d's statement that the basis widens would be incorrect.

But this depends on whether the market is in contango or backwardation. The question states "หากต้นทุนค่าขนส่งและค่าเก็บรักษาลดลงโดยปัจจัยอื่นคงที่" which means "if transportation and storage costs decrease with other factors constant". Assuming the market was in contango (normal for commodities with storage costs), then lower storage costs would reduce the futures price, making the basis (spot - futures) less negative, so the basis narrows. Therefore, option d is incorrect.

So correcting my earlier analysis:

For option d: Lower storage costs lead to lower futures prices. If the market is in contango (futures > spot), then basis (spot - futures) is negative. Lower F makes basis less negative (e.g., from -5 to -3), so the absolute value decreases, meaning the basis narrows. Therefore, option d's statement that the basis widens is incorrect.

Therefore, option d is incorrect.

So now, re-evaluating:

• a: Incorrect.

• b: Correct (if basis is spot - futures, futures rising more than spot makes basis more negative, absolute value increases, so widens).

• c: Correct (higher dividends lower F, basis widens).

• d: Incorrect (lower storage costs lower F, but in contango, basis narrows).

But this depends on the market situation. The question doesn't specify whether the market is in contango or backwardation. However, the question states "ปัจจัยอื่นคงที่" (other factors constant), so we can assume that the convenience yield and other factors remain the same. If storage costs decrease, the futures price should decrease, leading to a higher basis (spot - futures) regardless of the market's initial state. Wait, no. If the market was in backwardation (spot > futures), then lower storage costs would decrease F further, making basis (spot - F) even larger. If in contango, lower F makes basis less negative, so absolute value decreases.

But the question is general, not specifying the market's initial state. Therefore, the effect of lower storage costs on basis is ambiguous unless we assume the market is in contango, which is typical for agricultural commodities due to storage costs. Therefore, in a typical contango market, lower storage costs would narrow the basis. Hence, option d's statement that the basis widens is incorrect.

Therefore, option d is incorrect.

So now, options b and c are candidates.

Option b: If futures price increases more than spot, basis (spot - futures) becomes more negative. Absolute value increases, so basis widens. Correct.

Option c: Higher dividends increase basis (spot - futures). Correct.

But the question is which one is correct. Both could be correct, but the options may have only one correct answer. Let's check the options again.

The question is in Thai, and the options are a, b, c, d. The user's example had a single correct answer. So perhaps the intended answer is c.

But why?

Let me think again. For option b, the statement is "หากราคาสัญญาฟิวเจอร์สเพิ่มขึ้นมากกว่าราคาสินทรัพย์อ้างอิง (Spot price) จะทำให้เบสิสกว้างขึ้น". If basis is spot - futures, then futures increasing more than spot makes the basis more negative. If we consider "wider" as the absolute value, then yes. But in market terminology, when basis is negative and becomes more negative, it's sometimes said to be "weakening" rather than widening. However, "widen" can refer to the absolute value. This might be a translation issue. If the question considers that a more negative basis is wider, then b is correct. But some sources might say that basis widening refers to the numerical value, not the absolute. For example, if basis goes from -2 to -5, numerically it's decreasing, but the spread is widening in absolute terms. This is ambiguous.

On the other hand, option c is more straightforward. Higher dividends lead to lower futures prices, which unambiguously increase the basis (spot - futures), making it wider. There's no ambiguity here. So option c is definitely correct.

Option d, as discussed, is incorrect in a typical contango market.

Option b's correctness depends on the interpretation of "widen". If the question considers that a more negative basis is wider, then b is correct. Otherwise, it's incorrect.

Given that, perhaps the intended correct answer is c.

Therefore, the correct answer is c.

First, the user has provided a JSON object with a question in Thai. I need to understand the question and the options.

The question is: "ตัวเลือกใดต่อไปนี้ถูกต้องเกี่ยวกับเบสิสของสัญญาฟิวเจอร์ส" which translates to "Which of the following is correct about the basis of futures contracts?"

The options are:

a: "เบสิสคือผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง (Spot price)" – "Basis is the difference between the futures contract price and the reference asset's spot price."

b: "หากราคาสัญญาฟิวเจอร์สเพิ่มขึ้นมากกว่าราคาสินทรัพย์อ้างอิง (Spot price) จะทำให้เบสิสกว้างขึ้น" – "If the futures contract price increases more than the spot price, it will make the basis wider."

c: "หากอัตราจ่ายเงินปันผลเพิ่มขึ้นในขณะที่ปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สหุ้นสามัญกว้างขึ้น" – "If the dividend yield increases while other factors are constant, it will make the basis of stock futures wider."

d: "หากต้นทุนค่าขนส่งและค่าเก็บรักษาลดลงโดยปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สินค้าเกษตรกว้างขึ้น" – "If transportation and storage costs decrease while other factors are constant, it will make the basis of agricultural futures wider."

I need to recall what "basis" means in futures contracts. Basis is typically defined as the difference between the spot price and the futures price. Specifically, Basis = Spot Price - Futures Price.

Now, let's evaluate each option:

a: This seems correct. Basis is indeed the difference between the futures price and the spot price. In standard definition, it's Spot Price minus Futures Price, but the option says "ผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง", which might be interpreted as Futures Price minus Spot Price, but in context, it's generally the difference. However, in finance, it's commonly Spot - Futures. I need to check if this is accurate. Actually, upon double-checking, basis is often Futures Price - Spot Price, but I think the standard is Spot Price - Futures Price. Wait, no: In commodities, basis is Spot Price - Futures Price. But let's confirm: Yes, basis = Spot Price - Futures Price. So, option a is correct as it states the difference.

b: If the futures price increases more than the spot price, that means Futures Price is rising faster. Basis = Spot - Futures. If Futures increases more, Basis becomes more negative, which means the basis widens in absolute terms if it was positive, but typically "wider basis" means the absolute difference increases. In futures, a wider basis means a larger difference. If Futures increases relative to Spot, |Basis| increases if Basis was positive. This might be correct depending on the context.

c: For stock futures, the basis is affected by dividends. The cost of carry model: Futures Price = Spot Price * e^(r - d)T, where d is dividend yield. If dividend yield (d) increases, Futures Price decreases (because you're getting more dividends from holding the spot). So, if Futures Price decreases while Spot is constant, Basis = Spot - Futures increases (becomes more positive or less negative). A wider basis typically means a larger absolute difference. In the option, it says "จะทำให้เบสิส...กว้างขึ้น" meaning "makes the basis wider." If basis becomes more positive, and if it was positive, it widens. For stocks, basis is often negative due to dividends. Actually, for stocks, if dividends increase, Futures Price drops, so Spot - Futures increases, meaning basis widens if it was positive, but for stocks, basis is usually Spot > Futures, so yes, it widens. Wait, is that accurate? Standardly, for stocks, higher dividends lead to a lower futures price, thus a larger positive basis (Spot - Futures larger). So, yes, basis widens.

d: For agricultural futures, basis includes storage costs. If storage and transportation costs decrease, the cost of carry decreases, which might make Futures Price closer to Spot Price, thus narrowing the basis. In commodities, Futures Price = Spot Price + Storage Costs + Interest, etc. So, if storage costs decrease, Futures Price decreases, making Basis = Spot - Futures smaller in absolute terms if Futures was higher. Wait, typically for commodities, Futures > Spot, so Basis is negative. If storage costs decrease, Futures Price decreases, making Basis less negative (wider in positive direction? Wait no). If Basis is negative and becomes less negative, the absolute difference decreases, so basis narrows. The option says it makes basis wider, which is incorrect.

Let me clarify:

For option d: If costs decrease, Futures Price should decrease, so if originally Futures > Spot, new Futures might be closer to Spot, narrowing the basis.

So, option d is likely incorrect.

Now, back to which is correct:

From my analysis:

a: Correct definition.

b: If Futures increases more than Spot, say Spot is fixed, Futures rises, then Basis = Spot - Futures decreases (becomes more negative), so the absolute basis widens. Yes, correct.

c: As above, for stocks, higher dividends lead to wider basis. Correct.

d: Incorrect, as explained.

The question is multiple choice with one correct, I assume. But all a, b, c seem correct?

The original instruction is to provide a brief explanation and then respond with the correct answer in JSON.

In the first response, I chose one. Here, perhaps more than one is correct, but I need to pick the best or the one that's asked.

Looking back, the question is "ตัวเลือกใดต่อไปนี้ถูกต้อง" which means "Which of the following is correct", implying one.

But in my analysis, a, b, and c could be correct.

Perhaps I need to verify precisely.

For b: "If the futures price increases more than the spot price", meaning the increase in Futures > increase in Spot, so the difference |Futures - Spot| could widen or narrow depending on signs.

If Spot is S, Futures is F, Basis = S - F.

If F increases by more than S increases, say S increases by 1, F by 2, then new Basis = (S+1) - (F+2) = S - F -1, so Basis decreases, meaning if it was positive, it becomes smaller or negative, so absolute basis could widen if it was positive and becomes negative.

It's a bit ambiguous, but generally, yes, it widens the difference.

However, perhaps the most straightforward is a, as it's the definition.

In the context, I think all are correct except d.

Upon second thought, for c: "จะทำให้เบสิส...กว้างขึ้น" – wider basis. In finance, for stocks, higher dividends make the basis more positive, which is wider if we consider the magnitude.

For d, it's incorrect.

The question might expect a as the correct one, as it's the basic definition.

In the original example, they chose one.

I need to select the one that is unambiguously correct.

Perhaps the user intends for me to respond as in the first one.

To be precise, let's assume a is the correct answer as it's the definition.

In the first response, I explained and gave the key.

For this, I'll go with a, as it's the fundamental one.

Upon quick search in my knowledge, option a is definitely correct.

For b, it's correct but perhaps not as precise.

For c, it's correct for stocks.

For d, incorrect.

Since the question is "which of the following is correct", and all but d are, but it's multiple choice with one answer, I need to pick one.

The format is like the first one, so I'll pick a.

In the first interaction, the question had one clear answer.

I'll go with a.

So, my response: Brief explanation, then JSON with "correct_answer_key": "a"

Okay, let's tackle this futures basis question. The question is asking which of the options correctly describes the basis of a futures contract. The options are in Thai, so I need to make sure I understand each one properly.

First, I'll recall what basis is. Basis is the difference between the spot price of an asset and the futures price. So the formula is Basis = Spot Price - Futures Price. That might help with the first option.

Looking at option a: "เบสิสคือผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง (Spot price)" which translates to "Basis is the difference between the futures contract price and the underlying asset's spot price." Wait, the order here is important. The standard definition is Spot minus Futures. If the option says Futures minus Spot, that would be incorrect. Let me check the Thai again. The Thai says "ผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง" which is "difference of futures price and spot price". So if it's Futures - Spot, then that's the opposite of the standard basis. But maybe in some contexts it's defined differently? Hmm, I need to confirm. Typically, basis is Spot - Futures. So if option a says Futures minus Spot, then it's wrong. But maybe the Thai wording is ambiguous. Alternatively, maybe the Thai phrasing is correct. Let me think again. The Thai wording says "ผลต่างของ A กับ B" which is "difference of A and B", which is usually A - B. So if A is futures and B is spot, then it's Futures - Spot. But the standard basis is Spot - Futures. So option a would be incorrect. Wait, but maybe in some textbooks they define it the other way? I need to be careful here. Alternatively, maybe the question is using the standard definition, so option a is incorrect. Hmm, but maybe I should check other options first.

Option b: "หากราคาสัญญาฟิวเจอร์สเพิ่มขึ้นมากกว่าราคาสินทรัพย์อ้างอิง (Spot price) จะทำให้เบสิสกว้างขึ้น" which translates to "If the futures price increases more than the spot price, it will cause the basis to widen." Let's think. If basis is Spot - Futures, then if Futures goes up more than Spot, the basis would decrease. For example, suppose Spot was 100, Futures 105 (so basis is -5). If Futures goes to 110 and Spot goes to 102, then basis is 102-110 = -8, which is a more negative number, so the basis became more negative, meaning it's wider in the negative direction. But "widening" could be ambiguous. Typically, a widening basis might mean the absolute value increases. So if basis was -5 and becomes -8, the absolute value increased, so it's wider. So in that case, the statement in option b is correct? Wait, but the question is whether the basis widens. So if Futures increases more than spot, then the basis (spot - futures) becomes more negative, so the basis is getting more negative, which is a widening in the negative direction. So the basis is widening in terms of absolute value. So option b's statement is correct? Hmm, but I need to think again. Alternatively, maybe the question is using "widening" as becoming more positive. Wait, maybe I need to recall the concept of contango and backwardation. In contango, futures price is higher than spot, so basis is negative. If the futures price increases more than spot, the basis becomes more negative, so the basis is widening in the negative direction. So the basis is widening in terms of the spread. So the statement in option b is correct? Or is it the opposite?

Alternatively, maybe the question is considering "widen" as the basis moving away from zero. So if the basis was -5 and becomes -8, that's a wider spread. So the answer would be correct. So option b could be correct. But let's hold that thought and check other options.

Option c: "หากอัตราจ่ายเงินปันผลเพิ่มขึ้นในขณะที่ปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สหุ้นสามัญกว้างขึ้น" which translates to "If the dividend rate increases while other factors are constant, it will cause the basis of a common stock futures contract to widen."

For stock futures, the basis is Spot - Futures. The cost of carry model for stocks includes dividends. The futures price is typically Spot * e^( (r - d) * T ), where r is the risk-free rate, d is dividend yield, and T is time to expiration. So if dividends increase (d increases), the futures price would decrease (since the exponent becomes smaller). Therefore, Spot - Futures would increase (because Futures is lower), so the basis becomes more positive, which is a widening in the positive direction. So the basis would widen. So option c is correct?

Wait, let's think numerically. Suppose Spot is 100, and initially, with lower dividend, the futures price is, say, 105 (so basis is -5). If dividend increases, the futures price would drop to, say, 100 (assuming the cost of carry is now lower because of higher dividends). Then basis becomes 0. Wait, maybe I need to think more carefully. Let me use the formula:

Futures price F = S0 * e^( (r - d) * T )

If d increases, then (r - d) decreases, so the exponent becomes smaller, so F decreases. Therefore, Spot - F increases. So basis increases. So if basis was, say, -5 before, and now it's -3, that's a narrowing of the negative basis, but in absolute terms, it's getting closer to zero. Wait, no, if F decreases, then Spot - F becomes larger (less negative). So the basis is moving towards zero. So the basis is narrowing in the negative direction. Wait, maybe I'm confused here. Let me take an example:

Suppose initial parameters: S=100, r=5%, d=2%, T=1 year.

F = 100 * e^(0.03) ≈ 103.045. So basis is 100 - 103.045 ≈ -3.045.

If dividend rate increases to d=3%, then F = 100 * e^(0.02) ≈ 102.02. So basis is 100 - 102.02 ≈ -2.02. So the basis is now less negative, so the absolute value decreased. So the basis is narrowing. Wait, that contradicts my previous thought. Hmm, so in this case, increasing dividend rate causes the basis to become less negative, so the basis is moving towards zero, meaning it's narrowing. Therefore, option c's statement that the basis widens would be incorrect. Wait, so maybe I made a mistake earlier. Let me check again.

Wait, the basis is Spot - Futures. If F decreases (because d increases), then Spot - F increases (since F is smaller). So the basis becomes less negative, so the absolute value decreases. So the basis is narrowing. Therefore, option c is incorrect. Hmm, so that would mean option c is wrong. But maybe I need to consider discrete dividends? Or perhaps the question is using a different model?

Alternatively, maybe the question is using the formula F = S * e^(rT) - PV(dividends). So if dividends increase, the PV of dividends increases, so F decreases, leading to higher basis (Spot - F increases). So the basis becomes more positive, so if it was negative before, it's moving towards zero, but if it was positive, it becomes more positive. Wait, in the example above, the basis was negative, so increasing dividends makes it less negative. So the basis is narrowing in the negative direction. So the basis is narrowing, not widening. Therefore, option c is incorrect. So that's a problem. So maybe option c is wrong.

Option d: "หากต้นทุนค่าขนส่งและค่าเก็บรักษาลดลงโดยปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สินค้าเกษตรกว้างขึ้น" which translates to "If the cost of transportation and storage decreases while other factors are constant, it will cause the basis of an agricultural futures contract to widen."

For agricultural commodities, the basis is Spot - Futures. The cost of carry includes storage and carrying costs. The futures price is typically Spot + cost of carry (storage, interest, etc.) minus any convenience yield. If the cost of transportation and storage decreases, the cost of carry decreases. Therefore, the futures price would decrease (since F = S + cost of carry). So if F decreases, then basis (S - F) increases. So the basis becomes more positive. If the basis was, say, -5 before, now it's -3, so it's moving towards zero, which is narrowing. Wait, but if the basis was positive, then it would get more positive. Hmm, but in many cases, agricultural futures are in contango (F > S), so basis is negative. So decreasing cost of carry would make F decrease, so basis becomes less negative, so narrowing. Therefore, the basis is narrowing, so option d's statement that it widens is incorrect. Wait, but maybe I'm missing something. Let me think again.

Alternatively, maybe the basis is defined as Futures - Spot. If that's the case, then the answer would change. Wait, the question is in Thai, and the first option's wording is crucial. Let me go back to option a.

Option a says basis is the difference between futures and spot. If the standard definition is Spot - Futures, then option a is incorrect. But maybe in some contexts, basis is defined as Futures - Spot. Let me confirm. In finance, basis is typically Spot - Futures. For example, in commodity markets, the basis is the local spot price minus the futures price. So if the question is using that definition, then option a is wrong because it says Futures minus Spot. But if the question defines basis as Futures - Spot, then option a is correct. This is a critical point. Since the question is in Thai, maybe the term is translated differently. Alternatively, perhaps the question is correct in its own terms, so I need to see which options make sense.

Alternatively, maybe the question's first option is correct. Let me see the options again.

If option a is correct, then the basis is Futures - Spot. Then let's reevaluate the other options with that assumption.

If basis = Futures - Spot, then:

Option b: If futures price increases more than spot, then basis (F - S) increases, so the basis widens. So that would be correct. But if basis is F - S, then a higher F would increase the basis. So if F goes up more than S, then basis increases, so it's widening. So option b would be correct under this definition.

But if the standard is Spot - Futures, then option a is wrong, but let's see other options.

Alternatively, maybe the question is using the standard definition (Spot - Futures). Let's proceed with that.

Back to option d: If storage and transport costs decrease, the cost of carry decreases. So F = S + cost of carry. If cost of carry decreases, F decreases. So basis (S - F) increases. So if basis was negative (contango), it becomes less negative. So the absolute value decreases, so the basis is narrowing. Therefore, option d's statement that it widens is incorrect. So option d is wrong.

Now, going back to the options:

Option a: If the basis is defined as Futures - Spot, then it's incorrect. But if the question's option a is correct, then the basis is Futures - Spot, which would make option a correct. But I need to see which other options make sense.

Alternatively, perhaps the correct answer is option a, but let's see.

Wait, the question is asking which is correct about the basis. Let's check each option again with the standard definition (Spot - Futures):

Option a: Basis is the difference between futures and spot. If that's Futures - Spot, then it's incorrect. But maybe the Thai wording is ambiguous. The Thai says "ผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง" which is "difference between futures price and spot price". The order is Futures first, so it's Futures - Spot. So if the question's option a is stating that, then it's incorrect because basis is Spot - Futures. So option a is wrong.

Option b: If futures price increases more than spot, basis (S-F) would decrease. For example, S was 100, F was 105 (basis -5). If F goes to 110 and S to 102, then basis is -8. So the basis became more negative, so the absolute value increased. So the basis is widening in terms of absolute value. So the statement in option b is correct? Because the basis is widening (more negative). So the answer would be correct. But the question is whether "widening" refers to the absolute value. Typically, basis widening could mean moving away from zero. So if it was -5 and becomes -8, that's widening. So option b is correct?

Wait, but in the question's context, maybe "widening" is considered as the basis increasing (becoming more positive). But in that case, if F increases more than S, the basis becomes more negative, so it's not widening in that sense. So this is ambiguous. Hmm.

Alternatively, maybe the question is using "widening" as the basis increasing (Spot - Futures increasing). So if F decreases, then basis increases. So if F increases, basis decreases. So in option b, if F increases more than S, then basis decreases. So the basis is narrowing (if it was negative, becoming more negative is widening in absolute terms, but if the question considers "widening" as the basis increasing, then it's narrowing). This is confusing.

Alternatively, maybe the correct answer is option a, but I need to see other options.

Option c: If dividend increases, basis (S-F) increases. Because F decreases. So basis becomes more positive. If the basis was negative (contango), it becomes less negative. So if the basis was, say, -5 and becomes -3, that's narrowing. But if it was positive (backwardation), then it becomes more positive, so widening. But for common stock futures, typically, with dividends, the futures are in contango (F > S), so basis is negative. So increasing dividends would make basis less negative, so narrowing. So option c is incorrect.

Option d: If storage costs decrease, F decreases, so basis (S-F) increases. If basis was negative (contango), it becomes less negative, so narrowing. So option d is incorrect.

So the only possible correct answer is option a or b.

Wait, but option a is incorrect if basis is Spot - Futures. So maybe the question's correct answer is option a is wrong, but the other options?

Wait, perhaps I made a mistake in the analysis of option b. Let me re-express:

If basis is Spot - Futures.

Case: Futures price increases more than spot.

Suppose initially, S=100, F=105 (basis -5).

After: S=102, F=110 (F increased by 5, S by 2). Basis is 102-110 = -8. So the basis is now -8, which is more negative. The absolute value increased from 5 to 8. So the basis has widened in terms of absolute value. So the statement in option b is correct if "widening" refers to the absolute value. So the answer would be option b is correct.

Alternatively, if "widening" means the basis increasing (becoming more positive), then it's incorrect. But in finance, when they talk about basis widening, it usually refers to the absolute value increasing. For example, in contango, a widening basis would mean the contango (F - S) increases, so the basis (S-F) becomes more negative. So in that case, option b is correct.

Therefore, option b is correct?

Wait, but let me check the options again.

Option b says: "If the futures price increases more than the spot price, the basis widens." If basis is S-F, then yes, the basis becomes more negative, so the absolute value increases, so it's widening. So option b is correct.

But then why is option a incorrect? Because option a says basis is the difference between futures and spot (F - S), which is the opposite of the standard definition. So option a is incorrect.

Wait, but maybe the question is using the opposite definition. If the question defines basis as F - S, then option a is correct, and option b would be: if F increases more than S, then F - S increases, so basis widens. So that would also be correct. But then there could be two correct answers, which is unlikely.

Hmm, this is a problem. The question must have only one correct answer. Let me check again.

Alternatively, perhaps the correct answer is option a is correct, and the other options are wrong. Let me see:

If option a is correct (basis is F - S), then:

Option b: If F increases more than S, then F - S increases, so basis widens. So that's correct. But then both a and b would be correct, which can't be.

Alternatively, maybe the question's correct answer is a, and the other options are wrong. Let me see:

Option a is the definition. If that's correct, then the other options must be evaluated with basis = F - S.

Option c: If dividend increases, then F decreases (because of higher dividends), so basis (F - S) decreases. So the basis narrows. So option c's statement that it widens is wrong.

Option d: If storage costs decrease, F decreases (since cost of carry is lower), so basis (F - S) decreases. So basis narrows. So option d is wrong.

So if a is correct, then the answer is a. But I need to confirm the definition.

Alternatively, maybe the question's correct answer is a, but I thought basis is Spot - Futures. Let me check a source.

According to Investopedia: "The basis is an asset's spot price minus its futures price." So basis = Spot - Futures. Therefore, option a is incorrect because it says Futures - Spot. So option a is wrong.

Therefore, the correct answer must be option b, assuming that "widening" refers to the absolute value increasing.

Wait, but let me check option c again with the correct basis definition (Spot - Futures):

If dividend increases, F decreases, so basis (S-F) increases. So if basis was negative (contango), it becomes less negative. So the absolute value decreases. So the basis is narrowing. So option c is incorrect.

Option d: storage costs decrease, so F decreases, so basis increases (S-F). If basis was negative (contango), it becomes less negative, so narrowing. So option d is incorrect.

Thus, the only correct option is b.

Wait, but let me think again about option b. If the basis is S-F, and F increases more than S, then the basis becomes more negative. So the basis is moving further into contango, which is a widening of the contango spread. So in terms of the basis (S-F), it's becoming more negative, so the absolute value increases. So the basis is widening in absolute terms. So the answer is b.

Therefore, the correct answer is option b.

Wait, but the user's previous example had the correct answer as "c" for an apples question, so the format is to output the correct_answer_key in JSON. So here, the correct answer is option b?

Wait, but let me check again.

Wait, the question is in Thai, and the options are:

a: basis is futures - spot (incorrect per standard def)

b: if futures increases more than spot, basis widens (correct if widening is absolute)

c: if dividend increases, stock basis widens (incorrect)

d: if storage costs decrease, agri basis widens (incorrect)

Thus, the correct answer is b.

But wait, let me check another angle. Maybe the question's correct answer is a?

No, because the standard definition is spot - futures. So a is wrong.

Alternatively, maybe the question's correct answer is a, but the user might have a different definition. But according to standard finance, it's spot - futures. So a is wrong.

Therefore, the correct answer is option b.

Alright! Let's tackle this question about the basis of futures contracts. The user provided a multiple-choice question in Thai, asking which statement is correct regarding the basis. The options are labeled a through d.

First, I need to recall what "basis" means in the context of futures markets. From what I remember, the basis is generally the difference between the spot price (current market price of the asset) and the futures price (price of the futures contract). So, basis = spot price - futures price. A positive basis means the spot price is higher than the futures price, and a negative basis means the opposite.

Looking at option a: "Basis is the difference between the futures price and the spot price." Wait, that seems off because I thought it was spot minus futures. If the futures price is higher than the spot, the basis would be negative according to the standard formula. So, option a might not be accurate because it reverses the order.

Option b: "If the futures price increases more than the spot price, the basis will widen." Hmm, if futures increase more than spot, the difference (basis) could change. For example, if spot goes up by $1 and futures go up by $2, the basis (spot - futures) would decrease by $1. So, a widening basis here doesn't seem right. Maybe this option is incorrect.

Option c: "If the dividend yield increases while other factors remain constant, the basis of the stock futures will widen." Dividends can affect futures pricing because holding the physical stock entitles you to dividends, whereas futures do not. An increase in dividend yield should theoretically make the spot price more attractive compared to futures, potentially increasing the basis (spot - futures). So, this could be a correct statement.

Option d: "If transportation and storage costs decrease while other factors remain constant, the basis of agricultural futures will widen." Lower costs should reduce the convenience yield, which is the benefit of holding the physical asset. This might cause futures prices to rise relative to spot prices, thereby decreasing the basis (spot - futures). So, this option might not be correct.

Putting it all together, option c seems to be the correct answer because an increase in dividend yield should lead to a wider basis for stock futures.