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.

This is a question in Thai about basis in futures contracts. Let me translate and analyze each option:

a) "Basis is the difference between futures price and spot price" b) "If futures price increases more than spot price, the basis will widen" c) "If dividend yield increases while other factors remain constant, the basis of common stock futures will widen" d) "If transportation and storage costs decrease while other factors remain constant, the basis of agricultural futures will widen"

Let me analyze each option:

a) This is correct. Basis = Futures price - Spot price

b) This is correct. If futures price increases more than spot price, the difference (basis) becomes larger/wider.

c) For stock futures, the theoretical futures price = Spot × e^((r-q)T), where r is risk-free rate and q is dividend yield. If dividend yield increases, the futures price decreases, making the basis narrower (more negative), not wider. This is incorrect.

d) For commodity futures with cost of carry, futures price = Spot + Storage costs + Transportation costs. If these costs decrease, the futures price decreases, making the basis narrower, not wider. This is incorrect.

So options a and b are correct. Since the question asks which option is correct (singular), I need to check if this is asking for all correct options or just one. The question format seems to be asking for which option is correct, implying there might be multiple correct answers. However, given the standard multiple choice format, I should identify the most fundamentally correct answer.

Option a) is the fundamental definition of basis, while option b) is a consequence of that definition. So option a) would be the primary correct answer.

This is a Thai language question about futures contracts basis. Let me translate and analyze each option:

The question asks: "Which of the following options is correct about the basis of futures contracts?"

Let me analyze each option:

a) "เบสิสคือผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง (Spot price)" Translation: "Basis is the difference between futures price and underlying asset price (Spot price)"

This is correct. Basis = Futures Price - Spot Price

b) "หากราคาสัญญาฟิวเจอร์สเพิ่มขึ้นมากกว่าราคาสินทรัพย์อ้างอิง (Spot price) จะทำให้เบสิสกว้างขึ้น" Translation: "If futures price increases more than the underlying asset price (Spot price), it will make the basis wider"

This is correct. If futures price increases more than spot price, the basis (F-S) becomes larger/wider.

c) "หากอัตราจ่ายเงินปันผลเพิ่มขึ้นในขณะที่ปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สหุ้นสามัญกว้างขึ้น" Translation: "If dividend yield increases while other factors remain constant, it will make the basis of stock futures wider"

Let me think about this. For stock futures, the theoretical fair value is: F = S × e^((r-d)×T) Where r is risk-free rate, d is dividend yield, T is time to maturity

If dividend yield increases, the futures price will actually decrease. This means the basis would narrow, not widen. The statement is incorrect.

d) "หากต้นทุนค่าขนส่งและค่าเก็บรักษาลดลงโดยปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สินค้าเกษตรกว้างขึ้น" Translation: "If transportation and storage costs decrease while other factors remain constant, it will make the basis of commodity futures wider"

I'll analyze the impact of storage costs on futures pricing. Lower storage costs typically reduce the futures price relative to the spot price, which would narrow the basis.

I'm carefully comparing the options, recognizing subtle nuances in their definitions. Option (a) provides a basic basis definition, while option (b) describes basis behavior. The key is understanding how futures and spot prices interact.

The critical insight is how basis is defined - most financial contexts use F-S as the standard calculation. This means carefully examining each statement's precise wording becomes crucial for determining accuracy.

I'm leaning towards option (a) as the most fundamental definition, since it establishes the core mathematical relationship between futures and spot prices. Option (b) describes a scenario, but doesn't capture the essential definitional aspect.

My systematic analysis suggests option (a) represents the most universally applicable and precise statement about basis in financial terminology.

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"

First, the user is providing another multiple-choice question in JSON format. I need to follow the same pattern as before: provide a brief explanation, then respond in JSON with the "correct_answer_key".

The question is in Thai: "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 price (Spot price)"

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

c: "หากอัตราจ่ายเงินปันผลเพิ่มขึ้นในขณะที่ปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สหุ้นสามัญกว้างขึ้น" – "If the dividend payout rate increases while other factors remain constant, it will make the basis of stock futures wider"

d: "หากต้นทุนค่าขนส่งและค่าเก็บรักษาลดลงโดยปัจจัยอื่นคงที่ จะทำให้เบสิสของสัญญาฟิวเจอร์สินค้าเกษตรกว้างขึ้น" – "If transportation and storage costs decrease while other factors remain 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.

Let me verify each option:

a: This directly states that basis is the difference between the futures price and the spot price. Actually, the standard definition is Basis = Spot Price - Futures Price. So, if it's "ผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง", it might be interpreted as Futures Price - Spot Price, which is the negative of the usual basis. Wait, no: in Thai, "ผลต่างของ A กับ B" could mean A minus B or the difference between A and B. But in financial contexts, it's often Spot minus Futures. I need to be precise.

Upon double-checking, in futures markets, Basis is commonly Spot Price minus Futures Price. Option a says: "ผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง", which translates to "the difference of the futures contract price with the reference asset price". This is ambiguous, but it might be interpreted as Futures minus Spot, which is not the standard definition. Wait, actually, some sources define it as Futures minus Spot, but I believe the most common is Spot minus Futures.

This is tricky. Let me think: In many textbooks, Basis = Spot Price - Futures Price. For example, if Spot is 100 and Futures is 102, Basis is -2, meaning contango.

But option a might be correct if it's just stating the difference, regardless of order. However, to be accurate, I should check if it's precisely defined.

Perhaps a is correct as it is the basic definition.

b: If futures price increases more than spot price, say spot stays the same, futures goes up, then if Basis = Spot - Futures, an increase in Futures would make Basis more negative, so the absolute difference might widen, but "กว้างขึ้น" means "widens", which could refer to the magnitude.

In futures, a widening basis typically means the difference is getting larger in absolute terms.

If Futures increases while Spot stays the same, Basis (Spot - Futures) becomes more negative, so the basis is widening (from say 0 to -5).

So, b seems correct.

c: For stock futures, the basis is affected by dividends. The cost of carry model: Futures price = Spot price + interest - dividends.

If dividends increase, that would decrease the Futures price (all else equal), so Basis = Spot - Futures would increase (become less negative or positive).

If dividends increase, Futures price decreases, so Spot - Futures increases (if it was negative, it becomes less negative).

But the option says "จะทำให้เบสิส...กว้างขึ้น" meaning "make the basis wider".

If Basis was negative and becomes less negative, it's narrowing, not widening.

For example, suppose Basis was -5, and after increase in dividends, Futures drops, say Basis becomes -3, that's narrowing.

So, c is incorrect because increasing dividends would narrow the basis for stocks, not widen it.

d: For agricultural futures, basis includes storage costs. If storage and transportation costs decrease, that would affect the Futures price.

In the cost of carry, lower costs would mean lower Futures price for commodities that require storage.

For commodities, Futures price = Spot + storage costs + interest.

If storage costs decrease, Futures price decreases, so Basis = Spot - Futures increases (less negative).

Again, this would narrow the basis if it was negative.

So, d says it would make the basis wider, which is incorrect; it should narrow it.

Therefore, only a and b seem potentially correct, but let's confirm.

Upon second thought, for b: If futures price increases more than spot, say spot increases by 1, futures by 3, then Basis = Spot - Futures: suppose initially Spot 100, Futures 102, Basis -2.

After, Spot 101, Futures 105, Basis 101-105 = -4, so wider (from -2 to -4).

If spot stays the same and futures increases, it widens.

So b is correct.

The question is "which of the following is correct", and it might be multiple, but it's multiple choice, so likely one.

The original format is single choice.

Option a might be incorrect if the definition is not precise.

Upon checking online or standard definition: Basis is often "the difference between the local cash price and the futures price", and it can be Spot minus Futures.

In the option, it says "ผลต่างของราคาสัญญาฟิวเจอร์สกับราคาสินทรัพย์อ้างอิง", which is "the difference of futures price with spot price", which could be Futures minus Spot.

In Thai, it's ambiguous, but in English, it's "the difference between A and B" is |A-B|, but in finance, it's specified.

Perhaps in this context, a is intended to be correct.

Maybe the correct one is b, as it's more precisely stated.

Let's think: the question is from a Thai source, and in Thai finance, it's likely standard.

Upon reflection, I believe a is correct, as it's the definition.

The user might expect b as correct, but I need to choose one.

Perhaps all are to be evaluated, and only a and b are correct, but since it's multiple choice with a single answer, maybe a is the primary one.

The JSON has a, b, c, d, so likely single choice.

From my analysis, c and d are incorrect, a and b are correct, but the question implies one.

Perhaps the question is to identify the correct statement, and both a and b are, but I need to see the original intent.

Maybe in the context, a is the definition, so it's correct.

To match the previous response, I need to pick one.

Perhaps the correct answer is a, as it's the basic definition.

Let's assume a is correct.

In my initial thought, b is also correct.

Perhaps the question is designed for a as the answer.

To be precise, I'll go with a, as it's the fundamental one.

No, let's double-check the options. The user provided it as is, and I need to respond with one.

Upon second thought, in the previous interaction, the answer was c for that question.

For this, I need to decide.

Perhaps I can look for which one is unequivocally correct.

Another way: in some tests, a is the definition, so it's correct.

I think I'll go with a as the correct answer.

So, brief explanation: The basis in futures contracts is indeed the difference between the futures price and the spot price.

Then, respond 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.