With answers from 41 AI models.
กําหนดให้อัตราผลตอบแทนทีแท้จริงทีปราศจากความเสี่ยงเท่ากับ 2.5% อัตราผลตอบแทนทีเป็นตัวเงินทีปราศจากความเสี่ยงเท่ากับ 4% และส่วนชดเชยความเสี่ยงจากการลงทุนในหุ้นกู้ทีผู้ลงทุนให้ความสนใจจะลงทุนเท่ากับ 5% ให้คํานวณหาอัตราผลตอบแทนทีแท้จริงจากการลงทุนในหุ้นกู้ดังกล่าว โดยวิธีใช้ค่าประมาณการ
Using dataset from ThaiExam Dataset.
Let me break this down:
Therefore, the real return on the bond would be approximately 9%, which corresponds to option C.
{"correct_answer_key":"c"}
To solve this problem, I need to find the real return on the bond investment.
Given:
First, I need to find the nominal return on the bond: Nominal bond return = Nominal risk-free rate + Risk premium Nominal bond return = 4% + 5% = 9%
To convert this nominal return to a real return using approximation: Real return ≈ Nominal return - Inflation rate
The inflation rate can be derived from the Fisher equation: Nominal risk-free rate ≈ Real risk-free rate + Inflation rate 4% ≈ 2.5% + Inflation rate Inflation rate ≈ 1.5%
Therefore: Real return on the bond ≈ 9% - 1.5% = 7.5%
{"correct_answer_key":"b"}
Let me analyze this question in Thai and break it down:
The question is asking us to calculate the real rate of return on a bond investment using an approximation method, given the following:
First, I need to understand what formula to use. For finding the real rate of return, I can use the approximation method which essentially adds the risk premium to the real risk-free rate.
Real return ≈ Real risk-free rate + Risk premium
So in this case: Real return ≈ 2.5% + 5% = 7.5%
Let me verify this with another approach:
The difference between the nominal risk-free rate (4%) and the real risk-free rate (2.5%) is approximately the inflation rate, which is 1.5%.
The nominal return on the bond would be: Nominal return = Nominal risk-free rate + Risk premium = 4% + 5% = 9%
And to convert from nominal to real return using the approximation method: Real return ≈ Nominal return - Inflation rate = 9% - 1.5% = 7.5%
Both approaches give us 7.5%, which corresponds to option B.
Actually, let's double-check my work. The Fisher equation states that: (1 + Nominal rate) = (1 + Real rate) × (1 + Inflation rate)
We can rearrange to find the inflation rate: (1 + Inflation rate) = (1 + Nominal rate) / (1 + Real rate) (1 + Inflation rate) = (1 + 0.04) / (1 + 0.025) (1 + Inflation rate) = 1.04 / 1.025 (1 + Inflation rate) = 1.01463 Inflation rate ≈ 0.01463 or about 1.46%
Now, the nominal return on the bond is: Nominal return = Nominal risk-free rate + Risk premium = 4% + 5% = 9%
To find the real return using the Fisher equation: (1 + Real return) = (1 + Nominal return) / (1 + Inflation rate) (1 + Real return) = (1 + 0.09) / (1 + 0.01463) (1 + Real return) = 1.09 / 1.01463 (1 + Real return) = 1.0743 Real return ≈ 0.0743 or about 7.43%
This is very close to our approximation of 7.5%, confirming that option B is the correct answer.
The answer is B: 7.50%
This Thai question asks to calculate the real rate of return on a bond investment using an approximation method.
Given:
Using the approximation method, the real rate of return would be: Real return ≈ Real risk-free rate + Risk premium Real return ≈ 2.5% + 5% = 7.5%
This corresponds to option B.
{"correct_answer_key":"b"}
To solve this problem, we need to understand the relationship between the risk-free rate, the equity risk premium, and the required return on the investment. The formula to calculate the required return on an investment is:
Required Return = Risk-Free Rate + Equity Risk Premium
Given:
However, the question also mentions a "risk-free return in terms of money" of 4%, which seems to be a distraction or an additional piece of information not directly needed for the calculation of the required return on the bond investment. The key is the risk-free rate and the equity risk premium.
Using the formula:
Required Return = 2.5% + 5% = 7.5%
Thus, the correct answer is:
{"correct_answer_key":"b"}
The question involves calculating the real rate of return for a bond investment using the approximation method. Here's the breakdown:
Given:
Approximation Formula for Real Rate of Return (Real Yield): The approximation method for the real rate of return is: [ \text{Real Rate} \approx \text{Nominal Rate} - \text{Inflation Rate} ] However, we need to derive the inflation rate (π) first.
Calculate Inflation Rate (π): The Fisher equation (approximation) relates the nominal rate, real rate, and inflation: [ i \approx r + \pi ] Rearranged to solve for inflation: [ \pi \approx i - r = 4% - 2.5% = 1.5% ]
Nominal Rate for the Bond: The nominal rate for the bond includes the risk-free nominal rate and the risk premium: [ \text{Nominal Rate (Bond)} = i + \text{RP} = 4% + 5% = 9% ]
Real Rate for the Bond (Approximation): Using the approximation formula: [ \text{Real Rate (Bond)} \approx \text{Nominal Rate (Bond)} - \pi = 9% - 1.5% = 7.5% ]
The real rate of return for the bond is 7.5%, which corresponds to option B.
{"correct_answer_key":"b"}
Okay, let's try to figure out this problem. So, the question is about calculating the real rate of return from investing in a bond, using an estimation method. The given data includes a real risk-free rate of 2.5%, a nominal risk-free rate of 4%, and a risk premium for the bond investment of 5%. The options are a) 1.50%, b) 7.50%, c) 9.00%, d) 11.50%.
First, I need to recall the relationship between nominal and real rates. I remember the Fisher equation, which relates nominal interest rate, real interest rate, and inflation. The formula is:
Nominal rate ≈ Real rate + Inflation rate
But here, we have the nominal risk-free rate and the real risk-free rate. So maybe we can rearrange this to find the inflation rate. Let's see:
Inflation rate ≈ Nominal risk-free rate - Real risk-free rate Inflation rate = 4% - 2.5% = 1.5%
So the expected inflation rate is 1.5%. Now, the problem mentions a risk premium of 5% for investing in the bond. The total nominal return on the bond would be the nominal risk-free rate plus the risk premium. Wait, but the risk-free rate is already given as 4%, which is the nominal risk-free rate. So adding the risk premium to that would give the nominal return of the bond.
Nominal return on bond = Nominal risk-free rate + Risk premium Nominal return = 4% + 5% = 9%
But the question asks for the real rate of return on the bond. To convert the nominal return to real return, we subtract the inflation rate. Using the approximation method (since the question mentions using an estimate), the real return ≈ Nominal return - Inflation rate.
Real return ≈ 9% - 1.5% = 7.5%
So the real rate of return would be 7.5%, which is option b. Let me double-check. The real risk-free rate is 2.5%, and the risk premium is 5%, but since we're dealing with real returns, maybe there's another way. Wait, no. The risk premium is added to the nominal risk-free rate to get the nominal return, then subtract inflation to get real return. That seems right. Alternatively, could the real risk-free rate plus risk premium be the real return? That would be 2.5% +5% =7.5%, which is the same answer. So either way, the answer is 7.5%, option b.
The real risk-free rate is 2.5%, and the nominal risk-free rate is 4%. The inflation rate (approximated) is the difference: 4% - 2.5% = 1.5%. The bond's nominal return includes the risk premium: 4% (nominal risk-free) + 5% (risk premium) = 9%. Subtract inflation to get the real return: 9% - 1.5% = 7.5%. Thus, the real rate of return is 7.5%.
{"correct_answer_key":"b"}
This question is in Thai and asks about calculating the real rate of return on a bond investment using an approximation method. Here's the translation and solution:
Question: Given a real risk-free rate of return of 2.5%, a nominal risk-free rate of return of 4%, and a risk premium for the bond investment of interest equal to 5%, calculate the real rate of return on the said bond investment using the approximation method.
Solution:
The approximation method for calculating the real rate of return is:
Real Rate of Return ≈ Nominal Rate of Return - Inflation Rate
We can derive the inflation rate from the Fisher equation approximation:
Nominal Rate of Return ≈ Real Rate of Return + Inflation Rate
Therefore, Inflation Rate ≈ Nominal Rate of Return - Real Rate of Return
Inflation Rate ≈ 4% - 2.5% = 1.5%
Now, the nominal rate of return for the bond is the nominal risk-free rate plus the risk premium:
Nominal Return (Bond) = Nominal Risk-Free Rate + Risk Premium Nominal Return (Bond) = 4% + 5% = 9%
Finally, we can calculate the approximate real rate of return for the bond:
Real Return (Bond) ≈ Nominal Return (Bond) - Inflation Rate Real Return (Bond) ≈ 9% - 1.5% = 7.5%
{"correct_answer_key": "b"}
The question is in Thai and asks to calculate the real return on a bond investment using an approximation method. Here's the breakdown:
First, we need to find the nominal return on the bond. This is the nominal risk-free rate plus the risk premium: 4% + 5% = 9%.
Next, we approximate the real return by subtracting the inflation rate (implied by the difference between nominal and real risk-free rates) from the nominal return on the bond. The approximate inflation rate is 4% - 2.5% = 1.5%.
Therefore, the approximate real return on the bond is 9% - 1.5% = 7.5%.
{"correct_answer_key":"b"}
The question asks for the real return on a bond investment. We are given the real risk-free rate (2.5%), the nominal risk-free rate (4%), and a risk premium for the bond (5%). The real return on the bond can be approximated by adding the risk premium to the real risk-free rate.
Real Return (Bond) ≈ Real Risk-Free Rate + Risk Premium Real Return (Bond) ≈ 2.5% + 5% = 7.5%
{"correct_answer_key":"b"}
Explanation: The question is asking for the real return of a corporate bond using the approximation method. First, we need to find the inflation rate using the risk-free rates. Nominal risk-free rate ≈ Real risk-free rate + Inflation 4% ≈ 2.5% + Inflation Inflation ≈ 4% - 2.5% = 1.5%
Next, we need to find the nominal return of the corporate bond. Nominal return of corporate bond ≈ Nominal risk-free rate + Risk premium Nominal return of corporate bond ≈ 4% + 5% = 9%
Finally, we calculate the real return of the corporate bond. Nominal return of corporate bond ≈ Real return of corporate bond + Inflation 9% ≈ Real return of corporate bond + 1.5% Real return of corporate bond ≈ 9% - 1.5% = 7.5%
Therefore, the real return of the corporate bond is approximately 7.5%.
{"correct_answer_key":"b"}
คำนวณอัตราเงินเฟ้อที่คาดหวังโดยประมาณจากอัตราผลตอบแทนที่ปราศจากความเสี่ยง (4% - 2.5% = 1.5%) จากนั้นคำนวณอัตราผลตอบแทนที่เป็นตัวเงินจากการลงทุนในหุ้นกู้ (4% + 5% = 9%) และสุดท้ายคำนวณอัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้โดยประมาณ (9% - 1.5% = 7.5%)
{"correct_answer_key":"b"}
The question asks to calculate the real return on a bond investment using an approximation method, given the real risk-free rate, the nominal risk-free rate, and the risk premium for the bond.
Here's the breakdown:
Therefore, the approximate real return on the bond investment is 7.50%.
{"correct_answer_key":"b"}
Explanation:
The question asks for the approximate real rate of return on the bond investment. This can be calculated by adding the real risk-free rate to the risk premium for the bond.
Approximate Real Rate of Return on Bond = Real Risk-Free Rate + Risk Premium Approximate Real Rate of Return on Bond = 2.5% + 5% = 7.5%
Therefore, the approximate real rate of return on the bond investment is 7.5%.
{"correct_answer_key":"b"}
The question asks for the real rate of return on a bond, given the real risk-free rate, the nominal risk-free rate, and the risk premium. We can use the Fisher equation and the concept of risk premium to solve this.
The Fisher equation states: Nominal Rate = Real Rate + Inflation Expectation. We are given the real risk-free rate (2.5%) and the nominal risk-free rate (4%), so we can find the inflation expectation: 4% = 2.5% + Inflation, therefore Inflation = 1.5%.
The required rate of return on the bond is the risk-free rate plus the risk premium: 4% + 5% = 9%. Since the 4% is a nominal rate, and we're asked for the real rate of return, we need to adjust for inflation. However, the question asks us to use an approximation. The most direct approximation is to simply add the risk premium to the real risk-free rate: 2.5% + 5% = 7.5%. While a more precise calculation would involve adjusting the nominal rate for inflation, the question specifically asks for the approximate value.
{"correct_answer_key":"b"}
คำอธิบาย:
อัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้ ≈ อัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยง + ส่วนชดเชยความเสี่ยง
= 2.5% + 5% = 7.5%
ดังนั้น คำตอบที่ถูกต้องคือ ข้อ b
{"correct_answer_key":"b"}
The question asks to calculate the real rate of return on a bond investment using the approximation method. Given:
The approximate real rate of return on the bond is calculated by subtracting the inflation premium (nominal risk-free rate - real risk-free rate) from the total nominal return (nominal risk-free rate + risk premium):
Real return ≈ (Nominal risk-free rate + Risk premium) - (Nominal risk-free rate - Real risk-free rate)
= (4% + 5%) - (4% - 2.5%)
= 9% - 1.5%
= 7.5%
Therefore, the approximate real rate of return is 7.5%, which corresponds to option B.
{"correct_answer_key":"b"}
คำอธิบาย:
อัตราผลตอบแทนทีแท้จริงจากการลงทุนในหุ้นกู้สามารถคำนวณได้โดยการบวกส่วนชดเชยความเสี่ยงจากการลงทุนในหุ้นกู้ (5%) เข้ากับอัตราผลตอบแทนทีเป็นตัวเงินทีปราศจากความเสี่ยง (4%) แล้วลบด้วยอัตราผลตอบแทนทีแท้จริงทีปราศจากความเสี่ยง (2.5%) ซึ่งเป็นการประมาณค่าเบื้องต้น (approximate method):
ผลตอบแทนทีแท้จริง = 4% + 5% - 2.5% = 6.5%
แต่ในตัวเลือกไม่มี 6.5% จึงอาจเป็นการประมาณค่าที่ใกล้เคียงที่สุดในตัวเลือก ซึ่งคือ 7.50% (ตัวเลือก B)
{"correct_answer_key":"b"}
อัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้ สามารถคำนวณได้โดยใช้ค่าประมาณดังนี้:
อัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้ ≈ อัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยง + ส่วนชดเชยความเสี่ยง
= 2.5% + 5%
= 7.5%
ดังนั้น คำตอบที่ถูกต้องคือข้อ b (7.50%)
{"correct_answer_key":"b"}
To find the real rate of return on the bond investment, we can use the Fisher equation, which relates the nominal rate, real rate, and inflation rate. However, in this context, we are given the real risk-free rate, the nominal risk-free rate, and the risk premium for the bond. The real rate of return on the bond can be approximated by adding the real risk-free rate and the risk premium.
Given:
The real rate of return on the bond is approximately: Real risk-free rate + Risk premium = 2.5% + 5% = 7.5%
Thus, the correct answer is option B.
{"correct_answer_key":"b"}
ในการคำนวณอัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้ เราสามารถใช้สูตรดังนี้:
อัตราผลตอบแทนที่แท้จริง = อัตราผลตอบแทนที่เป็นตัวเงิน - ส่วนชดเชยความเสี่ยง
จากข้อมูลที่ให้มา:
ดังนั้น: อัตราผลตอบแทนที่แท้จริง = 4% - 5% = -1%
เนื่องจากไม่มีตัวเลือกที่ตรงกับผลลัพธ์นี้ อาจจะมีการเข้าใจผิดในคำถามหรือข้อมูลที่ให้มา แต่ถ้าต้องการคำนวณอัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้โดยใช้ค่าประมาณการ อาจจะต้องพิจารณาอัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยง (2.5%) และเพิ่มส่วนชดเชยความเสี่ยง (5%) ซึ่งจะได้:
อัตราผลตอบแทนที่แท้จริง = 2.5% + 5% = 7.5%
ดังนั้นคำตอบที่ถูกต้องคือ 7.50% ซึ่งตรงกับตัวเลือก b.
{"correct_answer_key":"b"}
To calculate the real rate of return on the bond investment, we start with the nominal risk-free rate of 4% and add the risk premium of 5% for investing in the bond. This gives a nominal return of 4% + 5% = 9%. Since the real risk-free rate is 2.5%, and assuming the real return adjusts similarly with the risk premium, the real rate of return on the bond can be approximated as the nominal return minus the inflation component. However, a simpler approximation often used is to directly consider the risk premium over the real risk-free rate. Given the options, the most consistent approximation is to add the risk premium to the real risk-free rate: 2.5% + 5% = 7.5%.
Thus, the real rate of return on the bond investment is approximately 7.5%, which corresponds to option B.
{"correct_answer_key":"b"}
First, the user has provided another multiple-choice question in JSON format. It's in Thai, but I need to understand it to provide a correct response.
Let me translate the question to English:
"กำหนดให้" means "Given that"
"อัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยง" means "real risk-free rate"
"เท่ากับ 2.5%" means "equal to 2.5%"
"อัตราผลตอบแทนที่เป็นตัวเงินที่ปราศจากความเสี่ยง" means "nominal risk-free rate" equal to 4%
"และส่วนชดเชยความเสี่ยงจากการลงทุนในหุ้นกู้ที่ผู้ลงทุนให้ความสนใจจะลงทุนเท่ากับ 5%" means "and the risk premium for investing in bonds that investors are interested in investing is equal to 5%"
"ให้คำนวณหาอัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้ดังกล่าว โดยวิธีใช้ค่าประมาณการ" means "Calculate the real rate of return from investing in the aforementioned bonds using approximation."
So, the question is: Given the real risk-free rate = 2.5%, the nominal risk-free rate = 4%, and the risk premium for bonds = 5%, calculate the real rate of return for the bonds using approximation.
Options:
a: 1.50%
b: 7.50%
c: 9.00%
d: 11.50%
Now, I need to recall the relationship between nominal and real rates. The Fisher equation relates them:
Nominal rate ≈ Real rate + Inflation rate
More precisely: (1 + nominal rate) = (1 + real rate) * (1 + inflation rate)
For approximation, nominal rate ≈ real rate + inflation rate
In this context, we have the real risk-free rate and the nominal risk-free rate.
The real risk-free rate is 2.5%, and the nominal risk-free rate is 4%. So, from these, we can find the inflation rate.
Using the Fisher equation:
Nominal risk-free rate = Real risk-free rate + Inflation rate (approximately)
So, Inflation rate ≈ Nominal risk-free rate - Real risk-free rate = 4% - 2.5% = 1.5%
For the bonds, the total expected return would include the risk premium.
The nominal return on bonds would be the nominal risk-free rate plus the risk premium.
So, Nominal return on bonds = Nominal risk-free rate + Risk premium = 4% + 5% = 9%
To find the real rate of return on bonds, we use the Fisher equation again:
Real return on bonds ≈ Nominal return on bonds - Inflation rate
From earlier, Inflation rate ≈ 1.5%
So, Real return on bonds ≈ 9% - 1.5% = 7.5%
That matches option b: 7.50%
Let me double-check.
The question asks for "อัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้" which is the real rate of return from investing in bonds.
And it specifies "โดยวิธีใช้ค่าประมาณการ" meaning using approximation.
So, yes, approximating real return = nominal return - inflation.
Where nominal return for bonds = risk-free nominal rate + risk premium = 4% + 5% = 9%
Inflation = nominal risk-free - real risk-free = 4% - 2.5% = 1.5%
Thus, real return = 9% - 1.5% = 7.5%
I think that's correct.
So, my response should be: First, a brief explanation, then respond in JSON with the "correct_answer_key".
Explanation: The real risk-free rate is 2.5%, and the nominal risk-free rate is 4%, so inflation is approximately 4% - 2.5% = 1.5%. The nominal return on bonds is 4% + 5% risk premium = 9%. Therefore, the real return on bonds is approximately 9% - 1.5% = 7.5%, which is option B.
Then, output: {"correct_answer_key":"b"}
อัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยงอยู่ที่ 2.5% และอัตราผลตอบแทนที่เป็นตัวเงินที่ปราศจากความเสี่ยงอยู่ที่ 4% ดังนั้น อัตราเงินเฟ้อโดยประมาณเท่ากับ 4% - 2.5% = 1.5%
อัตราผลตอบแทนที่เป็นตัวเงินจากการลงทุนในหุ้นกู้เท่ากับ อัตราผลตอบแทนที่เป็นตัวเงินที่ปราศจากความเสี่ยง + ส่วนชดเชยความเสี่ยง = 4% + 5% = 9%
อัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้โดยประมาณเท่ากับ 9% - 1.5% = 7.5% ซึ่งตรงกับตัวเลือก B
{"correct_answer_key":"b"}
อัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้สามารถคำนวณได้โดยการบวกอัตราผลตอบแทนที่เป็นตัวเงินกับส่วนชดเชยความเสี่ยง และแล้วลบด้วยอัตราเงินเฟ้อ (หรืออัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยง)
สูตรที่ใช้ในการคำนวณคือ:
อัตราผลตอบแทนที่แท้จริง = อัตราผลตอบแทนที่เป็นตัวเงิน + ส่วนชดเชยความเสี่ยง - อัตราเงินเฟ้อ
เมื่อแทนค่าที่กำหนดลงในสูตร:
อัตราผลตอบแทนที่แท้จริง = 4% (อัตราผลตอบแทนที่เป็นตัวเงิน) + 5% (ส่วนชดเชยความเสี่ยง) - 2.5% (อัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยง)
อัตราผลตอบแทนที่แท้จริง = 4% + 5% - 2.5%
อัตราผลตอบแทนที่แท้จริง = 6.5%
อย่างไรก็ตาม ตัวเลือกที่ใกล้เคียงที่สุดในคำถามคือ 7.50% ซึ่งอาจเกิดจากปัดเศษหรือการประมาณค่า
{"correct_answer_key":"b"}
To find the approximate real rate of return on the investment, we first need to understand the given information and the formula involved. The given information includes:
The nominal rate of return on the bond investment can be approximated by adding the nominal risk-free rate and the risk premium. So, nominal rate of return = 4% + 5% = 9%.
The real rate of return can be approximated using the formula: Real rate = Nominal rate - Inflation rate. However, we are not directly given the inflation rate, but we can derive it from the given real and nominal risk-free rates.
First, let's derive the inflation rate from the risk-free rates. The relationship between nominal and real risk-free rates is given by: (1 + Nominal risk-free rate) = (1 + Real risk-free rate) * (1 + Inflation rate).
Thus, (1 + 0.04) = (1 + 0.025) * (1 + Inflation rate). 1.04 = 1.025 * (1 + Inflation rate). 1 + Inflation rate = 1.04 / 1.025 = 1.0146. Inflation rate = 1.0146 - 1 = 0.0146 or 1.46%.
Now, to find the real rate of return on the bond, we use the nominal rate of return (9%) and the inflation rate (1.46%): Real rate of return = Nominal rate of return - Inflation rate = 9% - 1.46% = 7.54%.
Rounding to two decimal places as seen in the options, the closest value is 7.50%.
{"correct_answer_key":"b"}
To calculate the expected rate of return on the bond, we can use the Fisher equation and the concept of risk premium.
Given:
First, note that the difference between the nominal risk-free rate and the real risk-free rate can be approximated by the expected inflation rate. However, we are directly given these rates and the risk premium.
The nominal rate on the bond can be approximated by adding the risk premium to the nominal risk-free rate.
Nominal risk-free rate = 4% Risk premium = 5%
Thus, the expected nominal rate of return on the bond = Nominal risk-free rate + Risk premium = 4% + 5% = 9%
So, the correct answer is:
{"correct_answer_key":"c"}
To solve this problem, we need to calculate the expected return on investment considering the risk-free rate, the money market rate, and the risk premium. The formula to calculate the expected return is:
[ \text{Expected Return} = \text{Real Risk-Free Rate} + \text{Inflation Rate} + \text{Risk Premium} ]
Given:
We add these values together:
[ \text{Expected Return} = 2.5% + 4% + 5% = 11.5% ]
Therefore, the correct answer is option D.
{"correct_answer_key":"d"}
คำอธิบาย (โดยวิธีการคำนวณแบบประมาณการ):
• อัตราผลตอบแทนที่เป็นตัวเงินจากหุ้นกู้ = 4% (ปราศจากความเสี่ยง) + 5% (ส่วนชดเชยความเสี่ยง) = 9%
• ประมาณการอัตราเงินเฟ้อ = 4% (ตัวเงิน) − 2.5% (แท้จริง) = 1.5%
• ดังนั้น อัตราผลตอบแทนที่แท้จริงจากหุ้นกู้ ≈ 9% − 1.5% = 7.5%
ดังนั้นคำตอบที่ถูกต้องคือ:
{"correct_answer_key":"b"}
Risk‑free data allow us to infer expected inflation:
Approx. inflation ≈ nominal risk‑free – real risk‑free
≈ 4 % – 2.5 % = 1.5 %.
The bond’s expected nominal return = risk‑free nominal + risk premium
= 4 % + 5 % = 9 %.
Approximate real return on the bond ≈ nominal return – inflation
≈ 9 % – 1.5 % = 7.5 %.
Hence the real return is 7.50 %, choice (b).
{"correct_answer_key":"b"}
อัตราผลตอบแทนเป็นตัวเงินของหุ้นกู้ ≈ อัตราผลตอบแทนเป็นตัวเงินที่ปราศจากความเสี่ยง + ส่วนชดเชยความเสี่ยง
= 4% + 5% = 9%
อัตราเงินเฟ้อโดยประมาณ = อัตราผลตอบแทนเป็นตัวเงินที่ปราศจากความเสี่ยง – อัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยง
= 4% – 2.5% = 1.5%
อัตราผลตอบแทนที่แท้จริงของหุ้นกู้ ≈ 9% – 1.5% = 7.5%
{"correct_answer_key":"b"}
อัตราเงินเฟ้อคาดหวัง ≈ อัตราผลตอบแทนเป็นตัวเงินที่ปราศจากความเสี่ยง − อัตราผลตอบแทนแท้จริงที่ปราศจากความเสี่ยง
= 4% − 2.5% = 1.5%
อัตราผลตอบแทนเป็นตัวเงินของหุ้นกู้
= อัตราผลตอบแทนเป็นตัวเงินที่ปราศจากความเสี่ยง + ส่วนชดเชยความเสี่ยง
= 4% + 5% = 9%
อัตราผลตอบแทนแท้จริงของหุ้นกู้ (วิธีประมาณ)
≈ 9% − 1.5% = 7.5%
{"correct_answer_key":"b"}
The risk-free nominal rate is 4% and the risk-free real rate is 2.5%, which implies an inflation rate of approximately 1.5% (4% – 2.5%). When a risk premium of 5% is added to the risk-free nominal rate, the nominal yield for the bond becomes 9% (4% + 5%). Using the approximation method, the real yield is then roughly the nominal yield minus the inflation rate: 9% – 1.5% = 7.5%.
{"correct_answer_key": "b"}
การคํานวณโดยใช้วิธีค่าประมาณการจะใช้หลักการ Fisher Approximation ดังนี้
ดังนั้นคำตอบที่ถูกต้องคือ ตัวเลือก B.
{"correct_answer_key": "b"}
เพื่อหาผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้ ให้หาผลตอบแทนในรูปตัวเงินก่อนโดยบวกส่วนชดเชยความเสี่ยงเข้ากับอัตราผลตอบแทนที่เป็นตัวเงินที่ปราศจากความเสี่ยง คือ 4% + 5% = 9% จากนั้นหาดอกเบี้ยเงินเฟ้อโดยใช้วิธีประมาณการจากอัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยง ซึ่งคำนวณได้จาก 4% - 2.5% = 1.5% สุดท้ายคำนวณอัตราผลตอบแทนที่แท้จริงโดยการหักอัตราเงินเฟ้อออกจากผลตอบแทนที่ได้ในรูปตัวเงิน คือ 9% - 1.5% = 7.5%
{"correct_answer_key": "b"}
อัตราเงินเฟ้อโดยประมาณ = 4% – 2.5% = 1.5%
อัตราผลตอบแทนตราสารหนี้ = 4% + 5% = 9%
อัตราผลตอบแทนที่แท้จริง ≈ 9% – 1.5% = 7.5%
{"correct_answer_key":"b"}
อัตราผลตอบแทนตราสารหนี้ (nominal) ≈ อัตราปราศจากความเสี่ยงตัวเงิน 4% + ส่วนชดเชยความเสี่ยง 5% = 9%
อัตราเงินเฟ้อ ≈ 4% − 2.5% = 1.5%
อัตราผลตอบแทนที่แท้จริง ≈ 9% − 1.5% = 7.5%
{"correct_answer_key":"b"}
อัตราผลตอบแทนจากหุ้นกู้ (nominal) = 4% + 5% = 9%
ค่าเงินเฟ้อโดยประมาณ = 4% − 2.5% = 1.5%
อัตราผลตอบแทนที่แท้จริง ≈ 9% − 1.5% = 7.5%
{"correct_answer_key":"b"}
To calculate the real rate of return on the bond, we can use the Fisher equation, which relates the nominal rate, real rate, and inflation rate. The formula is:
[ 1 + \text{Nominal Rate} = (1 + \text{Real Rate}) \times (1 + \text{Inflation Rate}) ]
Given:
First, calculate the nominal rate for the bond:
[ \text{Nominal Rate for Bond} = \text{Nominal Risk-Free Rate} + \text{Risk Premium} = 0.04 + 0.05 = 0.09 \text{ or } 9% ]
Next, calculate the inflation rate using the real and nominal risk-free rates:
[ 1 + 0.04 = (1 + 0.025) \times (1 + \text{Inflation Rate}) ]
[ 1.04 = 1.025 \times (1 + \text{Inflation Rate}) ]
[ 1 + \text{Inflation Rate} = \frac{1.04}{1.025} \approx 1.01463 ]
[ \text{Inflation Rate} \approx 0.01463 \text{ or } 1.463% ]
Now, use the Fisher equation to find the real rate of return for the bond:
[ 1 + \text{Nominal Rate for Bond} = (1 + \text{Real Rate for Bond}) \times (1 + \text{Inflation Rate}) ]
[ 1.09 = (1 + \text{Real Rate for Bond}) \times 1.01463 ]
[ 1 + \text{Real Rate for Bond} = \frac{1.09}{1.01463} \approx 1.074 ]
[ \text{Real Rate for Bond} \approx 0.074 \text{ or } 7.4% ]
Using approximation, the closest answer is 7.50%.
{"correct_answer_key":"b"}
ในการคำนวณอัตราผลตอบแทนที่แท้จริง (real rate of return) จากการลงทุนในหุ้นกู้ เราใช้ความสัมพันธ์ระหว่างอัตราผลตอบแทนที่แท้จริง (real rate) อัตราเงินเฟ้อ (inflation rate) และอัตราผลตอบแทนที่เป็นตัวเงิน (nominal rate) ดังนี้:
$$ \text{Nominal Rate} = \text{Real Rate} + \text{Inflation Rate} + (\text{Real Rate} \times \text{Inflation Rate}) $$
แต่ในกรณีนี้ เราจะใช้วิธีประมาณการง่าย ๆ โดยไม่พิจารณาผลคูณของ real rate และ inflation rate:
ข้อมูลที่ให้มา:
คำนวณอัตราเงินเฟ้อ (Inflation Rate): อัตราเงินเฟ้อสามารถประมาณได้จากความแตกต่างระหว่างอัตราผลตอบแทนที่เป็นตัวเงินและอัตราผลตอบแทนที่แท้จริง: $$ \text{Inflation Rate} = \text{Nominal Risk-Free Rate} - \text{Real Risk-Free Rate} $$ $$ \text{Inflation Rate} = 4% - 2.5% = 1.5% $$
คำนวณอัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้: อัตราผลตอบแทนที่แท้จริงจากการลงทุนในหุ้นกู้สามารถประมาณได้โดยการเพิ่มส่วนชดเชยความเสี่ยงเข้ากับอัตราผลตอบแทนที่แท้จริงที่ปราศจากความเสี่ยง: $$ \text{Real Rate of Return on Bond} = \text{Real Risk-Free Rate} + \text{Risk Premium} $$ $$ \text{Real Rate of Return on Bond} = 2.5% + 5% = 7.5% $$
ดังนั้น คำตอบคือ 7.50% ซึ่งตรงกับตัวเลือก b.
{"correct_answer_key":"b"}
Okay, let's tackle this problem step by step. The question is in Thai, but I'll try to parse it carefully. The user wants to calculate the real return on a bond investment using some given rates. Let me break down the information provided.
First, the problem states:
They want the real return on the bond using an estimation method. Hmm, I need to recall the relationship between these terms.
I remember that the nominal risk-free rate (like a Treasury bill) is typically the real risk-free rate plus inflation. But here, maybe they're using the Fisher equation or something similar. Wait, but the question mentions a risk premium for the bond. So the total required return on the bond would be the nominal risk-free rate plus the risk premium? Or is it the real risk-free rate plus inflation plus risk premium?
Wait, let me think again. The nominal risk-free rate already includes the real rate plus expected inflation. So if the real risk-free rate is 2.5% and the nominal is 4%, then the inflation premium would be 4% - 2.5% = 1.5%.
Then, when calculating the required return on a risky asset like a corporate bond, the formula is usually:
Required return = Real risk-free rate + Inflation premium + Risk premium.
Alternatively, sometimes it's presented as the nominal risk-free rate plus the risk premium. Wait, but the nominal risk-free rate already includes inflation. Let me check the components again.
The nominal risk-free rate (like T-bill) is real risk-free rate + inflation. So if the nominal is 4% and real is 2.5%, inflation is 1.5%.
Then, for a corporate bond, the required return would be the nominal risk-free rate (4%) plus the risk premium (5%), totaling 9%. But that would be the nominal return. However, the question asks for the real return.
Alternatively, maybe the real return is calculated as (1 + nominal return)/(1 + inflation) -1. But I need to see what exactly the question is asking for. The question says "อัตราผลตอบแทนทีแท้จริงจากการลงทุนในหุ้นกู้" which translates to the real return on the bond investment.
Wait, perhaps the question is expecting to use the real risk-free rate plus the risk premium? Because the real risk-free rate is already adjusted for inflation, so adding the risk premium would give the real return. Let me see:
If the real risk-free rate is 2.5%, and the risk premium is 5%, then the real return would be 2.5% +5% =7.5%? But that might not account for inflation. Alternatively, maybe the nominal return is 4% (nominal risk-free) +5% risk premium =9%, then convert that to real return by subtracting inflation? Wait, but inflation here is 1.5% (since 4% nominal =2.5% real +1.5% inflation).
So if the nominal return on the bond is 9%, then the real return would be (9% -1.5%) =7.5%? Or using the Fisher equation: (1 + nominal)/(1 + inflation) -1 = (1.09)/(1.015) -1 ≈ 7.38%, which is close to 7.5%. But the options have 7.5% as option b. Alternatively, maybe the question is simpler, just adding the real risk-free rate and the risk premium, ignoring inflation? That would give 2.5+5=7.5.
Alternatively, maybe the question is considering that the nominal risk-free rate is 4%, which includes inflation, so the real return on the bond would be nominal rate (4%) plus risk premium (5%) minus inflation (1.5%)? That would be 4+5=9, then subtract inflation? Wait, that might not be right.
Alternatively, perhaps the real return is calculated as the nominal return minus inflation. The nominal return on the bond is the nominal risk-free rate (4%) plus the risk premium (5%) =9%. Then real return is 9% -1.5% inflation =7.5%. That would be option b.
Alternatively, maybe the question is expecting to use the real risk-free rate plus the risk premium, so 2.5 +5 =7.5. That would also give option b.
Looking at the options, 7.5% is option b. The other options: a is 1.5 which is the inflation, c is 9 which is the nominal return, d is higher.
The question says "อัตราผลตอบแทนทีแท้จริง" which is real return. So the correct approach is to take the nominal return (4% +5% =9%) and subtract inflation (1.5%) to get real return of 7.5%. Alternatively, using the formula: real return = (nominal return - inflation).
Alternatively, using the Fisher equation: real return ≈ nominal return - inflation. So 9% -1.5% =7.5%.
Therefore, the correct answer should be B)7.50%.
The real return on the bond is calculated by first determining the nominal return (nominal risk-free rate + risk premium) and then adjusting for inflation. The nominal risk-free rate (4%) includes an inflation premium of 1.5% (4% - 2.5%). The bond's nominal return is 4% + 5% = 9%. Subtracting the inflation premium (1.5%) gives the real return: 9% - 1.5% = 7.5%. This corresponds to option B.
{"correct_answer_key":"b"}
To find the real return on the investment, we need to subtract the inflation rate from the nominal return. The nominal return is the sum of the risk-free rate and the risk premium.
The risk-free rate is 2.5% (real) and 4% (nominal). The risk premium is 5%.
First, we need to find the inflation rate. The inflation rate can be calculated as the difference between the nominal and real risk-free rates: 4% - 2.5% = 1.5%.
Now, we can find the nominal return on the investment: 4% (risk-free nominal) + 5% (risk premium) = 9%.
Finally, we can find the real return on the investment by subtracting the inflation rate from the nominal return: 9% - 1.5% = 7.5%.
So, the real return on the investment is 7.5%, which corresponds to option B.
{"correct_answer_key":"b"}
Alright! Let's tackle this problem step by step. The user provided a question in Thai about calculating the real risk-free rate of return on an investment. The given data includes the real risk-free rate (2.5%), the nominal risk-free rate (4%), and the risk premium (5%). The options are percentages, so I need to figure out the correct percentage that represents the real risk-free rate from the investment.
First, I recall that the relationship between these rates can be approximated using the Fisher equation. The Fisher equation states that the nominal interest rate is approximately equal to the sum of the real interest rate and the expected inflation rate. However, in this case, we're dealing with the real risk-free rate and the risk premium, so I need to adjust my approach.
The risk premium is the excess return demanded by investors for taking on additional risk compared to a risk-free investment. So, if the nominal risk-free rate is 4% and the risk premium is 5%, the total expected return from the risky investment would be the sum of these two, which is 9%.
But wait, the question asks for the real risk-free rate from the investment. Since the real risk-free rate given is 2.5%, and we've calculated the total expected return as 9%, I need to reconcile these numbers. It seems there might be some confusion here because the real risk-free rate is already provided, and the risk premium is an additional component.
Perhaps the question is asking to confirm the real risk-free rate in the context of the given nominal rate and risk premium. If the nominal rate is 4% and the risk premium is 5%, the real risk-free rate should still be 2.5% as it's independent of the risk premium. The risk premium is added to the nominal risk-free rate to account for risk, resulting in a total expected return of 9%, but the real risk-free rate remains unchanged at 2.5%.
Looking at the options, option A is 1.50%, which is lower than the given real rate. Option B is 7.50%, which doesn't align with the given data. Option C is 9.00%, which matches the total expected return but not the real risk-free rate. Option D is 11.50%, which is even higher. Therefore, none of the options directly match the given real risk-free rate of 2.5%. This suggests there might be a misunderstanding in the problem setup or the options provided.
However, considering the closest logical answer based on standard financial formulas, if we were to calculate the real rate from the nominal rate and an implied inflation rate, but since inflation isn't mentioned, it's unclear. Given the information, the most accurate answer we can provide is that the real risk-free rate is 2.5%, but since that's not an option, there might be an error in the question or options.
{"correct_answer_key":"a"}