| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | 要计算异常收益（Abnormal Return），我们需要按照以下步骤进行： 1. **使用资本资产定价模型（CAPM）计算投资组合的预期收益。** 2. **计算投资组合的实际收益。** 3. **从实际收益中减去预期收益以找到异常收益。** ### 1. 计算预期收益（Expected Return） 根据CAPM公式，预期收益可以表示为： \[ \text{Expected Return} = R_f + \beta \times (R_m - R_f) \] 其中： - \( R_f \) 是无风险利率（4%） - \( R_m \) 是市场预期收益率（12%） - \( \beta \) 是投资组合的贝塔系数（1.8） 将这些值代入公式，我们得到： \[ \text{Expected Return} = 0.04 + 1.8 \times (0.12 - 0.04) \] \[ \text{Expected Return} = 0.04 + 1.8 \times 0.08 \] \[ \text{Expected Return} = 0.04 + 0.144 \] \[ \text{Expected Return} = 0.184 \text{ 或 } 18.4\% \] ### 2. 计算实际收益（Actual Return） 实际收益可以通过投资组合的期初值和期末值计算： \[ \text{Actual Return} = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \] 将给定的期初值和期末值代入公式： \[ \text{Actual Return} = \frac{60,000 - 50,000}{50,000} \] \[ \text{Actual Return} = \frac{10,000}{50,000} \] \[ \text{Actual Return} = 0.2 \text{ 或 } 20\% \] ### 3. 计算异常收益（Abnormal Return） 异常收益是实际收益减去预期收益： \[ \text{Abnormal Return} = \text{Actual Return} - \text{Expected Return} \] 将计算得出的实际收益和预期收益代入公式： \[ \text{Abnormal Return} = 0.2 - 0.184 \] \[ \text{Abnormal Return} = 0.016 \text{ 或 } 1.6\% \] ### 结论 投资组合的异常收益为 **1.6%**。 |
0.016 |
| deepseekr1 | The abnormal return is calculated by subtracting the expected return (from CAPM) from the actual return of the portfolio. Here's the step-by-step solution: 1. **Calculate Actual Return**: \[ \text{Actual Return} = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} = \frac{60,000 - 50,000}{50,000} = 20\% \] 2. **Calculate Expected Return (CAPM)**: \[ \text{Expected Return} = R_f + \beta \times (R_m - R_f) = 4\% + 1.8 \times (12\% - 4\%) = 4\% + 14.4\% = 18.4\% \] 3. **Determine Abnormal Return**: \[ \text{Abnormal Return} = \text{Actual Return} - \text{Expected Return} = 20\% - 18.4\% = 1.6\% \] **Answer**: The abnormal return is **1.6%**. |
0.016 |
| gpto1 | To calculate the abnormal return, we'll follow these steps: **1. Calculate the Expected Return using the Capital Asset Pricing Model (CAPM):** \[ \text{Expected Return (E(Rp))} = Rf + \beta_p (R_m - Rf) \] Where: - \( Rf \) = Risk-free rate = 4% - \( \beta_p \) = Beta of the portfolio = 1.8 - \( R_m \) = Market return = 12% First, calculate \( R_m - Rf \): \[ R_m - Rf = 12\% - 4\% = 8\% \] Then, calculate the expected return: \[ \begin{align*} E(Rp) &= 4\% + 1.8 \times 8\% \\ &= 4\% + 14.4\% \\ &= 18.4\% \end{align*} \] **2. Calculate the Actual Return of the Portfolio:** \[ \text{Actual Return} = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \] \[ \text{Actual Return} = \frac{\$60,000 - \$50,000}{\$50,000} = \frac{\$10,000}{\$50,000} = 0.20 \text{ or } 20\% \] **3. Calculate the Abnormal Return:** \[ \text{Abnormal Return} = \text{Actual Return} - \text{Expected Return} = 20\% - 18.4\% = 1.6\% \] **Answer: The abnormal return is 1.6%.** |
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| GPT-4o | To calculate the abnormal return, we need to follow these steps: 1. **Calculate the Portfolio Return:** The portfolio return can be calculated using the beginning and ending values of the portfolio. \[ \text{Portfolio Return (Rp)} = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \times 100 \] Plugging in the values: \[ \text{Rp} = \frac{60,000 - 50,000}{50,000} \times 100 = \frac{10,000}{50,000} \times 100 = 20\% \] 2. **Calculate the Expected Return using the Capital Asset Pricing Model (CAPM):** The expected return (Re) can be determined using the CAPM formula: \[ \text{Expected Return (Re)} = Rf + \beta \times (Rm - Rf) \] Where: - \( Rf \) is the risk-free rate - \( \beta \) is the beta of the portfolio - \( Rm \) is the market return Given: - \( Rf = 4\% \) - \( \beta = 1.8 \) - \( Rm = 12\% \) Plugging in these values: \[ \text{Re} = 4\% + 1.8 \times (12\% - 4\%) = 4\% + 1.8 \times 8\% = 4\% + 14.4\% = 18.4\% \] 3. **Calculate the Abnormal Return:** The abnormal return is the difference between the actual portfolio return and the expected portfolio return. \[ \text{Abnormal Return} = \text{Rp} - \text{Re} \] Plugging in the calculated values: \[ \text{Abnormal Return} = 20\% - 18.4\% = 1.6\% \] Therefore, the abnormal return is 1.6%. |
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| llama3.1-70B-Instruct | To calculate the abnormal return, we need to first calculate the expected return of the portfolio using the Capital Asset Pricing Model (CAPM). The CAPM formula is: Expected Return = Rf + β(Rm - Rf) Where: Rf = Risk-free rate = 4% Rm = Market return = 12% β = Beta of the portfolio = 1.8 Plugging in the values, we get: Expected Return = 4% + 1.8(12% - 4%) = 4% + 1.8(8%) = 4% + 14.4% = 18.4% Next, we need to calculate the actual return of the portfolio. We can do this by finding the percentage change in the portfolio's value: Actual Return = (Ending Value - Beginning Value) / Beginning Value = ($60,000 - $50,000) / $50,000 = $10,000 / $50,000 = 20% Now, we can calculate the abnormal return by subtracting the expected return from the actual return: Abnormal Return = Actual Return - Expected Return = 20% - 18.4% = 1.6% Therefore, the abnormal return is 1.6%. |
0.016 |
| llama3.1-405B-Instruct | To calculate the abnormal return, we first need to calculate the expected return of the portfolio using the Capital Asset Pricing Model (CAPM). The CAPM formula is: Expected Return = Rf + β(Rm - Rf) Where: - Rf is the risk-free rate (4% in this case) - β is the beta of the portfolio (1.8 in this case) - Rm is the return of the market (12% in this case) Plugging in the values, we get: Expected Return = 4% + 1.8(12% - 4%) Expected Return = 4% + 1.8(8%) Expected Return = 4% + 14.4% Expected Return = 18.4% Next, we need to calculate the actual return of the portfolio. The actual return is the difference between the ending value and the beginning value, divided by the beginning value. Actual Return = (Ending Value - Beginning Value) / Beginning Value Actual Return = ($60,000 - $50,000) / $50,000 Actual Return = $10,000 / $50,000 Actual Return = 20% Finally, we can calculate the abnormal return by subtracting the expected return from the actual return. Abnormal Return = Actual Return - Expected Return Abnormal Return = 20% - 18.4% Abnormal Return = 1.6% Therefore, the abnormal return is 1.6%. This means that the portfolio earned a return that was 1.6% higher than what was expected based on its beta and the market return. |
0.016 |
| DeepSeek-Coder-V2 | To calculate the abnormal return, we need to follow these steps: 1. Calculate the expected return of the portfolio using the Capital Asset Pricing Model (CAPM). 2. Calculate the actual return of the portfolio. 3. Subtract the expected return from the actual return to find the abnormal return. Step 1: Calculate the expected return using CAPM The CAPM formula is: Expected Return (ER) = Rf + Beta * (Rm - Rf) Where: - Rf = Risk-free rate (4%) - Rm = Market return (12%) - Beta = Beta of the portfolio (1.8) Plugging in the values: ER = 4% + 1.8 * (12% - 4%) ER = 4% + 1.8 * 8% ER = 4% + 14.4% ER = 18.4% Step 2: Calculate the actual return of the portfolio Actual Return (AR) = (Ending Value - Beginning Value) / Beginning Value Where: - Ending Value = $60,000 - Beginning Value = $50,000 Plugging in the values: AR = ($60,000 - $50,000) / $50,000 AR = $10,000 / $50,000 AR = 0.20 or 20% Step 3: Calculate the abnormal return Abnormal Return (ABR) = Actual Return (AR) - Expected Return (ER) Plugging in the values: ABR = 20% - 18.4% ABR = 1.6% The abnormal return is 1.6%. |
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| Qwen2-72B-Instruct | To calculate the abnormal return, we first need to determine the expected return of the portfolio using the Capital Asset Pricing Model (CAPM) formula. The CAPM formula is: Expected Return = Rf + Beta * (Rm - Rf) where: Rf = Risk-free rate (4% or 0.04) Rm = Market return (12% or 0.12) Beta = Beta of the portfolio (1.8) Plugging the values into the formula: Expected Return = 0.04 + 1.8 * (0.12 - 0.04) Expected Return = 0.04 + 1.8 * 0.08 Expected Return = 0.04 + 0.144 Expected Return = 0.184 or 18.4% Next, we need to calculate the actual return of the portfolio. The return can be calculated using the following formula: Return = (Ending Value - Beginning Value) / Beginning Value where: Beginning Value = $50,000 Ending Value = $60,000 Plugging the values into the formula: Return = ($60,000 - $50,000) / $50,000 Return = $10,000 / $50,000 Return = 0.20 or 20% Finally, we can calculate the abnormal return by subtracting the expected return from the actual return: Abnormal Return = Actual Return - Expected Return Abnormal Return = 0.20 - 0.184 Abnormal Return = 0.016 or 1.6% Therefore, the abnormal return is 1.6%. |
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| baichuan4 | To calculate the abnormal return, we first need to determine the expected return of the portfolio using the Capital Asset Pricing Model (CAPM) formula: \[ E(R_i) = R_f + \beta_i (R_m - R_f) \] where: - \(E(R_i)\) is the expected return of the portfolio, - \(R_f\) is the risk-free rate (4%), - \(\beta_i\) is the beta of the portfolio (1.8), - \(R_m\) is the expected market return (12%). Let's plug in the values: \[ E(R_i) = 4\% + 1.8 \times (12\% - 4\%) \] \[ E(R_i) = 4\% + 1.8 \times 8\% \] \[ E(R_i) = 4\% + 14.4\% \] \[ E(R_i) = 18.4\% \] The expected return of the portfolio is 18.4%. Next, we calculate the actual return of the portfolio using the beginning and ending values: \[ \text{Actual Return} = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \] \[ \text{Actual Return} = \frac{\$60,000 - \$50,000}{\$50,000} \] \[ \text{Actual Return} = \frac{\$10,000}{\$50,000} \] \[ \text{Actual Return} = 20\% \] Now, we can calculate the abnormal return, which is the difference between the actual return and the expected return: \[ \text{Abnormal Return} = \text{Actual Return} - E(R_i) \] \[ \text{Abnormal Return} = 20\% - 18.4\% \] \[ \text{Abnormal Return} = 1.6\% \] Therefore, the abnormal return of the portfolio is 1.6%. |
0.016 |
| doubao | Expected return = Rf + Beta * (Rm - Rf) = 4% + 1.8 * (12% - 4%) = 4% + 1.8 * 8% = 4% + 14.4% = 18.4% Actual return = ($60,000 - $50,000) / $50,000 = 20% Abnormal return = Actual return - Expected return = 20% - 18.4% = 1.6% |
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| minimax | To calculate the abnormal return, we first need to determine the expected return based on the Capital Asset Pricing Model (CAPM). The CAPM formula is: \[ E(R_i) = R_f + \beta_i (R_m - R_f) \] where: - \( E(R_i) \) is the expected return on the investment - \( R_f \) is the risk-free rate - \( \beta_i \) is the beta of the investment (or portfolio) - \( R_m \) is the expected return of the market Given the information: - \( R_f = 4\% \) or 0.04 - \( R_m = 12\% \) or 0.12 - \( \beta_i = 1.8 \) Let's calculate the expected return: \[ E(R_i) = 0.04 + 1.8 (0.12 - 0.04) \] \[ E(R_i) = 0.04 + 1.8 (0.08) \] \[ E(R_i) = 0.04 + 0.144 \] \[ E(R_i) = 0.184 \] or \( 18.4\% \) Now, we need to calculate the actual return of the portfolio. The actual return is the percentage increase in the value of the portfolio over the period, which can be calculated as: \[ \text{Actual Return} = \frac{\text{Ending Value of Portfolio} - \text{Beginning Value of Portfolio}}{\text{Beginning Value of Portfolio}} \] Given the information: - Beginning Value of Portfolio = $50,000 - Ending Value of Portfolio = $60,000 Let's calculate the actual return: \[ \text{Actual Return} = \frac{60,000 - 50,000}{50,000} \] \[ \text{Actual Return} = \frac{10,000}{50,000} \] \[ \text{Actual Return} = 0.20 \] or \( 20\% \) Finally, the abnormal return is the difference between the actual return and the expected return: \[ \text{Abnormal Return} = \text{Actual Return} - \text{Expected Return} \] \[ \text{Abnormal Return} = 20\% - 18.4\% \] \[ \text{Abnormal Return} = 1.6\% \] Therefore, the abnormal return of the portfolio is \( 1.6\% \). |
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| kimi | To calculate the abnormal return, we first need to understand what abnormal return means. Abnormal return is the difference between the actual return of an investment and the expected return based on the Capital Asset Pricing Model (CAPM). CAPM is a model that describes the relationship between systematic risk and the expected return for assets, especially stocks. The formula for the expected return (E(Ri)) based on CAPM is: E(Ri) = Rf + β * (Rm - Rf) Where: - E(Ri) is the expected return on the investment - Rf is the risk-free rate of return (4% in this case) - β (beta) is the beta of the portfolio (1.8 in this case) - Rm is the expected market return (12% in this case) Let's calculate the expected return first: E(Ri) = Rf + β * (Rm - Rf) E(Ri) = 4% + 1.8 * (12% - 4%) E(Ri) = 4% + 1.8 * 8% E(Ri) = 4% + 14.4% E(Ri) = 18.4% Now, let's calculate the actual return of the portfolio: Actual Return = (Ending Value - Beginning Value) / Beginning Value Actual Return = ($60,000 - $50,000) / $50,000 Actual Return = $10,000 / $50,000 Actual Return = 0.2 or 20% The abnormal return (AR) is the difference between the actual return and the expected return: AR = Actual Return - Expected Return AR = 20% - 18.4% AR = 1.6% So, the abnormal return for the portfolio is 1.6%. |
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| wenxinyiyan | To calculate the abnormal return, we first need to determine the expected return using the Capital Asset Pricing Model (CAPM). The CAPM formula is: Expected Return = Rf + Beta * (Rm - Rf) where: - Rf is the risk-free rate, - Rm is the market return, - Beta is the Beta of the portfolio. Given the values: - Rf = 4% = 0.04 - Rm = 12% = 0.12 - Beta = 1.8 We can calculate the expected return as follows: Expected Return = 0.04 + 1.8 * (0.12 - 0.04) = 0.04 + 1.8 * 0.08 = 0.04 + 0.144 = 0.184 = 18.4% Now, we need to calculate the actual return of the portfolio. The formula for actual return is: Actual Return = (Ending Value - Beginning Value) / Beginning Value Given the values: - Beginning Value = $50,000 - Ending Value = $60,000 We can calculate the actual return as follows: Actual Return = ($60,000 - $50,000) / $50,000 = $10,000 / $50,000 = 0.2 = 20% Finally, we can calculate the abnormal return, which is the difference between the actual return and the expected return: Abnormal Return = Actual Return - Expected Return = 20% - 18.4% = 1.6% Therefore, the abnormal return is 1.6%. |
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| zhipu | To calculate the abnormal return, we need to follow these steps: 1. **Calculate the actual return of the portfolio.** 2. **Calculate the expected return of the portfolio using the Capital Asset Pricing Model (CAPM).** 3. **Subtract the expected return from the actual return to get the abnormal return.** ### Step 1: Calculate the Actual Return of the Portfolio The actual return (\( R_p \)) can be calculated using the beginning and ending values of the portfolio: \[ R_p = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \] Given: - Beginning Value = $50,000 - Ending Value = $60,000 \[ R_p = \frac{60,000 - 50,000}{50,000} = \frac{10,000}{50,000} = 0.20 \text{ or } 20\% \] ### Step 2: Calculate the Expected Return Using CAPM The CAPM formula is: \[ E(R_p) = R_f + \beta_p \times (R_m - R_f) \] Where: - \( R_f \) = Risk-free rate = 4% or 0.04 - \( R_m \) = Market return = 12% or 0.12 - \( \beta_p \) = Beta of the portfolio = 1.8 \[ E(R_p) = 0.04 + 1.8 \times (0.12 - 0.04) \] \[ E(R_p) = 0.04 + 1.8 \times 0.08 \] \[ E(R_p) = 0.04 + 0.144 \] \[ E(R_p) = 0.184 \text{ or } 18.4\% \] ### Step 3: Calculate the Abnormal Return The abnormal return (\( AR \)) is the difference between the actual return and the expected return: \[ AR = R_p - E(R_p) \] Given: - \( R_p \) = 20% - \( E(R_p) \) = 18.4% \[ AR = 0.20 - 0.184 \] \[ AR = 0.016 \text{ or } 1.6\% \] ### Conclusion The abnormal return of the portfolio is **1.6%**. |
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| gpto1 | To calculate the abnormal return, we'll follow these steps: **1. Calculate the Expected Return using the Capital Asset Pricing Model (CAPM):** \[ \text{Expected Return (E(Rp))} = Rf + \beta_p (R_m - Rf) \] Where: - \( Rf \) = Risk-free rate = 4% - \( \beta_p \) = Beta of the portfolio = 1.8 - \( R_m \) = Market return = 12% First, calculate \( R_m - Rf \): \[ R_m - Rf = 12\% - 4\% = 8\% \] Then, calculate the expected return: \[ \begin{align*} E(Rp) &= 4\% + 1.8 \times 8\% \\ &= 4\% + 14.4\% \\ &= 18.4\% \end{align*} \] **2. Calculate the Actual Return of the Portfolio:** \[ \text{Actual Return} = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \] \[ \text{Actual Return} = \frac{\$60,000 - \$50,000}{\$50,000} = \frac{\$10,000}{\$50,000} = 0.20 \text{ or } 20\% \] **3. Calculate the Abnormal Return:** \[ \text{Abnormal Return} = \text{Actual Return} - \text{Expected Return} = 20\% - 18.4\% = 1.6\% \] **Answer: The abnormal return is 1.6%.** |
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| deepseekv3 | To calculate the **abnormal return**, we need to follow these steps: --- ### **Step 1: Calculate the actual return of the portfolio** The actual return is the percentage change in the value of the portfolio over the given period. \[ \text{Actual Return} = \frac{\text{Ending Value} - \text{Beginning Value}}{\text{Beginning Value}} \times 100 \] Substitute the given values: \[ \text{Actual Return} = \frac{60,000 - 50,000}{50,000} \times 100 = 20\% \] --- ### **Step 2: Calculate the expected return using CAPM** The expected return is calculated using the **Capital Asset Pricing Model (CAPM)**: \[ \text{Expected Return} = R_f + \beta \times (R_m - R_f) \] Where: - \( R_f \) = Risk-free rate = 4% - \( R_m \) = Market return = 12% - \( \beta \) = Beta of the portfolio = 1.8 Substitute the values: \[ \text{Expected Return} = 4 + 1.8 \times (12 - 4) = 4 + 1.8 \times 8 = 4 + 14.4 = 18.4\% \] --- ### **Step 3: Calculate the abnormal return** Abnormal return is the difference between the actual return and the expected return. \[ \text{Abnormal Return} = \text{Actual Return} - \text{Expected Return} \] Substitute the values: \[ \text{Abnormal Return} = 20 - 18.4 = 1.6\% \] --- ### **Final Answer:** The abnormal return is **1.6%**. |
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