| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | To determine whether Mr. Wong has done a better job than Ms. Petrov by measuring Jensen’s alpha, we need to calculate Jensen’s alpha for both portfolios using the given data. Jensen’s alpha is calculated as follows: \[ \alpha = \text{Portfolio Return} - [\text{Risk-Free Rate} + \beta \times (\text{Market Return} - \text{Risk-Free Rate})] \] Let's break down the calculation for both managers: ### Mr. Wong's Jensen's Alpha - **Portfolio Return (R_p):** 14% or 0.14 - **Risk-Free Rate (R_f):** 2% or 0.02 - **Market Return (R_m):** 11% or 0.11 - **Beta (β):** 1.2 \[ \alpha_{\text{Wong}} = 0.14 - [0.02 + 1.2 \times (0.11 - 0.02)] \] \[ \alpha_{\text{Wong}} = 0.14 - [0.02 + 1.2 \times 0.09] \] \[ \alpha_{\text{Wong}} = 0.14 - [0.02 + 0.108] \] \[ \alpha_{\text{Wong}} = 0.14 - 0.128 \] \[ \alpha_{\text{Wong}} = 0.012 \] ### Ms. Petrov's Jensen's Alpha - **Portfolio Return (R_p):** 16% or 0.16 - **Risk-Free Rate (R_f):** 2% or 0.02 - **Market Return (R_m):** 11% or 0.11 - **Beta (β):** 1.6 \[ \alpha_{\text{Petrov}} = 0.16 - [0.02 + 1.6 \times (0.11 - 0.02)] \] \[ \alpha_{\text{Petrov}} = 0.16 - [0.02 + 1.6 \times 0.09] \] \[ \alpha_{\text{Petrov}} = 0.16 - [0.02 + 0.144] \] \[ \alpha_{\text{Petrov}} = 0.16 - 0.164 \] \[ \alpha_{\text{Petrov}} = -0.004 \] ### Comparison - **Mr. Wong’s Jensen’s Alpha:** 0.012 - **Ms. Petrov’s Jensen’s Alpha:** -0.004 Since Jensen’s alpha for Mr. Wong is positive (0.012) and higher than that of Ms. Petrov (which is negative at -0.004), we can conclude that Mr. Wong has indeed done a better job according to Jensen’s alpha. ### Conclusion **True**: By measuring Jensen’s alpha, Mr. Wong has done the better job. |
True |
| deepseekr1 | To determine if Mr. Wong has a higher Jensen’s alpha than Ms. Petrov, we calculate the alpha for each using the formula: **Alpha = Portfolio Return - [Risk-Free Rate + Beta × (Market Return - Risk-Free Rate)]** **For Mr. Wong:** - Expected Return = 2% + 1.2 × (11% - 2%) = 2% + 1.2 × 9% = **12.8%** - Alpha = 14% - 12.8% = **1.2%** **For Ms. Petrov:** - Expected Return = 2% + 1.6 × (11% - 2%) = 2% + 1.6 × 9% = **16.4%** - Alpha = 16% - 16.4% = **-0.4%** Mr. Wong’s positive alpha (1.2%) indicates outperformance relative to his risk (beta), while Ms. Petrov’s negative alpha (-0.4%) shows underperformance. Thus, **Mr. Wong has a higher Jensen’s alpha**, making the statement **True**. **Answer:** True |
True |
| gpto1 | To determine whether the statement "By measuring Jensen’s alpha, Mr. Wong has done the better job" is correct, we need to calculate Jensen's alpha for both Mr. Wong and Ms. Petrov. **Jensen's Alpha Formula:** \[ \alpha = R_p - [R_f + \beta_p (R_m - R_f)] \] where: - \(\alpha\) = Jensen's alpha - \(R_p\) = Portfolio return - \(R_f\) = Risk-free rate - \(\beta_p\) = Portfolio beta - \(R_m\) = Market return **Given Data:** For Mr. Wong: - Portfolio return (\(R_{p1}\)) = 14% - Beta (\(\beta_1\)) = 1.2 For Ms. Petrov: - Portfolio return (\(R_{p2}\)) = 16% - Beta (\(\beta_2\)) = 1.6 Common data: - Risk-free rate (\(R_f\)) = 2% - Market return (\(R_m\)) = 11% **Calculations:** **1. Calculate Expected Return using CAPM:** For Mr. Wong: \[ E(R_{wong}) = R_f + \beta_1 (R_m - R_f) = 2\% + 1.2 \times (11\% - 2\%) = 2\% + 1.2 \times 9\% = 2\% + 10.8\% = 12.8\% \] For Ms. Petrov: \[ E(R_{petrov}) = R_f + \beta_2 (R_m - R_f) = 2\% + 1.6 \times (11\% - 2\%) = 2\% + 1.6 \times 9\% = 2\% + 14.4\% = 16.4\% \] **2. Calculate Jensen's Alpha:** For Mr. Wong: \[ \alpha_{wong} = R_{p1} - E(R_{wong}) = 14\% - 12.8\% = 1.2\% \] For Ms. Petrov: \[ \alpha_{petrov} = R_{p2} - E(R_{petrov}) = 16\% - 16.4\% = -0.4\% \] **Conclusion:** Mr. Wong's Jensen's alpha is **+1.2%**, indicating he outperformed the expected return given his portfolio's beta. Ms. Petrov's Jensen's alpha is **–0.4%**, indicating she underperformed relative to the expected return. **Answer: True.** |
True |
| GPT-4o | To determine whether Mr. Wong has done a better job than Ms. Petrov, we can use Jensen's alpha. Jensen's alpha measures the risk-adjusted return of a portfolio, considering the portfolio's beta and the expected return based on the Capital Asset Pricing Model (CAPM). The formula for Jensen's alpha is: \[ \alpha = R_p - [R_f + \beta (R_m - R_f)] \] Where: - \( R_p \) is the portfolio return. - \( R_f \) is the risk-free rate (US Treasury security rate). - \( \beta \) is the portfolio's beta. - \( R_m \) is the market return (S&P 500 return). Let's calculate Jensen's alpha for both Mr. Wong and Ms. Petrov. ### Mr. Wong's Portfolio: - Average return (\( R_p \)): 14% or 0.14 - Beta (\( \beta \)): 1.2 - Risk-free rate (\( R_f \)): 2% or 0.02 - Market return (\( R_m \)): 11% or 0.11 \[ \alpha_{Wong} = 0.14 - [0.02 + 1.2 (0.11 - 0.02)] \] \[ \alpha_{Wong} = 0.14 - [0.02 + 1.2 \times 0.09] \] \[ \alpha_{Wong} = 0.14 - [0.02 + 0.108] \] \[ \alpha_{Wong} = 0.14 - 0.128 \] \[ \alpha_{Wong} = 0.012 \] ### Ms. Petrov's Portfolio: - Average return (\( R_p \)): 16% or 0.16 - Beta (\( \beta \)): 1.6 - Risk-free rate (\( R_f \)): 2% or 0.02 - Market return (\( R_m \)): 11% or 0.11 \[ \alpha_{Petrov} = 0.16 - [0.02 + 1.6 (0.11 - 0.02)] \] \[ \alpha_{Petrov} = 0.16 - [0.02 + 1.6 \times 0.09] \] \[ \alpha_{Petrov} = 0.16 - [0.02 + 0.144] \] \[ \alpha_{Petrov} = 0.16 - 0.164 \] \[ \alpha_{Petrov} = -0.004 \] ### Comparison: - Mr. Wong's Jensen's alpha: \( \alpha_{Wong} = 0.012 \) - Ms. Petrov's Jensen's alpha: \( \alpha_{Petrov} = -0.004 \) Since Mr. Wong has a positive Jensen's alpha and Ms. Petrov has a negative Jensen's alpha, Mr. Wong has indeed done a better job in terms of risk-adjusted return. Therefore, the statement "By measuring Jensen’s alpha, Mr. Wong has done the better job" is **True**. |
True |
| llama3.1-70B-Instruct | To determine whether Mr. Wong has done a better job than Ms. Petrov based on Jensen's alpha, we first need to calculate Jensen's alpha for each of them. Jensen's alpha is a measure of the excess return of a portfolio over and above what the Capital Asset Pricing Model (CAPM) predicts, given its beta and the average market return. The formula for Jensen's alpha is: Jensen's Alpha = R_p - [R_f + β(R_m - R_f)] Where: - R_p is the return of the portfolio, - R_f is the risk-free rate (the return of the US Treasury security), - β is the beta of the portfolio, - R_m is the return of the market (the S&P 500 in this case). Given data: - Mr. Wong's portfolio return (R_p) = 14%, - Ms. Petrov's portfolio return (R_p) = 16%, - Risk-free rate (R_f) = 2%, - Market return (R_m) = 11%, - Mr. Wong's beta (β) = 1.2, - Ms. Petrov's beta (β) = 1.6. Calculating Jensen's alpha for Mr. Wong: Jensen's Alpha (Wong) = 14% - [2% + 1.2(11% - 2%)] = 14% - [2% + 1.2(9%)] = 14% - [2% + 10.8%] = 14% - 12.8% = 1.2% Calculating Jensen's alpha for Ms. Petrov: Jensen's Alpha (Petrov) = 16% - [2% + 1.6(11% - 2%)] = 16% - [2% + 1.6(9%)] = 16% - [2% + 14.4%] = 16% - 16.4% = -0.4% Since Mr. Wong's Jensen's alpha (1.2%) is higher than Ms. Petrov's Jensen's alpha (-0.4%), it indicates that Mr. Wong has indeed done a better job, according to Jensen's alpha measurement. Therefore, the answer is: **True** |
True |
| llama3.1-405B-Instruct | To determine whether Mr. Wong or Ms. Petrov has done the better job based on Jensen's alpha, we need to calculate Jensen's alpha for each manager. Jensen's alpha is a measure of the excess return of a portfolio over the expected return, given its beta and the market return. It is calculated as follows: Jensen's alpha = Portfolio return - (Risk-free rate + Beta x (Market return - Risk-free rate)) For Mr. Wong: Jensen's alpha = 14% - (2% + 1.2 x (11% - 2%)) = 14% - (2% + 1.2 x 9%) = 14% - (2% + 10.8%) = 14% - 12.8% = 1.2% For Ms. Petrov: Jensen's alpha = 16% - (2% + 1.6 x (11% - 2%)) = 16% - (2% + 1.6 x 9%) = 16% - (2% + 14.4%) = 16% - 16.4% = -0.4% Since Mr. Wong's Jensen's alpha (1.2%) is greater than Ms. Petrov's (-0.4%), Mr. Wong has done the better job. Answer: True. |
True |
| DeepSeek-Coder-V2 | To solve this problem, we need to calculate Jensen's alpha for both Mr. Wong and Ms. Petrov and compare them. Jensen's alpha is a measure of portfolio performance that adjusts for the portfolio's beta (systematic risk) relative to the market. The formula for Jensen's alpha is: \[ \alpha = R_p - [R_f + \beta_p \times (R_m - R_f)] \] Where: - \( R_p \) is the portfolio's average return. - \( R_f \) is the risk-free rate (US Treasury security rate). - \( \beta_p \) is the portfolio's beta. - \( R_m \) is the market return (S&P 500 return). Given data: - \( R_f = 2\% \) - \( R_m = 11\% \) For Mr. Wong: - \( R_p = 14\% \) - \( \beta_p = 1.2 \) For Ms. Petrov: - \( R_p = 16\% \) - \( \beta_p = 1.6 \) Now, let's calculate Jensen's alpha for both managers. **Mr. Wong's Jensen's alpha:** \[ \alpha_{Wong} = 14\% - [2\% + 1.2 \times (11\% - 2\%)] \] \[ \alpha_{Wong} = 14\% - [2\% + 1.2 \times 9\%] \] \[ \alpha_{Wong} = 14\% - [2\% + 10.8\%] \] \[ \alpha_{Wong} = 14\% - 12.8\% \] \[ \alpha_{Wong} = 1.2\% \] **Ms. Petrov's Jensen's alpha:** \[ \alpha_{Petrov} = 16\% - [2\% + 1.6 \times (11\% - 2\%)] \] \[ \alpha_{Petrov} = 16\% - [2\% + 1.6 \times 9\%] \] \[ \alpha_{Petrov} = 16\% - [2\% + 14.4\%] \] \[ \alpha_{Petrov} = 16\% - 16.4\% \] \[ \alpha_{Petrov} = -0.4\% \] Comparing the Jensen's alphas: - Mr. Wong's alpha: \( 1.2\% \) - Ms. Petrov's alpha: \( -0.4\% \) Since Mr. Wong's Jensen's alpha is higher than Ms. Petrov's, Mr. Wong has indeed done the better job. Answer: True |
True |
| Qwen2-72B-Instruct | To determine whether Mr. Wong has done a better job than Ms. Petrov based on Jensen's alpha, we need to calculate the alpha for both managers. Jensen's alpha measures the excess return of a portfolio over the return predicted by the capital asset pricing model (CAPM). The formula for Jensen's alpha is: Alpha = Portfolio Return - [Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)] For Mr. Wong: Portfolio Return = 14% Beta = 1.2 Risk-Free Rate = 2% Market Return = 11% Alpha_Wong = 14% - [2% + 1.2 * (11% - 2%)] Alpha_Wong = 14% - [2% + 1.2 * 9%] Alpha_Wong = 14% - [2% + 10.8%] Alpha_Wong = 14% - 12.8% Alpha_Wong = 1.2% For Ms. Petrov: Portfolio Return = 16% Beta = 1.6 Risk-Free Rate = 2% Market Return = 11% Alpha_Petrov = 16% - [2% + 1.6 * (11% - 2%)] Alpha_Petrov = 16% - [2% + 1.6 * 9%] Alpha_Petrov = 16% - [2% + 14.4%] Alpha_Petrov = 16% - 16.4% Alpha_Petrov = -0.4% Since Mr. Wong has a positive alpha of 1.2%, while Ms. Petrov has a negative alpha of -0.4%, it is correct to say that Mr. Wong has done the better job based on Jensen's alpha. Answer: True. |
True |
| baichuan4 | False. To determine which investment manager has done the better job by measuring Jensen's alpha, we need to calculate the alpha values for both managers. Jensen's alpha is a measure of the performance of a portfolio or investment relative to a benchmark, after adjusting for systematic risk. It is calculated using the following formula: α = Rp - [Rf + β(Rm - Rf)] where: - α is Jensen's alpha, - Rp is the average return on the portfolio, - Rf is the average risk-free rate (US Treasury security rate), - β is the beta of the portfolio, - Rm is the average return on the market (S&P 500). Let's calculate Jensen's alpha for both managers: Mr. Wong's alpha: α = 14% - [2% + 1.2(11% - 2%)] α = 14% - [2% + 1.2(9%)] α = 14% - [2% + 10.8%] α = 14% - 12.8% α = 1.2% Ms. Petrov's alpha: α = 16% - [2% + 1.6(11% - 2%)] α = 16% - [2% + 1.6(9%)] α = 16% - [2% + 14.4%] α = 16% - 16.4% α = -0.4% Since Mr. Wong's alpha (1.2%) is higher than Ms. Petrov's alpha (-0.4%), it means that Mr. Wong has outperformed Ms. Petrov relative to the benchmark (S&P 500) after adjusting for systematic risk. Therefore, by measuring Jensen's alpha, Mr. Wong has done the better job. |
True |
| doubao | Jensen's alpha = average return - (risk-free rate + beta * (market return - risk-free rate)). For Mr. Wong: alpha = 14% - (2% + 1.2 * (11% - 2%)) = 14% - (2% + 1.2 * 9%) = 14% - (2% + 10.8%) = 14% - 12.8% = 1.2%. For Ms. Petrov: alpha = 16% - (2% + 1.6 * (11% - 2%)) = 16% - (2% + 1.6 * 9%) = 16% - (2% + 14.4%) = 16% - 16.4% = -0.4%. Since Mr. Wong's Jensen's alpha is positive and higher than Ms. Petrov's, the statement is True. |
True |
| minimax | To determine whether Mr. Wong has done the better job according to Jensen's alpha, we need to calculate the alpha for both investment managers' portfolios. Jensen's alpha is a measure of the excess returns that a portfolio generates over its expected returns based on the capital asset pricing model (CAPM). The formula for Jensen's alpha is: \[ \alpha = R_p - (R_f + \beta_p (R_m - R_f)) \] Where: - \( \alpha \) is Jensen's alpha - \( R_p \) is the actual return of the portfolio - \( R_f \) is the risk-free rate - \( \beta_p \) is the beta of the portfolio - \( R_m \) is the return of the market Let's calculate Jensen's alpha for both Mr. Wong and Ms. Petrov. For Mr. Wong: - \( R_p \) = 14% - \( R_f \) = 2% - \( \beta_p \) = 1.2 - \( R_m \) = 11% \[ \alpha_{Wong} = 0.14 - (0.02 + 1.2 \times (0.11 - 0.02)) \] \[ \alpha_{Wong} = 0.14 - (0.02 + 1.2 \times 0.09) \] \[ \alpha_{Wong} = 0.14 - (0.02 + 0.108) \] \[ \alpha_{Wong} = 0.14 - 0.128 \] \[ \alpha_{Wong} = 0.012 \text{ or } 1.2\% \] For Ms. Petrov: - \( R_p \) = 16% - \( R_f \) = 2% - \( \beta_p \) = 1.6 - \( R_m \) = 11% \[ \alpha_{Petrov} = 0.16 - (0.02 + 1.6 \times (0.11 - 0.02)) \] \[ \alpha_{Petrov} = 0.16 - (0.02 + 1.6 \times 0.09) \] \[ \alpha_{Petrov} = 0.16 - (0.02 + 0.144) \] \[ \alpha_{Petrov} = 0.16 - 0.164 \] \[ \alpha_{Petrov} = -0.004 \text{ or } -0.4\% \] Based on the calculations, Mr. Wong has a positive Jensen's alpha of 1.2%, while Ms. Petrov has a negative Jensen's alpha of -0.4%. This means that Mr. Wong's portfolio performed better than expected given its level of risk, while Ms. Petrov's portfolio underperformed relative to the expected return based on its risk level. Therefore, the statement "By measuring Jensen’s alpha, Mr. Wong has done the better job." is True. |
True |
| kimi | To determine whether Mr. Wong has done a better job than Ms. Petrov by measuring Jensen's alpha, we need to calculate the Jensen's alpha for both investment managers. Jensen's alpha is a measure of the return on an investment compared to the return of a benchmark index, adjusted for risk. It is calculated using the following formula: \[ \text{Jensen's Alpha} = R_p - (R_f + \beta_p \times (R_m - R_f)) \] Where: - \( R_p \) is the return of the portfolio - \( R_f \) is the risk-free rate - \( \beta_p \) is the beta of the portfolio - \( R_m \) is the return of the market Let's calculate Jensen's alpha for both Mr. Wong and Ms. Petrov: For Mr. Wong: \[ R_p = 14\% \] \[ R_f = 2\% \] \[ \beta_p = 1.2 \] \[ R_m = 11\% \] \[ \text{Jensen's Alpha}_{\text{Wong}} = 14\% - (2\% + 1.2 \times (11\% - 2\%)) \] \[ \text{Jensen's Alpha}_{\text{Wong}} = 14\% - (2\% + 1.2 \times 9\%) \] \[ \text{Jensen's Alpha}_{\text{Wong}} = 14\% - (2\% + 10.8\%) \] \[ \text{Jensen's Alpha}_{\text{Wong}} = 14\% - 12.8\% \] \[ \text{Jensen's Alpha}_{\text{Wong}} = 1.2\% \] For Ms. Petrov: \[ R_p = 16\% \] \[ R_f = 2\% \] \[ \beta_p = 1.6 \] \[ R_m = 11\% \] \[ \text{Jensen's Alpha}_{\text{Petrov}} = 16\% - (2\% + 1.6 \times (11\% - 2\%)) \] \[ \text{Jensen's Alpha}_{\text{Petrov}} = 16\% - (2\% + 1.6 \times 9\%) \] \[ \text{Jensen's Alpha}_{\text{Petrov}} = 16\% - (2\% + 14.4\%) \] \[ \text{Jensen's Alpha}_{\text{Petrov}} = 16\% - 16.4\% \] \[ \text{Jensen's Alpha}_{\text{Petrov}} = -0.4\% \] Comparing the two: - Mr. Wong's Jensen's alpha is \( 1.2\% \) - Ms. Petrov's Jensen's alpha is \( -0.4\% \) Since Mr. Wong's Jensen's alpha is positive and higher than Ms. Petrov's, it indicates that Mr. Wong has outperformed the market after adjusting for risk, while Ms. Petrov has underperformed the market after adjusting for risk. Therefore, the statement "By measuring Jensen’s alpha, Mr. Wong has done the better job" is True. |
True |
| wenxinyiyan | To answer this question, we need to calculate Jensen's alpha for both Mr. Wong and Ms. Petrov. Jensen's alpha is a measure of a portfolio's excess return over its expected return, given its beta and the market return. The formula for Jensen's alpha is: Jensen's Alpha = Portfolio Return - [Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)] Let's calculate Jensen's alpha for both managers: For Mr. Wong: Portfolio Return = 14% Risk-Free Rate = 2% (US Treasury security rate) Beta = 1.2 Market Return = 11% (S&P 500 return) Jensen's Alpha (Mr. Wong) = 14% - [2% + 1.2 * (11% - 2%)] = 14% - [2% + 1.2 * 9%] = 14% - [2% + 10.8%] = 14% - 12.8% = 1.2% For Ms. Petrov: Portfolio Return = 16% Risk-Free Rate = 2% (US Treasury security rate) Beta = 1.6 Market Return = 11% (S&P 500 return) Jensen's Alpha (Ms. Petrov) = 16% - [2% + 1.6 * (11% - 2%)] = 16% - [2% + 1.6 * 9%] = 16% - [2% + 14.4%] = 16% - 16.4% = -0.4% Comparing the two Jensen's alpha values, we can see that Mr. Wong's portfolio has a positive Jensen's alpha of 1.2%, while Ms. Petrov's portfolio has a negative Jensen's alpha of -0.4%. A positive Jensen's alpha indicates that the portfolio has generated excess returns over what was expected based on its beta and the market return, while a negative Jensen's alpha indicates that the portfolio has not met its expected return. Therefore, based on the measurement of Jensen's alpha, it is correct to say that Mr. Wong has done the better job. The answer is True. |
True |
| zhipu | To determine if the statement "Mr. Wong has done the better job by measuring Jensen’s alpha" is correct, we need to calculate Jensen’s alpha for both Mr. Wong and Ms. Petrov. Jensen’s alpha is a measure of the excess return adjusted for the risk of the investment, specifically the systematic risk as measured by beta. The formula for Jensen’s alpha is: \[ \alpha = R_p - [R_f + \beta_p (R_m - R_f)] \] Where: - \( \alpha \) = Jensen's alpha - \( R_p \) = Portfolio return - \( R_f \) = Risk-free rate - \( \beta_p \) = Portfolio beta - \( R_m \) = Market return Let's calculate Jensen’s alpha for both Mr. Wong and Ms. Petrov. ### Mr. Wong's Alpha - \( R_p \) = 14% (average return) - \( R_f \) = 2% (US Treasury rate) - \( \beta_p \) = 1.2 - \( R_m \) = 11% (S&P 500 return) \[ \alpha_{Wong} = 14\% - [2\% + 1.2 \times (11\% - 2\%)] \] \[ \alpha_{Wong} = 14\% - [2\% + 1.2 \times 9\%] \] \[ \alpha_{Wong} = 14\% - [2\% + 10.8\%] \] \[ \alpha_{Wong} = 14\% - 12.8\% \] \[ \alpha_{Wong} = 1.2\% \] ### Ms. Petrov's Alpha - \( R_p \) = 16% (average return) - \( R_f \) = 2% (US Treasury rate) - \( \beta_p \) = 1.6 - \( R_m \) = 11% (S&P 500 return) \[ \alpha_{Petrov} = 16\% - [2\% + 1.6 \times (11\% - 2\%)] \] \[ \alpha_{Petrov} = 16\% - [2\% + 1.6 \times 9\%] \] \[ \alpha_{Petrov} = 16\% - [2\% + 14.4\%] \] \[ \alpha_{Petrov} = 16\% - 16.4\% \] \[ \alpha_{Petrov} = -0.4\% \] ### Conclusion - Mr. Wong's Jensen’s alpha is 1.2%. - Ms. Petrov's Jensen’s alpha is -0.4%. Since a higher Jensen’s alpha indicates better performance adjusted for risk, Mr. Wong indeed has a higher Jensen’s alpha compared to Ms. Petrov. **Therefore, the statement "Mr. Wong has done the better job by measuring Jensen’s alpha" is True.** |
True |
| gpto1 | To determine whether the statement "By measuring Jensen’s alpha, Mr. Wong has done the better job" is correct, we need to calculate Jensen's alpha for both Mr. Wong and Ms. Petrov. **Jensen's Alpha Formula:** \[ \alpha = R_p - [R_f + \beta_p (R_m - R_f)] \] where: - \(\alpha\) = Jensen's alpha - \(R_p\) = Portfolio return - \(R_f\) = Risk-free rate - \(\beta_p\) = Portfolio beta - \(R_m\) = Market return **Given Data:** For Mr. Wong: - Portfolio return (\(R_{p1}\)) = 14% - Beta (\(\beta_1\)) = 1.2 For Ms. Petrov: - Portfolio return (\(R_{p2}\)) = 16% - Beta (\(\beta_2\)) = 1.6 Common data: - Risk-free rate (\(R_f\)) = 2% - Market return (\(R_m\)) = 11% **Calculations:** **1. Calculate Expected Return using CAPM:** For Mr. Wong: \[ E(R_{wong}) = R_f + \beta_1 (R_m - R_f) = 2\% + 1.2 \times (11\% - 2\%) = 2\% + 1.2 \times 9\% = 2\% + 10.8\% = 12.8\% \] For Ms. Petrov: \[ E(R_{petrov}) = R_f + \beta_2 (R_m - R_f) = 2\% + 1.6 \times (11\% - 2\%) = 2\% + 1.6 \times 9\% = 2\% + 14.4\% = 16.4\% \] **2. Calculate Jensen's Alpha:** For Mr. Wong: \[ \alpha_{wong} = R_{p1} - E(R_{wong}) = 14\% - 12.8\% = 1.2\% \] For Ms. Petrov: \[ \alpha_{petrov} = R_{p2} - E(R_{petrov}) = 16\% - 16.4\% = -0.4\% \] **Conclusion:** Mr. Wong's Jensen's alpha is **+1.2%**, indicating he outperformed the expected return given his portfolio's beta. Ms. Petrov's Jensen's alpha is **–0.4%**, indicating she underperformed relative to the expected return. **Answer: True.** |
True |
| deepseekv3 | server error: Error code: 400 - {'error': {'code': 'RequestTimeOut', 'param': None, 'message': 'Request timed out, please try again later.', 'type': 'RequestTimeOut'}, 'id': 'chatcmpl-87912651-0c3b-9396-bf3f-7e711b3e3ed2', 'request_id': '87912651-0c3b-9396-bf3f-7e711b3e3ed2'} | True |