| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | 要计算Mutual Fund A的Sortino比率，我们需要按照以下步骤进行： 1. **获取Mutual Fund A的年化收益率**：15% 2. **获取Mutual Fund A的下行偏离度**：8% 3. **获取无风险利率**：2.5% Sortino比率的公式如下： \[ \text{Sortino Ratio} = \frac{R_p - R_f}{\sigma_d} \] 其中： - \( R_p \) 是投资组合的年化收益率，Mutual Fund A为15%。 - \( R_f \) 是无风险利率，为2.5%。 - \( \sigma_d \) 是下行偏离度，Mutual Fund A为8%。 接下来，我们将这些数值代入公式： \[ \text{Sortino Ratio} = \frac{0.15 - 0.025}{0.08} \] 计算过程如下： 1. 计算收益超额部分：\( 0.15 - 0.025 = 0.125 \) 2. 将超额收益除以下行偏离度：\( \frac{0.125}{0.08} = 1.5625 \) 因此，Mutual Fund A的Sortino比率为1.5625。 ### 结论 Mutual Fund A的Sortino比率为 **1.5625**。这个比率越高，表示基金在考虑下行风险后的风险调整收益越好。 |
1.56 |
| deepseekr1 | The Sortino ratio is calculated by subtracting the risk-free rate from the fund's annualized return and dividing the result by the downside deviation. For Mutual Fund A: **Step 1:** Calculate the excess return over the risk-free rate: \( 15\% - 2.5\% = 12.5\% \). **Step 2:** Divide by the downside deviation: \( \frac{12.5\%}{8\%} = 1.5625 \). **Answer:** The Sortino ratio for Fund A is \(\boxed{1.56}\) (rounded to two decimal places). |
1.56 |
| gpto1 | To calculate the Sortino ratio for Mutual Fund A, we'll use the Sortino ratio formula: \[ \text{Sortino Ratio} = \frac{R_p - R_f}{\sigma_d} \] Where: - \( R_p \) is the portfolio's annualized return. - \( R_f \) is the risk-free rate. - \( \sigma_d \) is the downside deviation. Given: - \( R_p = 15\% \) - \( R_f = 2.5\% \) - \( \sigma_d = 8\% \) Plugging the values into the formula: \[ \text{Sortino Ratio} = \frac{15\% - 2.5\%}{8\%} = \frac{12.5\%}{8\%} = 1.5625 \] **Answer:** 1.5625 |
1.56 |
| GPT-4o | To calculate the Sortino ratio for Fund A, we use the following formula: \[ \text{Sortino Ratio} = \frac{R_a - R_f}{\sigma_d} \] where: - \( R_a \) is the annualized return of the fund, - \( R_f \) is the risk-free rate, - \( \sigma_d \) is the downside deviation. Given the data: - Annualized return of Fund A (\( R_a \)) = 15% or 0.15 - Risk-free rate (\( R_f \)) = 2.5% or 0.025 - Downside deviation (\( \sigma_d \)) = 8% or 0.08 Substitute these values into the formula: \[ \text{Sortino Ratio} = \frac{0.15 - 0.025}{0.08} \] Calculate the numerator: \[ 0.15 - 0.025 = 0.125 \] Now, divide by the downside deviation: \[ \text{Sortino Ratio} = \frac{0.125}{0.08} \] \[ \text{Sortino Ratio} = 1.5625 \] Therefore, the Sortino ratio for Fund A is \( 1.5625 \). |
1.56 |
| llama3.1-70B-Instruct | To calculate the Sortino ratio for Fund A, we need to use the following formula: Sortino Ratio = (Expected Return - Risk-Free Rate) / Downside Deviation Given values are: * Expected Return (Fund A) = 15% * Risk-Free Rate = 2.5% * Downside Deviation (Fund A) = 8% Plugging in the values, we get: Sortino Ratio = (15% - 2.5%) / 8% = 12.5% / 8% = 1.5625 Therefore, the Sortino ratio for Fund A is 1.5625. |
1.56 |
| llama3.1-405B-Instruct | To calculate the Sortino ratio for Fund A, we need to use the following formula: Sortino Ratio = (Annualized Return - Risk-Free Rate) / Downside Deviation Plugging in the values for Fund A, we get: Sortino Ratio = (15% - 2.5%) / 8% Sortino Ratio = 12.5% / 8% Sortino Ratio = 1.56 Therefore, the Sortino ratio for Fund A is 1.56. This means that for every unit of downside risk taken, Fund A has generated 1.56 units of excess return above the risk-free rate. |
1.56 |
| DeepSeek-Coder-V2 | The Sortino ratio is a measure of a portfolio's risk-adjusted return that differentiates harmful volatility from total overall volatility by using the asset's downside deviation as opposed to its standard deviation. The formula for the Sortino ratio is: Sortino Ratio = (Rp - Rf) / σd Where: - Rp is the expected portfolio return (or in this case, the annualized return of the mutual fund) - Rf is the risk-free rate - σd is the downside deviation Given the problem: - Mutual Fund A's annualized return (Rp) is 15% - The risk-free rate (Rf) is 2.5% - Mutual Fund A's downside deviation (σd) is 8% Now, we can plug these values into the Sortino ratio formula: Sortino Ratio (Fund A) = (15% - 2.5%) / 8% First, calculate the numerator: 15% - 2.5% = 12.5% Then, divide by the downside deviation: 12.5% / 8% = 1.5625 So, the Sortino ratio for Fund A is 1.5625. |
1.56 |
| Qwen2-72B-Instruct | The Sortino ratio is a measure of risk-adjusted return that considers only the downside deviation (the volatility of negative returns) as a measure of risk. It is calculated as follows: Sortino Ratio = (Rp - Rf) / Downside Deviation Where: Rp = Expected or actual return of the portfolio (in this case, Mutual Fund A) Rf = Risk-free rate Downside Deviation = Standard deviation of the negative asset returns For Mutual Fund A: Rp = 15% Rf = 2.5% Downside Deviation = 8% Sortino Ratio for Fund A = (15% - 2.5%) / 8% Sortino Ratio for Fund A = 12.5% / 8% Sortino Ratio for Fund A = 1.5625 Therefore, the Sortino ratio for Mutual Fund A is 1.5625. |
1.56 |
| baichuan4 | The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative portfolio returns (downside deviation). The Sortino ratio is calculated as follows: Sortino Ratio = (Annualized Return - Risk-Free Rate) / Downside Deviation To calculate the Sortino ratio for Fund A, we will use the provided information: Fund A's Annualized Return: 15% Fund A's Downside Deviation: 8% Risk-Free Rate: 2.5% Now, let's plug in these values into the formula: Sortino Ratio for Fund A = (15% - 2.5%) / 8% Sortino Ratio for Fund A = 12.5% / 8% Sortino Ratio for Fund A = 1.5625 Therefore, the Sortino ratio for Fund A is 1.5625. This means that for every unit of downside risk, Fund A generates 1.5625 units of excess return over the risk-free rate. |
1.56 |
| doubao | The Sortino ratio is calculated as (annualized return - risk-free rate) / downside deviation. For Fund A, the Sortino ratio = (15% - 2.5%) / 8% = 12.5% / 8% = 1.5625. |
1.56 |
| minimax | The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the standard deviation of negative asset returns, called downside deviation. The Sortino ratio is calculated as follows: Sortino Ratio = (Rp - Rf) / σd Where: - Rp is the portfolio or investment return (annualized return of the fund) - Rf is the risk-free rate - σd is the downside deviation For Mutual Fund A, we have: - Rp = 15% (annualized return) - Rf = 2.5% (risk-free rate) - σd = 8% (downside deviation) Now, we can plug these values into the Sortino ratio formula: Sortino Ratio for Fund A = (15% - 2.5%) / 8% Sortino Ratio for Fund A = (12.5%) / 8% Sortino Ratio for Fund A = 1.5625 Therefore, the Sortino ratio for Mutual Fund A is 1.5625. |
1.56 |
| kimi | The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the standard deviation of negative asset returns, called the downside deviation. The Sortino ratio is used to assess the risk-adjusted return of an investment portfolio, but it only penalizes the volatility of negative returns. The formula for the Sortino ratio is: \[ Sortino\ Ratio = \frac{R_p - R_f}{\sigma_{d}} \] Where: - \( R_p \) is the annualized return of the portfolio (Mutual Fund A in this case) - \( R_f \) is the risk-free rate - \( \sigma_{d} \) is the downside deviation Given: - Annualized return of Mutual Fund A (\( R_p \)) = 15% - Risk-free rate (\( R_f \)) = 2.5% - Downside deviation of Mutual Fund A (\( \sigma_{d} \)) = 8% Let's calculate the Sortino ratio for Mutual Fund A: \[ Sortino\ Ratio = \frac{15\% - 2.5\%}{8\%} \] \[ Sortino\ Ratio = \frac{12.5\%}{8\%} \] \[ Sortino\ Ratio = 1.5625 \] So, the Sortino ratio for Fund A is 1.5625. |
1.56 |
| wenxinyiyan | To calculate the Sortino ratio for Fund A, we need to use the formula: Sortino Ratio = (Annualized Return - Risk-Free Rate) / Downside Deviation For Fund A, the annualized return is 15%, the risk-free rate is 2.5%, and the downside deviation is 8%. Plugging these values into the formula, we get: Sortino Ratio (Fund A) = (15% - 2.5%) / 8% = 12.5% / 8% = 1.5625 Therefore, the Sortino ratio for Fund A is 1.5625. |
1.56 |
| zhipu | The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using downside deviation instead of standard deviation in the calculation. The Sortino ratio is calculated using the following formula: \[ \text{Sortino Ratio} = \frac{R_p - R_f}{D_d} \] Where: - \( R_p \) is the actual or expected portfolio return, - \( R_f \) is the risk-free rate, - \( D_d \) is the downside deviation. Given the data: - For Mutual Fund A, \( R_p \) (the actual or expected return) is 15% or 0.15, - \( R_f \) (the risk-free rate) is 2.5% or 0.025, - \( D_d \) (the downside deviation) is 8% or 0.08. Let's plug these values into the formula: \[ \text{Sortino Ratio for Fund A} = \frac{0.15 - 0.025}{0.08} \] \[ \text{Sortino Ratio for Fund A} = \frac{0.125}{0.08} \] \[ \text{Sortino Ratio for Fund A} = 1.5625 \] Therefore, the Sortino ratio for Mutual Fund A is 1.5625. This ratio suggests that for every unit of downside risk, Mutual Fund A generates an excess return of 1.5625 units above the risk-free rate. A higher Sortino ratio indicates a better risk-adjusted performance of the fund. |
1.56 |
| gpto1 | To calculate the Sortino ratio for Mutual Fund A, we'll use the Sortino ratio formula: \[ \text{Sortino Ratio} = \frac{R_p - R_f}{\sigma_d} \] Where: - \( R_p \) is the portfolio's annualized return. - \( R_f \) is the risk-free rate. - \( \sigma_d \) is the downside deviation. Given: - \( R_p = 15\% \) - \( R_f = 2.5\% \) - \( \sigma_d = 8\% \) Plugging the values into the formula: \[ \text{Sortino Ratio} = \frac{15\% - 2.5\%}{8\%} = \frac{12.5\%}{8\%} = 1.5625 \] **Answer:** 1.5625 |
1.56 |
| deepseekv3 | To calculate the **Sortino Ratio** for Mutual Fund A, we use the following formula: \[ \text{Sortino Ratio} = \frac{\text{Annualized Return} - \text{Risk-Free Rate}}{\text{Downside Deviation}} \] ### Given: - Annualized Return for Fund A = **15%** (or 0.15 in decimal form) - Downside Deviation for Fund A = **8%** (or 0.08 in decimal form) - Risk-Free Rate = **2.5%** (or 0.025 in decimal form) ### Step 1: Subtract the Risk-Free Rate from the Annualized Return \[ \text{Excess Return} = \text{Annualized Return} - \text{Risk-Free Rate} \] \[ \text{Excess Return} = 0.15 - 0.025 = 0.125 \] ### Step 2: Divide by the Downside Deviation \[ \text{Sortino Ratio} = \frac{0.125}{0.08} = 1.5625 \] ### Final Answer: The **Sortino Ratio** for Mutual Fund A is **1.56**. |
1.56 |