| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | 要计算Fred投资的持有期收益率（Holding Period Return, HPR），我们需要按照以下步骤进行： ### 步骤1：确定初始投资金额 Fred在三年前投资了$10,000。 ### 步骤2：计算持有期内收到的总股息 Fred每年收到$100的股息，总共持有了三年。因此，总股息收入为： \[ 100 \times 3 = $300 \] ### 步骤3：确定股票的卖出价格 Fred今天以$12,000卖出了他的股票。 ### 步骤4：使用HPR公式计算收益率 持有期收益率的公式为： \[ \text{HPR} = \frac{\text{终值} - \text{初值} + \text{总股息}}{\text{初值}} \] 将已知数据代入公式： \[ \text{HPR} = \frac{12,000 - 10,000 + 300}{10,000} \] 计算： \[ \text{HPR} = \frac{2,300}{10,000} = 0.23 \] 因此，Fred的持有期收益率为23%。 ### 总结 Fred在三年内的持有期收益率为23%。这个结果表明，Fred通过持有ABC Corp的股票，获得了23%的总回报，包括股息和资本增值。 |
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| deepseekr1 | The holding period return (HPR) is calculated by considering both the capital gain and the dividends received over the investment period. Here's the step-by-step solution: 1. **Total Dividends Received**: $100/year × 3 years = **$300** 2. **Capital Gain**: Selling Price − Purchase Price = $12,000 − $10,000 = **$2,000** 3. **Total Return**: Dividends + Capital Gain = $300 + $2,000 = **$2,300** 4. **Holding Period Return (HPR)**: \[ \text{HPR} = \frac{\text{Total Return}}{\text{Initial Investment}} = \frac{\$2,300}{\$10,000} = 0.23 \text{ or } 23\% \] **Answer**: The holding period return is **23%**. |
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| gpto1 | To determine Fred's holding period return (HPR) on his investment in ABC Corp shares, we'll calculate the total return he earned over the holding period and express it as a percentage of his initial investment. **Holding Period Return (HPR) Formula:** \[ \text{HPR} = \frac{\text{Total Income} + (\text{Ending Value} - \text{Beginning Value})}{\text{Beginning Value}} \] Where: - **Total Income** = Sum of all dividends received during the holding period. - **Beginning Value** = Initial amount invested. - **Ending Value** = Value of the investment at the end of the holding period (sale price). --- ### **Step 1: Calculate Total Income (Dividends Received)** Fred received dividends annually for three years. \[ \text{Total Income} = \text{Annual Dividend} \times \text{Number of Years} = \$100 \times 3 = \$300 \] ### **Step 2: Determine the Capital Gain (or Loss)** \[ \text{Capital Gain} = \text{Ending Value} - \text{Beginning Value} = \$12,000 - \$10,000 = \$2,000 \] ### **Step 3: Calculate Total Return** Total return includes both the income from dividends and the capital gain. \[ \text{Total Return} = \text{Total Income} + \text{Capital Gain} = \$300 + \$2,000 = \$2,300 \] ### **Step 4: Compute the Holding Period Return** \[ \text{HPR} = \frac{\text{Total Return}}{\text{Beginning Value}} = \frac{\$2,300}{\$10,000} = 0.23 \] ### **Step 5: Convert to Percentage** \[ \text{HPR (\%)} = 0.23 \times 100\% = 23\% \] --- **Answer:** Fred's holding period return on his investment is **23%**. |
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| GPT-4o | To calculate the holding period return (HPR) for Fred's investment, we need to consider both the capital gain from the sale of the shares and the dividends he received during the holding period. The holding period return is given by the formula: \[ \text{HPR} = \frac{\text{Income from Investment} + \text{Ending Value of Investment} - \text{Initial Value of Investment}}{\text{Initial Value of Investment}} \times 100\% \] Let's break down the components of this formula: 1. **Initial Value of Investment (P0)**: This is the amount Fred initially invested, which is $10,000. 2. **Ending Value of Investment (P1)**: This is the amount Fred received when he sold his shares, which is $12,000. 3. **Income from Investment**: This includes the dividends Fred received over the holding period. Since Fred received $100 in dividends each year for 3 years, his total dividend income is: \[ 3 \times 100 = $300 \] Now, we can plug these values into the HPR formula: \[ \text{HPR} = \frac{\$300 + \$12,000 - \$10,000}{\$10,000} \times 100\% \] \[ \text{HPR} = \frac{\$2,300}{\$10,000} \times 100\% \] \[ \text{HPR} = 0.23 \times 100\% \] \[ \text{HPR} = 23\% \] Therefore, the holding period return of Fred's investment is **23%**. |
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| llama3.1-70B-Instruct | To calculate the holding period return (HPR) of Fred's investment, we need to consider both the dividends he received and the capital gain from selling the shares. 1. **Dividends Received**: Over the three years, Fred received $100 in dividends each year, totaling $300. 2. **Capital Gain**: Fred initially invested $10,000 and sold the shares for $12,000. The capital gain is $12,000 - $10,000 = $2,000. 3. **Total Return**: The total return on Fred's investment is the sum of the dividends received and the capital gain, which is $300 (dividends) + $2,000 (capital gain) = $2,300. 4. **Holding Period Return (HPR)**: The HPR is the total return divided by the initial investment. So, HPR = $2,300 / $10,000 = 0.23 or 23%. Therefore, the holding period return of Fred's investment is 23%. |
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| llama3.1-405B-Instruct | To calculate the holding period return (HPR) of Fred's investment, we need to consider both the dividends received and the capital gain (or loss) from the sale of the shares. First, let's calculate the total dividends received: Dividends per year = $100 Number of years = 3 Total dividends = Dividends per year x Number of years = $100 x 3 = $300 Next, let's calculate the capital gain (or loss) from the sale of the shares: Initial investment = $10,000 Sale price = $12,000 Capital gain = Sale price - Initial investment = $12,000 - $10,000 = $2,000 Now, we can calculate the holding period return (HPR) as follows: HPR = (Total dividends + Capital gain) / Initial investment = ($300 + $2,000) / $10,000 = $2,300 / $10,000 = 0.23 or 23% Therefore, the holding period return of Fred's investment is 23%. This means that Fred earned a 23% return on his investment over the 3-year period, considering both the dividends received and the capital gain from the sale of the shares. |
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| DeepSeek-Coder-V2 | To calculate the holding period return (HPR) of Fred's investment, we need to consider both the income he received from dividends and the capital gain from selling the shares. The formula for HPR is: HPR = (Income + Capital Gain) / Initial Investment Let's break down the components: 1. Income: Fred received $100 in dividends each year for three years, so his total income is $100 * 3 = $300. 2. Capital Gain: Fred initially invested $10,000 and sold his shares for $12,000. The capital gain is the difference between the selling price and the initial investment, which is $12,000 - $10,000 = $2,000. 3. Initial Investment: Fred's initial investment was $10,000. Now, we can plug these values into the HPR formula: HPR = ($300 + $2,000) / $10,000 HPR = $2,300 / $10,000 HPR = 0.23 or 23% So, the holding period return of Fred's investment is 23%. |
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| Qwen2-72B-Instruct | The holding period return (HPR) of an investment is calculated by dividing the total return of the investment (i.e., the sum of the capital gain and the income received) by the initial investment. In this case, Fred's initial investment was $10,000. Over the three-year period, he received a total of $300 in dividends. When he sold his shares, he received $12,000. The capital gain is the difference between the selling price and the initial investment, which is $12,000 - $10,000 = $2,000. The total return of the investment is the sum of the capital gain and the income received, which is $2,000 + $300 = $2,300. Therefore, the holding period return of Fred's investment is $2,300 / $10,000 = 0.23, or 23%. |
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| baichuan4 | To calculate the holding period return (HPR) of Fred's investment, we need to consider both the capital gain (or loss) and the dividend income. The HPR formula is: \[ HPR = \frac{P_1 + D - P_0}{P_0} \] where: - \(P_1\) = the price at which the shares were sold (ending value), - \(D\) = the total dividend income received during the holding period, - \(P_0\) = the initial purchase price of the shares (beginning value). Given the information in the problem: - \(P_1 = \$12,000\) (the selling price of the shares), - \(D = \$300\) (the total dividend income received over three years), - \(P_0 = \$10,000\) (the initial investment). Substituting these values into the formula: \[ HPR = \frac{\$12,000 + \$300 - \$10,000}{\$10,000} \] \[ HPR = \frac{\$2,300}{\$10,000} \] \[ HPR = 0.23 \text{ or } 23\% \] Therefore, the holding period return of Fred's investment is 23%. |
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| doubao | The initial investment is $10,000. The income from dividends is $300. The final value of the investment (sale price) is $12,000. The total return is the sum of the income and the increase in the value of the investment, so it is $300 + ($12,000 - $10,000) = $300 + $2000 = $2300. The holding period return is the total return divided by the initial investment and expressed as a percentage: ($2300 / $10,000) * 100% = 23%. |
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| minimax | To calculate the holding period return (HPR) of Fred's investment, we need to consider both the income he received from dividends and the capital gain or loss from selling the shares. The formula for holding period return is: \[ HPR = \frac{(Income + (Selling\ Price - Cost\ Price))}{Cost\ Price} \] Where: - Income is the total dividends received over the holding period. - Selling Price is the amount Fred sold the shares for. - Cost Price is the amount Fred initially invested. Given: - Income = $300 (since he received $100 each year for three years) - Selling Price = $12,000 - Cost Price = $10,000 Now, we can plug these values into the formula: \[ HPR = \frac{($300 + ($12,000 - $10,000))}{$10,000} \] \[ HPR = \frac{($300 + $2,000)}{$10,000} \] \[ HPR = \frac{$2,300}{$10,000} \] \[ HPR = 0.23 \] To express this as a percentage, we multiply by 100: \[ HPR = 0.23 \times 100\% \] \[ HPR = 23\% \] Therefore, the holding period return of Fred's investment in ABC Corp. shares over the three-year period is 23%. |
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| kimi | The holding period return (HPR) is the total return of an investment over a specific period, expressed as a percentage of the initial investment. It includes both capital gains (or losses) and income (such as dividends) received from the investment. To calculate the holding period return, we need to consider both the capital gain and the dividend income. 1. **Capital Gain**: This is the difference between the selling price and the purchase price of the shares. \[ \text{Capital Gain} = \text{Selling Price} - \text{Purchase Price} \] \[ \text{Capital Gain} = \$12,000 - \$10,000 = \$2,000 \] 2. **Dividend Income**: Fred received $100 in dividends each year for three years. \[ \text{Total Dividend Income} = \$100 \times 3 = \$300 \] 3. **Total Return**: This is the sum of the capital gain and the total dividend income. \[ \text{Total Return} = \text{Capital Gain} + \text{Total Dividend Income} \] \[ \text{Total Return} = \$2,000 + \$300 = \$2,300 \] 4. **Holding Period Return**: This is the total return expressed as a percentage of the initial investment. \[ \text{HPR} = \left( \frac{\text{Total Return}}{\text{Initial Investment}} \right) \times 100\% \] \[ \text{HPR} = \left( \frac{\$2,300}{\$10,000} \right) \times 100\% = 23\% \] So, the holding period return of Fred's investment is 23%. |
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| wenxinyiyan | To calculate Fred's holding period return on his investment, we need to consider both the dividends he received and the appreciation (or depreciation) in the value of his shares when he sold them. Fred's initial investment was $10,000. Over the three-year holding period, he received a total of $300 in dividends ($100 per year). When he sold his shares, he received $12,000. The holding period return can be calculated using the following formula: Holding Period Return = (Final Sale Price + Total Dividends Received - Initial Investment) / Initial Investment Plugging in the numbers: Holding Period Return = ($12,000 + $300 - $10,000) / $10,000 = ($2,300) / $10,000 = 0.23 = 23% So, Fred's holding period return on his investment in ABC Corp. shares was 23%. |
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| zhipu | The holding period return (HPR) is a measure of the total return on an investment over the period it was held. It takes into account both the income received from the investment (in this case, dividends) and the change in the value of the investment (capital gain or loss). To calculate the holding period return, we use the following formula: \[ \text{HPR} = \frac{\text{Income Received} + (\text{Ending Value} - \text{Beginning Value})}{\text{Beginning Value}} \] Where: - Income Received is the total income from the investment over the holding period. - Ending Value is the value of the investment at the end of the holding period. - Beginning Value is the initial value of the investment. Let's plug in the values from the problem: - Income Received: Fred received $100 in dividends each year for 3 years, so the total income is $300. - Ending Value: Fred sold his shares for $12,000. - Beginning Value: Fred initially invested $10,000. Now we can calculate the HPR: \[ \text{HPR} = \frac{300 + (12,000 - 10,000)}{10,000} \] \[ \text{HPR} = \frac{300 + 2,000}{10,000} \] \[ \text{HPR} = \frac{2,300}{10,000} \] \[ \text{HPR} = 0.23 \] To express the holding period return as a percentage, we multiply by 100: \[ \text{HPR} = 0.23 \times 100 = 23\% \] So, the holding period return of Fred's investment is 23%. |
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| gpto1 | To determine Fred's holding period return (HPR) on his investment in ABC Corp shares, we'll calculate the total return he earned over the holding period and express it as a percentage of his initial investment. **Holding Period Return (HPR) Formula:** \[ \text{HPR} = \frac{\text{Total Income} + (\text{Ending Value} - \text{Beginning Value})}{\text{Beginning Value}} \] Where: - **Total Income** = Sum of all dividends received during the holding period. - **Beginning Value** = Initial amount invested. - **Ending Value** = Value of the investment at the end of the holding period (sale price). --- ### **Step 1: Calculate Total Income (Dividends Received)** Fred received dividends annually for three years. \[ \text{Total Income} = \text{Annual Dividend} \times \text{Number of Years} = \$100 \times 3 = \$300 \] ### **Step 2: Determine the Capital Gain (or Loss)** \[ \text{Capital Gain} = \text{Ending Value} - \text{Beginning Value} = \$12,000 - \$10,000 = \$2,000 \] ### **Step 3: Calculate Total Return** Total return includes both the income from dividends and the capital gain. \[ \text{Total Return} = \text{Total Income} + \text{Capital Gain} = \$300 + \$2,000 = \$2,300 \] ### **Step 4: Compute the Holding Period Return** \[ \text{HPR} = \frac{\text{Total Return}}{\text{Beginning Value}} = \frac{\$2,300}{\$10,000} = 0.23 \] ### **Step 5: Convert to Percentage** \[ \text{HPR (\%)} = 0.23 \times 100\% = 23\% \] --- **Answer:** Fred's holding period return on his investment is **23%**. |
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| deepseekv3 | To calculate the **holding period return (HPR)** of Fred's investment, we need to consider both the **capital gain** (or loss) from the sale of the shares and the **dividends** received during the holding period. The formula for HPR is: \[ \text{HPR} = \frac{\text{Ending Value} - \text{Beginning Value} + \text{Income Received}}{\text{Beginning Value}} \] ### Step 1: Identify the values - **Beginning Value (Investment)**: $10,000 - **Ending Value (Sale Price)**: $12,000 - **Income Received (Dividends)**: $100 per year for 3 years = $300 ### Step 2: Plug the values into the formula \[ \text{HPR} = \frac{12,000 - 10,000 + 300}{10,000} \] ### Step 3: Simplify the calculation \[ \text{HPR} = \frac{2,300}{10,000} = 0.23 \] ### Step 4: Convert to a percentage \[ \text{HPR} = 0.23 \times 100 = 23\% \] ### Final Answer: The **holding period return** of Fred's investment is **23%**. |
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