To solve this problem, we will use Python and the yfinance library to download the Tesla stock data, calculate the continuously compounded returns, and then calculate the value of a $10,000 investment.

Here are the steps:

1. First, we need to install the yfinance library. You can do this by running `!pip install yfinance` in your Python environment.

2. Import the necessary libraries:

```python
import yfinance as yf
import numpy as np
```

3. Download the Tesla stock data from the first trading day of January 2021 to July 30th, 2021:

```python
data = yf.download('TSLA', start='2021-01-01', end='2021-07-30')
```

4. Calculate the continuously compounded returns. We can do this by taking the natural logarithm of the ratio of each day's adjusted closing price to the previous day's adjusted closing price:

```python
data['returns'] = np.log(data['Adj Close'] / data['Adj Close'].shift(1))
```

5. Calculate the cumulative return by taking the cumulative sum of the returns:

```python
data['cumulative_return'] = data['returns'].cumsum()
```

6. Calculate the value of a $10,000 investment. We can do this by multiplying the initial investment by the exponential of the cumulative return:

```python
investment_value = 10000 * np.exp(data['cumulative_return'].iloc[-1])
```

The `investment_value` variable will hold the value of a $10,000 investment in Tesla on July 30th, 2021.

Please note that the actual value will depend on the exact stock prices on the specified dates.

Question

To solve this problem, we will use Python and the yfinance library to download the Tesla stock data, calculate the continuously compounded returns, and then calculate the value of a $10,000 investment.

Here are the steps:

1. First, we need to install the yfinance library. You can do this by running `!pip install yfinance` in your Python environment.

2. Import the necessary libraries:

```python
import yfinance as yf
import numpy as np
```

3. Download the Tesla stock data from the first trading day of January 2021 to July 30th, 2021:

```python
data = yf.download('TSLA', start='2021-01-01', end='2021-07-30')
```

4. Calculate the continuously compounded returns. We can do this by taking the natural logarithm of the ratio of each day's adjusted closing price to the previous day's adjusted closing price:

```python
data['returns'] = np.log(data['Adj Close'] / data['Adj Close'].shift(1))
```

5. Calculate the cumulative return by taking the cumulative sum of the returns:

```python
data['cumulative_return'] = data['returns'].cumsum()
```

6. Calculate the value of a $10,000 investment. We can do this by multiplying the initial investment by the exponential of the cumulative return:

```python
investment_value = 10000 * np.exp(data['cumulative_return'].iloc[-1])
```

The `investment_value` variable will hold the value of a $10,000 investment in Tesla on July 30th, 2021.

Please note that the actual value will depend on the exact stock prices on the specified dates.

Knowee AI · Accepted Answer