To find the beta of the stock, we can use the formula for beta:

$\beta = \frac{\text{Covariance of the stock and the market}}{\text{Variance of the market}}$

This formula can be rewritten using the correlation coefficient as:

$\beta = \text{Correlation of the stock and the market} \times \frac{\text{Standard deviation of the stock}}{\text{Standard deviation of the market}}$

Given data:

• Standard deviation of the stock = 19.5% = 0.195
• Correlation between the stock and the market = 0.58
• Standard deviation of the market = 12.9% = 0.129

Substituting the values into the formula:

$\beta = 0.58 \times \frac{0.195}{0.129}$

Now, calculating the value:

$\beta = 0.58 \times 1.5116 \approx 0.876$

Therefore, the beta of the stock is approximately 0.88.

Would you like further details or have any other questions? Here are some related questions:

1. How is beta interpreted in investment theory?
2. What does a beta of 0.88 indicate about the stock’s relationship with the market?
3. How does the correlation between a stock and the market influence the beta?
4. What happens to a stock’s beta if the correlation with the market increases?
5. How do standard deviations of stock and market affect the calculation of beta?

Tip: A higher beta indicates more volatility compared to the market, while a lower beta suggests the stock is less volatile than the market.