Question 3Covariance of stock and index returns is 0.003, variance of index returns is 0.004. Calculate the beta1 point0.751.312

1. Break Down the Problem

To calculate beta, we need to use the formula for beta in finance, which is given by:

$\beta = \frac{\text{Cov}(R_{s}, R_{m})}{\text{Var}(R_{m})}$

Where:

• $\text{Cov}(R_{s}, R_{m})$ is the covariance of stock returns with market returns.
• $\text{Var}(R_{m})$ is the variance of market returns.

2. Relevant Concepts

We need to identify the values given in the problem:

• Covariance of stock and index returns, $\text{Cov}(R_{s}, R_{m}) = 0.003$
• Variance of index returns (market returns), $\text{Var}(R_{m}) = 0.004$

3. Analysis and Detail

Now, we will substitute the known values into the beta formula:

$\beta = \frac{0.003}{0.004}$

Calculating this gives:

$\beta = 0.75$

4. Verify and Summarize

The calculation shows that the beta is $0.75$. This indicates that the stock is less volatile compared to the market index. Typically, a beta less than 1 suggests that the stock tends to move less than the market.

Final Answer

$\beta = 0.75$