Questions: Question 50 3 pts Which of the following reveals the relationship of a given security's volatility relative to that of the market? Standard deviation. Beta. Treynor. Covariance.

Solution Steps

The covariance between the security returns \( X \) and the market returns \( Y \) is calculated as follows:

\[ \text{Cov}(X,Y) = 0.005 \]

Next, we calculate the standard deviations of both the security returns and the market returns.

For the security returns \( X \):

1. Mean \( \mu_X \) is calculated as: \[ \mu_X = \frac{\sum x_i}{n} = \frac{0.6000000000000001}{5} = 0.12 \]

2. Variance \( \sigma_X^2 \) is calculated as: \[ \sigma_X^2 = \frac{\sum (x_i - \mu_X)^2}{n-1} = 0.004 \]

3. Standard deviation \( \sigma_X \) is: \[ \sigma_X = \sqrt{0.004} = 0.0632 \]

For the market returns \( Y \):

1. Variance \( \sigma_Y^2 \) is calculated as: \[ \sigma_Y^2 = 0.004 \]

2. Standard deviation \( \sigma_Y \) is: \[ \sigma_Y = \sqrt{0.004} = 0.0632 \]

The correlation coefficient \( r \) is calculated using the formula:

\[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \]

Substituting the values:

\[ r = \frac{0.005}{0.0791 \times 0.0632} = 1.0 \]

Finally, we calculate Beta \( \beta \) using the formula:

\[ \beta = \frac{\text{Cov}(X,Y)}{\sigma_Y^2} \]

Substituting the values:

\[ \beta = \frac{0.005}{0.004} = 1.25 \]

Final Answer