Financial Risk Manager Part 1

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The return on a stock R exhibits the following relationship with the market return (MR).

R = \hat{a} + \hat{b} \times MR

Where $\hat{b}$ is the slope coefficient and $\hat{a}$ is the intercept. After gathering 36 observations, an analyst computed the estimated slope coefficient as 0.6 with a standard error of 0.2. Determine whether the estimated slope coefficient is different from 0 at a 95% confidence level with reference to the critical t-value. Click here to see critical values of the t-distribution.

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TTanishq

The slope coefficient is not significant.

The slope coefficient is statistically significant with a t-statistic of 2.03.

The slope coefficient is statistically significant with a t-statistic of 3.

The slope coefficient is statistically significant with a t-statistic of 1.015.

Explanation:

Explanation

To determine if the slope coefficient is statistically different from zero at a 95% confidence level, we perform a hypothesis test:

Null Hypothesis: $b = 0$
Alternative Hypothesis: $b \ne 0$
Test Type: Two-tailed test

Step 1: Calculate the t-statistic

t = \frac{\text{Sample statistic} - \text{Hypothesized value}}{\text{Standard error of the sample statistic}} = \frac{0.6 - 0}{0.2} = 3

Step 2: Determine the critical t-value

Confidence level: 95% (α = 0.05)
Two-tailed test: α/2 = 0.025
Degrees of freedom: n - 2 = 36 - 2 = 34
Critical t-value: ±2.03

Step 3: Compare and conclude

Since the calculated t-statistic (3) is greater than the critical t-value (2.03), we reject the null hypothesis.

Conclusion: The slope coefficient is statistically significant at the 95% confidence level with a t-statistic of 3.

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