Financial Risk Manager Part 1

Financial Risk Manager Part 1

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The estimated slope coefficient (β₁) for a certain stock is 0.8823 with a standard error equal to 0.0931. Assuming that the sample had 10 observations, carry out a statistical test to determine if the slope coefficient is statistically different than zero. Quote the test statistic and the decision rule using a 5% level of significance.

TTanishq

Explanation:

Detailed Explanation

Hypothesis Formulation

  • Null Hypothesis (H₀): β₁ = 0 (slope coefficient is not statistically different from zero)
  • Alternative Hypothesis (Hₐ): β₁ ≠ 0 (slope coefficient is statistically different from zero)

Test Statistic Calculation

  • Given: β₁ = 0.8823, standard error = 0.0931, n = 10 observations
  • Degrees of freedom = n - 2 = 10 - 2 = 8
  • Test statistic formula: t = (β₁ - β₀) / s.e.(β₁)
  • t = (0.8823 - 0) / 0.0931 = 9.477

Critical Values

  • For a 5% level of significance with a two-tailed test, α/2 = 0.025
  • Critical t-value (t₀.₀₂₅,₈) = ±2.306 (from t-distribution table)

Decision Rule

  • Rejection region: t < -2.306 or t > 2.306
  • Non-rejection region: -2.306 ≤ t ≤ 2.306

Conclusion

  • Since the calculated test statistic (9.477) > critical value (2.306), we reject the null hypothesis
  • This means we have sufficient evidence to conclude that the slope coefficient is statistically different from zero at the 5% significance level

Therefore, the correct answer is 9.477, reject H₀

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