Financial Risk Manager Part 1

Financial Risk Manager Part 1

Get started today

Ultimate access to all questions.

Elizabeth Graham, FRM, runs a regression of monthly stock returns on five independent variables over 66 months. The explained sum of squares is 270, and the sum of squared residuals is 250. Graham then performs a statistical test at the 10% significance level with the null hypothesis that all five of the independent variables are equal to zero. Quote the F-statistic and the conclusion.

TTanishq

Explanation:

Explanation

F-Statistic Calculation

The F-statistic is calculated using the formula:

F=[ESSk][SSR(nβˆ’kβˆ’1)]F = \frac{[\frac{\text{ESS}}{k}]}{[\frac{\text{SSR}}{(n-k-1)}]}

Where:

  • ESS (Explained Sum of Squares) = 270
  • SSR (Sum of Squared Residuals) = 250
  • k (number of independent variables) = 5
  • n (number of observations) = 66

Substituting the values:

F=[2705][250(66βˆ’5βˆ’1)]=[54][25060]=544.1667=12.96F = \frac{[\frac{270}{5}]}{[\frac{250}{(66-5-1)}]} = \frac{[54]}{[\frac{250}{60}]} = \frac{54}{4.1667} = 12.96

Hypothesis Testing

The hypotheses are:

  • Hβ‚€: B₁ = Bβ‚‚ = B₃ = Bβ‚„ = Bβ‚… = 0 (all coefficients are zero)
  • H₁: At least one Bβ±Ό β‰  0 (at least one coefficient is non-zero)

Critical Value Comparison

The critical F-value at 10% significance level with:

  • Numerator degrees of freedom = k = 5
  • Denominator degrees of freedom = n - k - 1 = 66 - 5 - 1 = 60

Critical F-value β‰ˆ 1.946

Since 12.96 > 1.946, we reject the null hypothesis.

Conclusion

We conclude that at least one of the five independent variables is significantly different from zero.

Therefore, option A is correct with F-statistic = 12.96 and the correct conclusion.

Powered ByGPT-5

Comments

Loading comments...