Financial Risk Manager Part 1

An analyst has regressed the annual return on a stock (R_stock) against the annual return on the NIFTY 50(R_index) for 30 years. The NIFTY is the National Stock Exchange (NSE) index in India. The results are as shown below. Regression equation:

R_index, t = â + b̂ × R_stock, t + ε_t

Coefficient	Coefficient Estimate	Standard Error
a	0.002	0.001
b	1.223	0.063

Interpret whether the regression coefficients are statistically different from zero at a 95% confidence level? Click here to see critical values of the t-distribution._

Exam-Like

Community

TTanishq

Intercept term (a): Yes; Slope coefficient (b): Yes

Intercept term (a): No; Slope coefficient (b): No

Intercept term (a): No; Slope coefficient (b): Yes

Intercept term (a): Yes; Slope coefficient (b): No

Explanation:

Explanation

To determine if the regression coefficients are statistically different from zero at a 95% confidence level, we perform t-tests for each coefficient.

Hypothesis Tests:

For intercept (a): H₀: a = 0 vs. H₁: a ≠ 0
For slope (b): H₀: b = 0 vs. H₁: b ≠ 0

Degrees of Freedom:

n = 30 years
Degrees of freedom = n - 2 = 30 - 2 = 28

Critical Value:

For a 95% confidence level (5% significance level, two-tailed)
Critical t-value = 2.048

Test Statistics:

For intercept (a):

t-statistic = (0.002 - 0) / 0.001 = 2.0
Since |2.0| < 2.048, we fail to reject H₀
Conclusion: Intercept is not statistically significant

For slope (b):

t-statistic = (1.223 - 0) / 0.063 = 19.413
Since |19.413| > 2.048, we reject H₀
Conclusion: Slope is statistically significant

Final Interpretation:

Intercept term (a): No (not statistically different from zero)
Slope coefficient (b): Yes (statistically different from zero)

This matches option C.