Financial Risk Manager Part 1
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An analyst has regressed the annual return on a stock (R_stock) against the annual return on the NIFTY 50(R_index) for 36 years. The NIFTY is the National Stock Exchange (NSE) index in India. Results are 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 |
An analyst wants to test the hypothesis given below at 5% significance level: H₀ : b ≤ 1 Hₐ : b > 1
Which of the following statement is correct about slope coefficient?_
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A
Estimated t-statistic: 1.223; Hypothesis: Fail to reject H₀
B
Estimated t-statistic: 3.54; Hypothesis: Reject H₀
C
Estimated t-statistic: 3.54; Hypothesis: Fail to reject H₀
D
Estimated t-statistic: 1.223; Hypothesis: Reject H₀
Explanation:
Explanation
Step 1: Calculate the t-statistic
- Given: b̂ = 1.223, standard error = 0.063, null hypothesis H₀: b ≤ 1
- t-statistic = (b̂ - b₀) / standard error = (1.223 - 1) / 0.063 = 0.223 / 0.063 = 3.54
Step 2: Determine degrees of freedom
- Sample size n = 36 years
- Degrees of freedom = n - 2 = 36 - 2 = 34
Step 3: Identify critical value
- This is an upper one-tailed test at 5% significance level
- Critical t-value for df = 34 at α = 0.05 (one-tailed) ≈ 1.69
Step 4: Decision rule
- Reject H₀ if calculated t-statistic > critical t-value
- 3.54 > 1.69, so we reject the null hypothesis
Step 5: Conclusion
- The estimated t-statistic is 3.54
- Since 3.54 > 1.69, we reject H₀
- This means there is sufficient evidence to conclude that the slope coefficient b is greater than 1
Therefore, the correct statement is: Estimated t-statistic: 3.54; Hypothesis: Reject H₀
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