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:
| 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:
Which of the following statement is correct about slope coefficient?
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Community
NNikitesh
A
Estimated t-statistic: 1.223; Hypothesis: Fail to reject
B
Estimated t-statistic: 3.54; Hypothesis: Reject
C
Estimated t-statistic: 3.54; Hypothesis: Fail to reject
D
Estimated t-statistic: 1.223; Hypothesis: Reject
Explanation:
Explanation:
-
Calculate the t-statistic:
- Given: b_hat = 1.223, standard error = 0.063, null hypothesis value = 1
- t-statistic = (b_hat - b_null) / standard error = (1.223 - 1) / 0.063 = 0.223 / 0.063 = 3.54
-
Determine degrees of freedom:
- Sample size n = 36 years
- Degrees of freedom = n - 2 = 36 - 2 = 34
-
Identify the test type:
- This is a one-tailed (right-tailed) test since H_a: b > 1
- Significance level α = 5% = 0.05
-
Find critical value:
- For a one-tailed t-test with df = 34 and α = 0.05, the critical value is approximately 1.69
-
Decision rule:
- Reject H_0 if t-statistic > critical value
- 3.54 > 1.69, so we reject the null hypothesis
-
Interpretation:
- The estimated slope coefficient of 1.223 is statistically significantly greater than 1 at the 5% significance level
- This suggests that the stock's beta (sensitivity to market returns) is greater than 1, indicating it's more volatile than the market
Therefore, the correct statement is: Estimated t-statistic: 3.54; Hypothesis: Reject H_0