Answer-first summary for fast verification
Answer: JB = 10.4069, and we reject the null that the portfolio return is normal.
## Explanation The Jarque-Bera test statistic is calculated using the formula: $$JB = n \times \left( \frac{S^2}{6} + \frac{(K-3)^2}{24} \right)$$ Where: - n = sample size = 252 - S = skewness = -0.2023 - K = kurtosis = 3.9118 **Calculation:** 1. **Skewness component:** $$\frac{S^2}{6} = \frac{(-0.2023)^2}{6} = \frac{0.04093}{6} = 0.00682$$ 2. **Kurtosis component:** $$\frac{(K-3)^2}{24} = \frac{(3.9118-3)^2}{24} = \frac{(0.9118)^2}{24} = \frac{0.8314}{24} = 0.03464$$ 3. **Total JB statistic:** $$JB = 252 \times (0.00682 + 0.03464) = 252 \times 0.04146 = 10.4069$$ **Decision:** - Critical value at 5% significance level = 5.99 - Since JB = 10.4069 > 5.99, we **reject** the null hypothesis that the portfolio return follows a normal distribution Therefore, the correct answer is **A**: JB = 10.4069, and we reject the null that the portfolio return is normal.
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A risk analyst is using the Jarque-Bera test to examine whether a client's portfolio return is compatible with a normal distribution. To do so, he collects the past 1-year data (the number of trading days is 252 days) and uses the statistical software to compute the moments of the return data. Specifically, the software reports an estimated skewness of -0.2023 and an estimated kurtosis of 3.9118. Compute the Jarque-Bera test-statistic and make the decision using a test size of 5% (so that the critical value is 5.99):
A
JB = 10.4069, and we reject the null that the portfolio return is normal.
B
JB = 10.4069, and we do not reject the null that the portfolio return is normal.
C
JB = 1.0730, and we reject the null that the portfolio return is normal.
D
JB = 1.0730, and we do not reject the null that the portfolio return is normal.