Eunyoung Hwang, David Wortham, Jongmin Lee
Autor: mybih1009 • September 19, 2015 • Term Paper • 1,069 Words (5 Pages) • 788 Views
Statistics Project 3
Team 9: Eunyoung Hwang, David Wortham, Jongmin Lee
Tommy wants to be advised of the best way to maximize his return on the $50,000 inheritance from his late uncle. He has heard about the potential growth of Korean stock market and has targeted KODEX Samsung Group (ETF) as an intriguing option based on advice from financial experts. Before Tommy makes any decision on his investment, he wants to know whether KODEX has twice as many positive monthly returns than negative returns. Additionally, he wishes to know whether KOSPI returns and KODEX returns are independent in their ups and downs. Furthermore, Tommy wonders if KOSPI and KODEX returns have any significant time trend, and how the two returns are correlated with each other.
1. Chi-square Test:
a) Goodness-of-fit Test
Hypothesis (H0): KODEX Samsung has twice as many positive returns than negative returns.
(Ha): Does not have twice as many positive returns than negative returns.
Chi-square test statistic: χ2 = [(25– 26.7)2/26.7] + [(15– 13.3)2/13.3] = 0.313 (more exact from excel)
- We rounded up the expected value in the equation listed above, but used the unrounded figures in calculating the test statistic.
P-value = 0.5762
For df=1 and α = 10%, the critical value is 2.7055. (α = 5%, 3.8415, α = 1%, 6.6349)
Since the test statistic is smaller than the critical value, we do not reject the hypothesis.
Actual | Up | Down | Total | Expected | Up | Down | Total |
KODEX Return | 25 | 15 | 40 | KODEX Return | 26.7 | 13.3 | 40 |
b) Independence Test
Hypothesis (H0): KOSPI returns and KODEX Samsung returns are independent.
(Ha): KOSPI and KODEX Samsung returns are not independent.
Chi-square test statistic: χ2 = [(21– 14.4)2/14.4] + [(4– 10.6)2/10.6] + [(2– 8.6)2/8.6] +
[(13–6.4)2/6.4] = 19.158 (more exact from excel)
- We rounded up the expected value in the equation listed above, but used the unrounded figures in calculating the test statistic.
P-value = 0.000012
We reject the hypothesis at the 10%, 5%, and 1% significance levels. Therefore, we can say KOSPI returns and KODEX Samsung returns are not independent.
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