EURO STOXX 50 and the S&P 500 Comparison – Statistics Assignment Help

Assignment Task

Task 

Succinct description of data used in the assignment and sources of data:
The two most important pieces of data used in this assignment were the Closing price for the EURO STOXX 50 and the S&P 500. We sourced data for EURO STOXX 50 from YAHOO finance with EURO currency. For S&P 500 we sourced the data from two sources: YAHOO finance for returns in USD and S&P Global for Returns in EURO. The reason for getting both USD and EURO will be discussed later. Other important data sources were our world in data for initial Covid dates as well as the STOXX Fact sheet for understanding the makeup of EURO STOXX 50.

To compare the returns of the two indices we need to adjust our dataset with both data sets being converted to daily returns. Daily returns allow comparison between the two indexes. Looking at table 1 below we see some key differences:

• A mean over 3 times higher in S&P 500
• Similar standard error, standard deviation, sample variance
• Similar Kurtosis Skewness and Range

Analysis:
When comparing data sets assume S&P 500 is in USD unless otherwise stated. With reference to figures 1-4 we see that both datasets follow an almost identical return distribution and a similar long run shape. This indicates a strong connection between the two distributions. This similar shape would indicate a higher R^2 estimate. The difference in mean but similar Standard deviation could indicate that the two indexes follow the same pattern just at different rates this also suggests that there could be a strong relationship between the two indexes. Similar shapes near the introduction of dummy variables however could reduce impact of dummy variables in regressions.

Tables 2 and 3 show arithmetic and geometric mean returns. Geometric returns are the only real important returns for our cancers Cellular and Molecular Basis of Cancer – Medical Science Assignment Helpas they are the only ones that account for the impact of growth. Comparing the two indexes we see that Euro STOXX 50 was always lower this reinforces the lower average growth in Table 1. In relation to the effect of S&P 500 on Euro STOXX 50 we do see that both indexes increase and decrease at the same time year on year.

For regression 1 you can see by table 4 and 5 that we rejected the null hypothesis for both test 1 and test 2 and 95% and 99.7% confidence intervals. This means that at 2 and 3 standard deviations the S&P 500 had a significant impact on the Euro STOXX 50. A rejection of test 1 indicates that with 99.7% confidence we can say that Beta is significant. A rejection of test 2 indicates however that with 99.7% confidence we can say that the Euro STOXX 50 doesn’t mirror the S&P 500. This indicates that there is a strong probability that there is other factors influencing Euro STOXX 50.

For regression 2 we come to the exact same conclusions as regression 1 with both tests being rejected. The important difference between regression 1 and regression 2 is in the adjusted R^2 value in table 12. The R^2 value is nearly 0.06 off or nearly 6% difference. This difference could be equal to the impact of the currency change. This however cannot be confirmed unless more testing is done.

For regression 3 we had 3 tests. 2 testing if the impact of dummy variables covid and RUWAR are significant and if the impact of the S&P500 was significantly different. For test 1 and 2 on both 95% and 99.7% there was not a significant difference and thus the H0 was not rejected. This indicates that we cannot say if Covid or RUWAR made a significant difference on Euro STOXX 50. For test 3 H0 was not rejected as well indicating that there was not a significant difference between beta in regression 1 and regression 3. R^2 for Regression 3 was nearly identical to regression 1 with it being the same at 3dp. This similar R^2 value indicates there is a small difference in the reliability of both models.

For regression 4 we came to the same conclusions for the 3 tests as regression 3. The difference in R^2 however was extremely close to the difference for regressions 1 and 2. This similar difference again highlights that Currency plays an important role in the relationship between the two currencies.

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