Nikkei 225 vs. S&P 500 – Are They Correlated?

(Click on the image to enlarge)

Muhammad is interviewing for the Market Data Analyst position. 

Question # 1
Interviewer: The above graphics comprise the daily closing data between July 1, 2018 and July 31, 2019. Are you familiar with these two indices?

Muhammad: Yes, I work with them quite frequently. S&P 500 is our broader market index, while the Nikkei 225 is the Japanese counterpart. 

Question # 2
Interviewer: Would you say these two indices are highly correlated? Qualify your answer with the appropriate statistic.

Muhammad: No. They have low to moderate correlation depending on the statistic you consider. Based on the correlation coefficient, they have moderate correlation, whereas the two regression r-squared(s) are demonstrating lower correlations. 

Question # 3
Interviewer: Considering Nikkei's significantly higher standard deviation, would you say it is more volatile than the S&P 500?

Muhammad: No. The standard deviations are not directly comparable because the underlying data values are significantly different. In fact, the graph axes show how different they are.

Question # 4
Interviewer: Given these statistics, how would you characterize the relative volatility here? 

Muhammad: Since the coefficient of variation is a normalized statistic (standard deviation divided by average), it is a better statistical indicator of the market volatility. Thus, Nikkei was slightly less volatile than the S&P 500 during this period.

Question # 5
Interviewer: If you are asked to establish a better correlation between these two markets, what would you do?

Muhammad: Instead of 13 months' worth of data, I would use a more extended data series, perhaps going back five to six years, thus smoothing out the scatter, resulting in more meaningful correlation statistics.

Question # 6
Interviewer: How did you decide on five to six years, rather than a longer series?

Muhammad: I used five to six years, to avoid having to pick any data from the bottom of the last recession. The real recovery started about six years ago so the last five to six years would provide more normal data.

Question # 7
Interviewer: By extending the series to five to six years, you will be introducing more noise and volatility. How is that statistically more prudent?

Muhammad: I will switch from the daily closings to weekly closings which are inherently smoother and less volatile. Weekly closings are more modelable as well.
  
Question # 8
Interviewer: The left header of the top graphic says "Statistics." Is that accurate?

Muhammad: Yes. Statistics are derived from samples, while parameters are extracted from the entire population. In this case, you are working out of a 13-month sample.

Question # 9
Interviewer: We have openings in both stock fund and index fund units. If you are allowed to choose, which one would you opt for and why?

Muhammad: Definitely the stock fund. It would be lot more challenging. I will get to research the entire sector, narrow my choices down and make recommendations on my final selections. I am looking forward to a challenging job like that.


Disclaimer - The author is not advocating the indices listed here. Consult your Registered Rep, RIA or Financial Planner for an appropriate asset allocation model and the suitability of stocks, indices and other holdings for your portfolio.

Good Luck!

Sid Som, MBA, MIM
President, Homequant, Inc.
homequant@gmail.com

Link to the Book
How to Solve Complex Data Problems in a Job Interview (20 Live Simulations with actual Market Data)

Does VIX Really Move in Tandem with S&P 500?

-- Intended for New Graduates --

VIX is the implied volatility index derived off the S&P 500, so it has become one of most widely watched and followed market metrics in the financial world, since its very inception. 

Many professional traders still define their market entry and exit based largely on the movement of the VIX and their  primary stock trading mantra continues to be:

"When VIX is high, it's time to buy.

When VIX is low, it's time to go."

So, let's use some recent market data (July 1, 2018 thru June 30, 2019) to examine if the S&P 500 index and VIX truly move in tandem and, if so, to what extent (meaning the extent of their statistical relationship).

As a student, you might have used the weekly closing data to establish such relationships, but now that you are ready to enter the corporate world, start making your case more emphatically with both daily and weekly closing data, where the daily serves as the "Champ" while the weekly "Challenges."

Though the correlation coefficient is the primary metric to derive and demonstrate such a relationship, a scatter plot with the trendline and the R-squared is as important considering it offers a more compelling visual case showing the line of best fit relative to the datapoints. 

In this instance, the correlation matrix of daily closings shows a high inverse correlation (-0.828) between them, meaning they move in tandem (not necessarily in lockstep) but in opposite directions. The daily scatter plot also confirms the same inverse relationship, with a fairly high R-squared (0.716). 

Therefore, the professional traders tend to use the VIX Options to hedge the S&P 500 Index (loosely, a long-short strategy).

As you expect, the correlation matrix of weekly closings would show a similar but smoother inverse relationship, and it certainly does (-0.842).

Likewise, the weekly scatter plot shows the same inverse relationship, as well as a negative trendline, predictably with a slightly tighter fit and a higher R-squared (rising to 0.747). 


PART-2


Now, let's simulate a job interview and frame a few meaningful questions out of the above presentation (remember, in a job interview they are not going to ask you some straight-forward questions like the definition of VIX or the S&P 500 Index, etc.)...

1. Interviewer: Megan, look at this Daily Scatter Plot and tell me if X and Y have been correctly graphed.

Megan: Yes, because VIX is a derivative of the S&P 500 index, and not the other way around. Using the basic math construct of Y is a function of X, VIX has been corrected depicted on the Y-axis.

2. Interviewer: Other than the two slightly different R-squared values, do you see any other difference between the Daily and Weekly Scatter Plots?

Megan: Yes, two basic differences: (a) obviously, the Daily plot has roughly five times more datapoints than the Weekly one, and (b) as expected, the Weekly Plot is smoother.

3. Interviewer: Do you see any technical inconsistency between the two scatters?

Megan: Yes, one. The X-scales are slightly different. They should have been held constant. 

4. Interviewer: Why do you think the Daily Correlation Coefficient is different from the Daily R-squared?

Megan: They are not apples-to-apples. The underlying maths are different. The Correlation Coefficient shows the overall statistical relationship between two variables, while R-squared shows to what extent (as a %) the independent variable explains the variations in the dependent variable.

5. Interviewer: As a follow-up to the prior question, why is the Daily Correlation Coefficient negative while the R-squared is positive?

Megan: Adding to my prior answer, the Correlation Coefficient can vary between +1 and -1, while the R-squared varies between 0 and 1 (cannot be negative), hence the difference. 

6. Interviewer: Why do you think we didn't show you any Regression output(s)?

Megan: Because it's a simple regression construct here, meaning one independent variable to the dependent variable. Had it been a multi-variate event, you would have produced a multiple regression output with the respective parameter estimates and the associated statistics.

7. Interviewer: You just indicated that had it been a multiple regression, we would have produced the respective parameter estimates with associated statistics. What sort of associated statistics would you have expected to see?

Megan: At a minimum, Standard Errors, T-stats and P-values.
   
8. Interviewer: Take a look at the two Scatter Plots and try to explain why a non-linear Trendline has been forced in.

Megan: Because of the slight tilt-up in the data at the outer end; I mean the most recent data seems to be bucking the trend a bit.  

9. Interviewer: Any guess as to the type of the Trendline?

Megan: Looks like, it's a 2nd or 3rd degree Polynomial.

Interviewer: Megan, we've a few more interviews this week so expect to hear back from us sometime next week. By the way, did you learn all this at school?

"No. My mom taught me."

Good Luck!

Disclaimer - The author is not advocating VIX or indices listed here. Consult your Registered Rep, RIA or Financial Planner for an appropriate asset allocation model and the suitability of stocks, indices and other holdings for your portfolio.


Sid Som, MBA, MIM
President, Homequant, Inc.
homequant@gmail.com