How Volatile has the Stock Market been?

 

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After recovering from the March 2020 lows, the major indices (Dow, Nasdaq, and S&P) have been on a tear, reclaiming the earlier highs. 

On its way to retesting the old highs, the market did dip several times, offering better buying opportunities, especially in late May and mid-September. For example, after reaching 27,000 in late May, Dow quickly fell back to 25,000 and provided a similar opportunity again in late September.

Though the growth has not been a perfectly linear, the investors nonetheless fared very well who stayed on or bought the dips.

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The High-to-Low ratio is one of the quickest ways to understand market volatility. Obviously, the bigger the spread, the higher the volatility. In a stable market, this ratio will be range-bound between 101 and 103. When it spikes above 105, the market enters a phase of turbulence.

The above graph confirms that the market experienced a very high level of volatility in late May and early June; for example, from a low of 102.74 on 5/18, it dramatically climbed to 109.98 on 6/8, steadily retracing back to 103.03 on 7/56. 

Many quantitative funds and traders take advantage of this volatility via liquid derivatives like options on Indices, VIX, etc.  

Stay safe!

-Sid Som

homequant@gmail.com

Understanding the On-going Market Volatility

As discussed in prior posts, there are different ways to study the market volatility. 

The two quickest way to eyeball volatility during very volatile periods: 

1. Develop Scatter Plot of Daily Closing Prices (top graph) -- Due to the Coronavirus outbreak in the US, the Dow Jones Industrial Average (DJIA) daily closing prices fell from 27,091 on 3/4 to 18,592 on 3/23 -- a historic 31% collapse in a mere 14 days. In fact, the intra-day high on 3/4 was 27,102 while the intra-day low on 3/23 was 18,214. 

Then, the index turned around and rose back to 24,009 on 4/9 -- a stunning 28% recovery (from the close on 3/23) in the next 14 days.

Since the first half was significantly more volatile, the Coefficient of Variation (COV) jumped to 13, compared to the second half when the COV fell to 6.   

2. Compute Intra-day High Price to Low Price Ratios (bottom graph) -- The intra-day high to low price ratio gives a pretty good understanding of the volatility during a certain period. Based  on this method, the volatility peaked on 3/13 (108%) and troughed on 4/9 (102%). 

The polynomial trendline is simply ignoring some of the abrupt spikes, retuning a much smoother surface.

Considering that the time series is quite short here, a priori smoothing is unreasonable; otherwise a 2-to-3 day moving average is generally applied to the raw data to smooth out the outliers before a meaningful trendline is derived.

-Sid Som
homequant@gmail.com

Also Read:
Understanding the Market Volatility ... 12/2/2019 thru 3/2/2020

Understanding the Market Volatility ... 12/2/2019 thru 3/2/2020

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Paula, a Research Analyst with a Master's in Public Health, is interviewing for a Senior Health Care Analyst position. Here is the simulation of the first interview, leading to the final interview.

Interviewer: Paula, since this is a general interview to narrow our choices down to the final ten, it is designed to test candidate's knowledge of the basis data analysis and modeling, rather than the health care data universe per se.

Paula: Sounds very reasonable.   

Question # 1
Interviewer: Lately, the stock market has been going through some serious turbulence so we decided to use the current market data as the basis for this general interview. Does the High/Low Ratio ("Hi/Low") proxy the VIX in this example?

Paula: Yes, it does. A high correlation coefficient of 0.88 confirms that they have been more or less moving in tandem. For example, when the Hi/Low jumped from 101.79% to 115.08%, the VIX also jumped from 17.08 to 40.11. They have a high positive correlation, meaning they move in the same direction.

Question # 2
Interviewer: So, are these two volatility metrics -- Hi/Low ratio and VIX -- interchangeable? If so, is there any need for the Hi/Low ratio? 

Paula: The two metrics are not inter-changeable. The Hi/Low ratio is a descriptive metric that helps analyze the past activity but does not project anything about the future sentiments of the market, whereas the VIX is computed in a more forward-looking manner to project out the short-term future sentiments of the market so they, in a way, complement each other.

Question # 3
Interviewer: In this example, 10 out of the 14 weeks, VIX remained within a tight range of 12.10 to 15.47. How come the average is 18.04?

Paula: Average is heavily influenced by the outliers. The two outlier data points of 40.11 and 41.94 are weighing in, pulling the average up. If you had used the median, it would be around 14, not 18.

Interviewer: Let me quickly check what the median would be. Yes, it's 13.85. Great mental math!

Question # 4
Interviewer: Using your logic of median, if we re-compute all components, what changes would we expect to see?

Paula: The impact of the two lower outlier data points of High, Low and Close would be minimized, thus pushing their median values up. On the contrary, the impact of the two unusually high outlier data points of Volume and Hi/Low would be significantly lessened, thus pushing their median values down.

Question # 5
Interviewer: Is there any other market component that demonstrates a similar relationship with the VIX?

Paula: Yes, the Volume component. In fact, VIX and Volume show even a higher correlation of 0.90. Case in point: When the Volume spiked from 1.096B to 3.019B, VIX jumped from 17.08 to 40.11, proving how they move almost in lockstep.

Question # 6
Interviewer: In terms of Volume, does anything else stand out?

Paula: Yes, the two traditionally-low Volume weeks of 12/23 and 12/30. If you compare the Volume of 12/23 with that of 2/24, you see a huge change -- in fact, a factor of 4.5. Of course, it's an aberration, not a norm.

Question # 7
Interviewer: Why did it happen?

Paula: It's strictly news-driven. The news pertaining to the outbreak of Coronavirus has been making the financial markets around the world very nervous. The uncertainty surrounding this outbreak has a prolonged impact. The financial community needs to have more clarity about this breakout before a real sense of calm returns to the market.    

Question # 8
Interviewer: You seem to think that the many unanswered questions about this outbreak are impacting the market. Please name one such unanswered question that is plaguing the healthcare industry. 

Paula: We do not know who will pay for the tests and possible hospitalizations for the millions that are uninsured. Even the millions that are insured with high deductibles are very nervous. For instance, my mom is self-employed so she pays for her own insurance, but to keep the premium manageable, she opted for a plan with a high deductible which is making her very nervous now.

Question # 9
Interviewer: Why do you think the Low and the Closing prices ("Close") have near-perfect positive correlation?

Paula: When the market has been trending down, Low and Close go more or less hand in hand. The flip-side is equally true -- simple collinearity!

Interviewer: Congrats, Paula! You have moved on to the final round. Any questions?

Paula: Thank you very much. If I get this job, do I get to report to you directly? Actually, I would love to be on your team.

Interviewer: I would love to have you on my team, too!

- Sid Som, MBA, MIM
sidsom1@gmail.com

The Final Interview

Link to the Book

FAANG – Review of 2019 Performance

** Intended for New Graduates **

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Wendy, a new college graduate with a major in Economics, is interviewing for the Market Analyst position.

Question # 1
Interviewer: Do you know what the acronym 'FAANG' stands for?

Wendy: Yes, it refers to five major stocks: Facebook, Amazon, Apple, Netflix and Google. In fact, I follow all of them very closely.

Question # 2
Interviewer: Okay, now take a look at the FAANG table and give us your interpretation of its overall performance.

Wendy: Obviously, Apple has hugely outperformed the other four components. While Facebook and Google produced fairly good returns, they were nonetheless below the S&P 500's 2019 return of 30%. Unfortunately, Amazon's return was sub-par while Netflix disappointed its investors. 

Question # 3
Interviewer: Why do you think we've added the Coefficient of Variation (COV)?

Wendy: COV is a very common metric used to demonstrate the volatility of asset classes and components. Amazon was the least volatile component while Apple was the most volatile in the FAANG complex.  

Question # 4
Interviewer: By simply glossing over the data series, would you have known that Apple was the most volatile in the complex?

Wendy: Yes, by simply looking at the data series I could have found it out. It has a much wider spread in the series than the rest, resulting in the highest COV and the volatility.


Question # 5
Interviewer: Was that the right use of the COV metric?

Wendy: It's perfectly fine in an interview setting. If I were compiling a report for a client, I would go back to the daily closing data, at least the weekly closing.

Question # 6
Interviewer: Okay, now switch to the Apple vs. Facebook chart and compare and contrast their performances. 

Wendy: They moved more or less in tandem during the first half of the year. Since then they produced significantly different performances. While Apple continued on a linear  growth path, Facebook moved sideways, remaining mostly range bound.

Question # 7
Interviewer: In terms of the market behavior, do you notice any similarity or dissimilarity between Amazon and Google?

Wendy: Yes, very dissimilar behavior. During the first half of the year, Amazon produced a nice run-up, while Google continued to decline. They however reversed courses in the second half.

Question # 8
Interviewer: Now let's move on to the Amazon chart. What is the point of overlaying the 2-month moving average trendline?

Wendy: To introduce a level of smoothing. It smooths out the noises that are inherent in month-over-month data series. For instance, the moving average trendline here is proving that the April and May data points are somewhat aberrations.   

Questions # 9
Interviewer: How would you graph all five components into one graph?

Wendy: By showing the month-over-month +/- growth rates, so they are apples-to-apples. 

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

Link to the Book

How did Dow Jones Industrial Average (DJIA) Fare in 2019?

** Intended for New Graduates **

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Jason is interviewing for Senior Research Analyst with a major brokerage house.

Interviewer
Question # 1: How would you interpret the 2019 DJIA trend?

Jason: Visually, it's a linear trend. It has been trending at 45 degree. 

Interviewer
Question # 2: When you say 'Visually,' do you mean there could be a better technical trend?

Jason: Yes, a polynomial trend would show better fit with significantly higher r-squared. Yet, I would stick to the linear trend as it would be easier to explain to the general clientele.  

Interviewer
Question # 3: What is the missing piece between these two graphs? Or, is there one?

Jason: Volatility. While the Weekly one depicts the market volatility, the Monthly one irons it out. 

Interviewer
Question # 4: Is there another way to depict the market volatility? If so, would that make the volatility case any stronger?

Jason: The Daily closing graph will show higher volatility but it won't make a better case than the Weekly one. As you know, a level of smoothing -- which the Weekly one incorporates -- is a better way to present volatility to the general clientele. 

Interviewer
Question # 5: What market event is common in these two graphs?

Jason: The precipitous market drop in May, bringing Dow under 25,000. Of course, by early July, Dow climbed to a new high, crossing the 27,000 mark. 

Interviewer
Question # 6: Do you think the May correction was driven by basic fundamentals of the market?

Jason: No. It was more news driven like trade, tariffs, etc. than pure market fundamentals. 

Interviewer
Question # 7: How did you come to the conclusion that it was news-driven rather than fundamentals-driven?

Jason: Had it been fundamentals driven, the correction would have lasted much longer. Instead, you can see the immediate V-shaped recovery leading to new market highs.

Interviewer
Question # 8: What is the difference between the 2-period and 3-period moving averages in the above graphs?

Jason: The 3-period in the Weekly graph points to 3-week moving average, whereas the 2-period in the Monthly refers to 2-month moving average.

Interviewer
Question # 9: Would you advise your clients to continue to pour in money in Dow in Q1-2020? 

Jason: Selectively. I will continue to recommend the Dow components with high dividend payouts. I will also urge them to keep some cash handy, just in case a correction occurs, leading to good buying opportunities.

-Sid Som, MBA, MIM
President, Homequant, Inc.
Homequant@Gmail.com

Link to the Book

Can Dow Jones Industrial Average (DJIA) Predict the Housing Market and vice versa?

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Suraj, a Harvard graduate with two years of experience as market strategist, is interviewing for Senior Quantitative Strategist.

Question # 1

Interviewer: Would you consider these two market segments predictive of each other?

Suraj: Absolutely. The Correlation Coefficient and Regression R-squared are showing they move in lockstep and in the same direction.

Question # 2

Interviewer: Is the linear trendline the best fit? Eyeball the scatter and use your best quantitative judgment.

Suraj: For a management presentation, the linear trendline is fine. For a technical presentation, I would use Polynomial trendline with 3rd order which would reduce the noise on the outer end of the curve.

Question # 3

Interviewer: By doing so, how much improvement do you expect to see? 

Suraj: I would expect the R-squared to move up in the vicinity of 0.96.

Interviewer: Okay, please give me a minute and let me find out. Yes, you are right. It's 0.956, so it's actually 0.96 rounded. I must say, you have developed an excellent eye for the data distribution.

Question # 4

Interviewer: Let's assume we are trying to hang our hat on this solution. Would you recommend this to our clients who enjoy short-term trading?

Suraj: No. This analysis is developed off the monthly data so it is not viable for the short-term traders. For the short-term housing traders, the analysis must be based off the local home sales data and for the short-term equity traders, it must be developed off the most recent 3-months of daily closing data or most recent 6-months of weekly closing data.  

Question # 5

Interviewer: Agreed, this is an analysis, not a solution. Either way, who would you recommend this analysis to? 

Suraj: Those who have much longer time horizon, like the Mutual and Pension Fund Managers, and other long-term investors.  

Question # 6

Interviewer: How would you improve upon this analysis in a very short period of time?

Suraj: I would try to study and isolate the seasonality in both data. For example, for the residential investors, Q1 might be better than Q3. Likewise, Q3 might be the best quarter to sell stocks to book profit. Analysis of seasonality is part and parcel of any long-term trend analysis.  

Question # 7

Interviewer: Would you stick to this data and time series to study the seasonality?

Suraj: No. The study of seasonality requires at least one full cycle of data, preferably more, so I would go back a few more years. Of course, this is a large enough sample to study the basic collinearity so I would expect the collinearity would still remain in the ballpark.

Question # 8

Interviewer: Don't you think the impact of new economic and fiscal policies and other major economic events would distort the seasonality analysis?

Suraj: No. Those impacts can be separated out. For instance, the new cap on SALT has been impacting the high-end residential market in high tax areas so the co-mingling of that sort of data would be imprudent. 

Question # 9

Interviewer: How would you (physically) separate out that data? Give me examples from both data series.

Suraj: In terms of the housing data, you are using the Case-Shiller Composite 20, meaning the largest 20 MSAs in the country. We know the pockets hit hardest by the SALT cap so they must be removed from the data. Similarly, I would not use the stretch of Dow Jones data post 9/11.     

  

* Case Shiller is a registered trademark of S&P CoreLogic.

-Sid Som, MBA, MIM
President, Homequant, Inc.

homequant@gmail.com

Link to the Book

High-Low Ratio is a Good Way to Measure Volatility of Stock Market Averages and Indices

-- Intended for New Analysts and Researchers --

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Stock market Volatility, particularly highly liquid individual stocks, averages and indices can be defined by the ratio of their Daily Highs and Lows. Simply put, the higher ratio represents higher volatility and vice versa. 

The Daily Volatility chart shows an elevated volatility in February through early April, gradually tapering in May, June and July. While the median ratio during this 7-month period was 1.01, it exceeded 1.04 on four occasions in February and 1.03 on five occasions thereafter. Obviously, the February standard deviation was significantly higher than the overall (Feb 0.0158 vs. Overall 0.0093).

As expected, the Weekly Volatility chart shows more extreme volatility as it depicts the weekly highs and lows. For instance, the median ratio and standard deviation were 1.0244 and 0.0180, respectively. The volatility peaked at 1.0925 (week of February 5th), keying off the weekly high of 25,521 and low of 23,360. Additionally, it exceeded 1.04 on six occasions - a wow feat indeed! The volatility waned in May-July.

If you decide to present one chart, the Weekly one is more meaningful as it cuts through the daily noise and hones in on true extremes. In that case, add the trendline. You may also normalize it by Closing Prices, making it more predictive.

Good Luck! 

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

Link to the Book

To Evaluate Performance of a Major Stock, Compare it with the Average/Index it Belongs to

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-- Intended for New Graduates & Analysts --

To understand the performance of a major stock, compare it with the primary index/average it belongs to. Since Goldman Sachs (GS) is one of the 30 stocks that comprise the Dow Jones Industrial Average (DJIA), its performance should be compared with the DJIA, a priori.

The top chart shows the weekly closing prices of both between 7/01/17 and 6/30/18. Though GS outperformed the DJIA through 3/10/18, it completely fell apart ever since, leading to the retesting of the 7/3/17 price. The DJIA, on the other hand, registered a solid 13.34% price appreciation during this one-year period.

The DJIA (middle chart) shows the meteoric rise from 21,400 to 26,600 (24.30% gain) through 1/22/18, but gave back 11% since then. Nonetheless, the remaining annual gain was noteworthy.

GS (bottom chart) performed equally well through 3/5/18, moving up from 222 to 270, with a gain of 21.32%. Unfortunately, that was also the tipping point leading to a linear decline. The trendline confirms the continued awful decline.

FYI - since the weekly closing prices are already smooth, you do not need to add the moving average trendline. When you use the daily closing prices, you do. 

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

- Sid Som, MBA, MIM

President, Homequant, Inc.

homequant@gmail.com

Link to the Book

A Scatter Plot of Weekly Closing Prices is a Good Starting Point to Analyze Stocks and Indices

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               -- Intended for New Analysts --

While there are many ways to learn to analyze stocks or the stock market as a whole, here is one simple way I generally propose:

1. Instead of starting with a Stock or ETF, consider a liquid Index/Average like Dow Jones Industrial Average (DJIA), which comprises the 30 largest cap stocks. You may look at it as the front-end of the stock market. This type of analysis is known as the top-down approach (analysis of individual stocks represents the bottom-up approach). Alternatively, you may use the S&P 500, a.k.a. the broader market.

2. Whether you decide to experiment with stocks or indices, the most common database will consist of these variables: Date, Open, High, Low, Close, Adj Close and Volume. In terms of frequency (time interval), the common choices are: daily, weekly and monthly. Some sites may offer yearly roll-up as well (yearly prices are used to study historical trends like Laureate Shiller's CAPE ratio, etc.).

3. Though the Daily Adj Closing Price is the most frequently used data (along with other variables) in defining trend and strategy, use the Weekly/Adj Price as part of your first attempt. As you can imagine, weekly prices are less noisy and much smoother (than the daily prices), leading to easier data visualization. Once you get into more advanced analysis and modeling, you will use the other variables either as ratios or as independent variables. 

4. The best way to get a good feel for the data, trend and outliers is to create a scatter plot. Eyeball the scatter and fit your trendline. Since you are dealing with weekly averages here, leave out the moving averages. As you learn to analyze the daily data, you will see the utility of 60 to 200-day moving averages which are standard metrics in this business. If you are unsure of the differences amongst linear, logarithmic, exponential, polynomial, power, etc. trendlines, go back to your text books and brush up your knowledge. 

5. One of the skills you must develop is to quickly identify the outliers (noise). If you are working on defining trends leading to business strategy, it is absolutely imperative to work with the data as outlier-free as possible. Look at the two scatter graphs above. The only difference between the top and the bottom is that the latter has three fewer data points (week of 1/7/18, 1/14/18 and 1/21/18), resulting in a much cleaner dataset with higher r-squared. If you remove two more data points (12/31/17 and 1/28/18), the r-squared jumps to 0.923 (not shown). Again, one of the skills (perhaps habits) you must develop is to be able to identify the outliers quickly; otherwise you will end up fitting wrong trendlines.

6. Once you have the data and trendlines under control, the first thing you will look for is the formation of supports. If the stock/index bounces off a price level repeatedly, a support is being buoyed. When the support extends out to form a double bottom (like W), any reversal tends to be bullish.

7. The next thing you need to learn is to identify the congestion level. If the stock/index makes an extended sideways move within a band, it is considered "stuck" within a congestion zone. For instance, if it remains range-bound between $40 and $45 for several weeks, it has developed a short-term congestion. Many professional traders take advantage of the congestion by "channeling" those stocks/indices.

8. Often, a stock/index makes a rally but falls apart quickly at a particular price point. For example, if the stock makes multiple attempts to cut through the $45 area but fails, it has developed a short-term resistance there. Traders who buy on strength tend to develop a watch list of such stocks/indices. Professional traders generally write covered calls when the stock fails to break out.

9. When a stock/index eclipses past the resistance and maintains the upward move, it is considered a breakout. Traders who buy on strength wait for a breakout to occur. As soon as the breakout is confirmed (closes above the breakout price), they start to initiate long positions (or buy calls, sell puts, etc.).

As you get started, these are some of the market basics you must be very comfortable with.

Good Luck!

- Sid Som, MBA, MIM

President, Homequant, Inc.

homequant@gmail.com

Link to the Book

How to Define, Compute and Manage True Volatility of Major Stocks

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The most widely-used metric to determine the volatility of a given stock is known as the Beta which shows the volatility of a stock relative to the overall market (generally S&P 500). When the stock moves in perfect tandem with the market, the Beta is 1. Likewise, when the stock is more volatile, Beta > 1 and vice versa. In the above example, Cisco (CSCO) an Intel (INTC) are the two most volatile stocks while Procter & Gamble (PG) and Coca-Cola (KO) are the least volatile ones.

While Beta is an external metric, an internal metric in the form of a Coefficient of Variation (COV=Std Dev/Mean) may be computed using the daily closing prices. Then, the combination of the external and internal metrics would help create a more efficient and predictive volatility factor (V-factor). FYI - COV is a better metric than Std Dev as it is normalized.

Here is why the aforesaid V-factor is more efficient and predictive than the Beta: Though CSCO has the highest Beta, it has low internal volatility (daily movement of prices) as reflected in the low COV, thus lowering the overall V-factor significantly (down to 6.21), even lower than GE's which tends to move almost in lockstep with the market.

Of course, there are other methods to capture the volatility including modeling the daily swings. 

Disclaimer - The author is not advocating any of the stocks listed here; instead, this is promoted as an alternative research in creating a statistically significant and more predictive volatility factor for individual stocks. Consult your Registered Rep, RIA or Financial Planner for an appropriate asset allocation model and the suitability of stocks and other holdings.  

--Sid Som, MBA, MIM
President, Homequant, Inc.

homequant@gmail.com

Link to the Book

How to Create a Statistically Significant Fund of Funds from Balanced Mutual Funds

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1. Screening Funds: It's important to select funds with very similar attributes which, in turn, will enhance collinearity of the portfolio. In selecting the above funds, the following set of criteria has been used: NAV > $7B; Morningstar Rating = 4 to 5; Track > 10 years; Yield = Positive; YTD Return > 8%.

2. Balanced Funds: Balanced Mutual Funds are inherently diversified (40-60% in stable/dividend stocks, 30-40% in fixed incomes and balance in Cash, Precious metals and other debt instruments). Since these funds are self-hedged by design, meaning stocks hedged by bonds etc., no additional hedge component is needed.

3. Fund of Funds: In order to create a statistically significant Fund of Funds from a group of Balanced Mutual Funds, it is imperative to draw them from a highly correlated group, as shown in the correlation matrix above. Thus, while reducing the number of funds, the "least" collinearity must be adhered to. For instance, since Dodge and Cox shows lower collinearity than its peers, it must be removed first from this line-up.

4. Risk Mitigation: A Fund of Funds  is more prudent from the investment point of view as it helps reduce the general risk embedded in a single balanced fund (risk scenarios: merger, change of ownership, departure of a veteran portfolio manager, etc.). 

Therefore, instead of investing $100K in one balanced fund, it's better to spread the sum over a group of highly correlated balanced funds (again, the highly correlated funds tend to project very similar attributes).

Disclaimer - The author is not advocating any of the funds listed here; instead, this is promoted as an alternative research in creating a statistical fund of funds. Consult your Registered Rep, RIA or Financial Planner for an appropriate asset allocation model and the suitability of mutual funds and other instruments.  

-Sid Som, MBA, MIM
President, Homequant, Inc.

homequant@gmail.com

Link to the Book

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

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