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

Link to the Book

A Diversified REIT ETF may Proxy Physical Real Estates in an Asset Allocation Model

The Correlation Matrix (top graphic) shows the correlation between the S&P 500 and five publicly traded Real Estate Investment Trust (REIT) ETFs. While MORT is a mortgage REIT, the other four are diversified equity (Real Estate) REITs. 

The Correlation Matrix shows almost negligible correlations between the S&P 500 and the REITs. This lack of correlation entices investors to own REITs as a separate asset class in their asset allocation model, proxying a portfolio of diversified real estates (residential, commercial, and industrial) without physically owning and managing them. 

To maintain the tax advantage status, REITs have to pay out at least 90% of their income as a dividend. Since REITs are designed to yield higher dividends, they tend to complement the fixed income (asset) class in the asset allocation model.

Correlation coefficients ranging between + 0.10 and -0.10 are considered uncorrelated. VNQ is the only one that falls outside of that range, showing a slightly negative correlation. Save MORT, the other four equity REITs are moving in lockstep, considering their top holdings (accounting for at least 35% of the portfolio) are virtually alike (e.g., American Tower, Simon Property, Crown Castle, Prologis, Public Storage, Avalon Bay, Equinix, Equity Residential, Digital Realty, etc.).

Though Mortgage REITs tend to generate much higher yields than their equity (real estate) counterparts, they are inherently more volatile as they are more prone to interest rate fluctuations. MORT currently has a yield of 7.77% compared to 3% to 4% for the equity ones.

   

The weekly graph (bottom graphic) is more telling. While the S&P 500 moved from 2,400 to 2,800 (between 8/1/17 and 7/31/18), both REITs (IYR and VNQ) remained range-bound between $74 and $82. As a result, the diversified equity REITs have low beta (usually between 0.5 and 0.7). 

Again, a diversified equity REIT ETF could be an excellent way to own this asset class (a wide variety of real estates) without physically owning and managing them.

Disclaimer - The author is not advocating any of the ETFs/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 your portfolio.

- Sid Som

homequant@gmail.com

Link to the Book

Can FAANG Stocks Predict Dow Jones Industrial Average (DJIA)?

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John, a new college graduate with co-concentrations (Econ and Math) is interviewing for Equity Analyst with a major Hedge Fund. 

Interviewer: Thanks for interviewing with us, John. On that corner laptop you'll find a spreadsheet containing one year of daily closing prices - between 7/1/2018 and 6/30/2019 - pertaining to the Dow Jones Industrial Average (DJIA) and FAANG (Facebook, Amazon, Apple, Netflix and Google) stocks. Please analyze the data and give us your conclusions as to:

a) The FAANG stock that is most predictive of the DJIA so, from time to time, we could recommend it to our clients in place of the Dow ETF.

b) The FAANG stock that best represents as a hedge to the DJIA so it could be recommended as the DJIA becomes over-valued.

c) Finally, the FAANG stock that is highly predictive of the DJIA but has low multi-collinearity within the mix.

Once you are ready, just press 201 on this dial and I'll be back to talk to you.

___________________________________________________

As the interviewer returns, John presents his conclusions:

1. John -- The above correlation matrix clearly demonstrates that Amazon (AMZN) is the FAANG stock that is most predictive of the DJIA. The regression output, with DJIA as the dependent variable in the equation, further confirms it via its smallest standard error.

Interviewer -- But Netflix (NFLX) has better t-stat and lower p-value? Doesn't it contradict your conclusion?

John -- No. The correlation coefficient, which is the primary metric here, makes Amazon a far better (DJIA) predictive choice than Netflix.

2. John -- Of the FAANG components, Facebook (FB) is best hedge as it has the lowest correlation with DJIA. The regression out also confirms it via its negative coefficient.

Interviewer -- Would it be okay to recommend Facebook as a DJIA hedge to our clients?

John -- If the choice is limited to the FAANG complex only, yes. But there are other ETFs with much lower correlations with DJIA. I'd rather research and recommend one from the outside universe.     

3. John -- Apple (AAPL) is the FAANG stock that is highly predictive of the DJIA, but has lower multi-collinearity with the other components. The graph shows how Apple diverges from Facebook (which is the inside hedge component) with very low r-squared.

Interviewer -- Would you play the FAANG complex? If so, how?

John -- Each component has its own contributory properties so the complex as a whole makes a good investment vehicle. I would play it via a liquid FAANG ETF and as the DJIA becomes over-valued I would introduce an ETF with good hedging property.

   

Disclaimer - The author is not advocating the stocks/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)

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

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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)

How to define Options Strategy from a Technical Chart

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Question #1
Interviewer: Would you consider this a strong technical chart? What sort of trend do you see here?

Candidate: Yes, it is a good technical chart with a strong linear trend.

Question #2
Interviewer: Why do you think it's a strong linear trend?

Candidate: When the R-squared is approaching 0.90, it is considered strong, if not very strong.

Question #3
Interviewer: Do you think the weekly closing prices would have made the chart more meaningful?

Candidate: No. Since you are using only 6 months of data here, daily closing prices are better. Weekly would be better if you were using at least 12 months of data. 

Question #4
Interviewer: What is the best inflection point on the chart?

Candidate: Around the 90th trading day when the stock reversed its direction from under $10 and started making sharp upward move.  

Question #5
Interviewer: Would you still consider that stretch linear?

Candidate: No. That particular stretch of data shows more of an exponential trend than linear trend. Of course, the overall trend is still linear.

Question #6
Interviewer: If you were analyzing that stretch of data only, would you have seen any difference in stats?

Candidate: Yes. The R-squared would be higher, perhaps around 0.90 (it's actually 0.90, though not shown).

Question #7
Interviewer: As one of our market analysts, would you advise our clients to sell covered calls now?

Candidate: No. When a stock keeps making higher highs everyday, I would not advise selling covered calls. I will let it continue its run, for now.

Question #8
Interviewer: When do you think it's appropriate to sell covered calls?

Candidate: When the stock breaches a major support like the 120-day moving average.   

Question #9
Interviewer: How would you decide what kind of covered call to sell? 

Candidate: If the decline is really sharp, I will sell in the money or deep in the money. If it is just trending down, I will sell at the money anticipating a short consolidation and then a quick reversal.  

Disclaimer - The author is not advocating the stocks/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. 

Link to the Book

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

Crude, Gold, Treasury Yields and VIX – Which one is most Predictive of Dow Jones Industrial Average?

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Julie is interviewing for an Equity Analyst position with a Wall Street Brokerage firm.

Question # 1
Interviewer: Julie, we used 13-months (i.e., 07/01/2018 thru 07/31/2019) worth of daily closing prices to compile this correlation matrix and the regression graph. Now, by looking at them, can you tell me what our objective here is?

Julie: You are trying to see if Gold, 10 and 30-year Treasury Yields, Crude and VIX collectively can predict Dow Jones Industrial Average (DJIA).

Question # 2
Interviewer: Why did we use ETFs like GLD and XOP instead of the actual futures data?

Julie: Futures contracts have different expiration dates so combining such data from different contract periods would be discontinuous. ETFs, instead, would be much better proxies.

Question # 3
Interviewer: In this example, is VIX the most un-correlated with DJIA? Qualify your answer with the underlying theory.

Julie: No. It's the most correlated of the five independent variables. Correlation can be positive or negative, hence the correlation coefficient varies between +1 and -1. VIX is negatively correlated with DJIA here.

Question # 4
Interviewer: In that case, which one is the least correlated independent variable here?

Julie: It's the crude ETF, that is the XOP variable in the equation.

Question # 5
Interviewer: Based on this correlation matrix, would you use all of the five independent variables in the regression equation? Qualify your answer with the underlying theory.    

Julie: No. I would remove GLD and 30-year Treasury Yield right off the top because they are failing the test of multi-collinearity. GLD is highly correlated with three others, while the 30-year Yield is moving in lockstep with the 10-year Yield.

Question # 6
Interviewer: Why did you choose 10-year Yield over 30-year Yield? Aren't they interchangeable here?

Julie: 10-year has better predictive relationship with the DJIA and lesser correlation with the VIX, while 30-year has only one positive, that is lesser correlation with XOP. Out of three, two positives here are better than one positive. Therefore, they are not necessarily interchangeable here.

Question # 7
Interviewer: The regression line shows a r-squared of 0.7633. What r-squared would the actual regression output show?

Julie: The same 0.7633. The regression value here represents all five independent variables against the same DJIA dependent variable so the r-squared would be identical. You are basically graphing the outcome of the actual regression.

Question # 8
Interviewer: If you are asked to fine-tune the model with an improved r-squared, what would you do? Qualify your answer with the underlying theory.

Julie: I would remove some outliers systematically from both ends of the curve. Unlike weekly closing prices, daily closing prices are inherently very volatile, so removing some outliers would be reasonable.

Question # 9
Interviewer: If you are forced to run a simple regression, rather than a multiple regression comprising these five variables, which one would you choose? And, what type of regression coefficient would you expect to see?

Julie: VIX, because it has the best predictive relationship with the DJIA. The regression coefficient would be negative as well, in line with the correlation coefficient.

Disclaimer - The author is not advocating the ETFs/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