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

Write Covered Calls to Create Cash-flows during Market Corrections

 Pros often use advanced options as one of their market strategies to manage portfolios. While professional options strategies require advanced knowledge of quantitative sciences, simple options hardly require any such experience. Buying some calls to take advantage of the rising markets or buying some puts to hedge downturns is relatively straightforward.

More importantly, the practice of writing covered calls, meaning selling calls against existing positions, to create cash-flows when the market gets overbought or is ready for an imminent correction is considered an excellent market strategy even for the individual investors in stocks, bonds, commodities, foreign exchanges, and real estate. Writing covered calls is even allowed in IRA accounts, considering the safety of it.

Buying vs. Selling Calls

While options-approved individual and professional investors often buy calls to take advantage of the rising markets, buying calls carries an inherent risk if the market suddenly turns negative or moves sideways, thus making those calls worthless or at least significantly eroding their time value. Of course, if the market behaves as expected, those calls gain in value. Therefore, buying calls is a speculative strategy, if not a total gamble. 

On the other hand, writing covered calls could be a very sound investment strategy to hedge market downturns or overbought conditions. For example, if you bought 1,000 X stocks at $30 (cost basis) at the bottom of the last correction and the same stock is now trading at $45, you may consider writing up to 10 covered calls (each option covers 100 shares) to create some temporary cash-flows, without having to liquidate the position. 

Of course, the mere fact that your stock has made a decent run-up should not force you to sell some calls. Make sure your research shows that the market is ready to correct or is way overbought, or at least, your stock is way ahead of the market and shows clear signs of an overbought condition. One such movement could be the breach of a statistically significant trend-line, e.g., the 200-day moving average. In such a changed market situation, writing some covered calls is an excellent way to create meaningful cash-flows.

Ideally, calls should be written against 50% of the covered positions, positioning the rest to ride out the market or take advantage of the further upside potential in the market just if your research turns out somewhat ill-timed. Of course, any such options strategy must always be reached in consultation with a registered investment professional to minimize speculation.

Again, while I am opposed to buying options – calls or puts – I am always in favor of writing limited calls as long as the market conditions, as mentioned earlier, are met and proper professional help is part and parcel of the decision-making process.

In the money vs. At the money vs. Out of the money

Options have two value attributes – intrinsic value and time value. Options contracts expiring shortly, say in six weeks, will have lesser time value than those expiring in six months. Therefore, while buying options, it is always advisable to buy with adequate time, preferably six to nine months remaining on the contract.

Likewise, while selling options, immediate contract months are preferred as market conditions are more predictable. Therefore, if your research shows the market could decline or remain range-bound and choppy in the next three months, consider writing your covered calls keeping the option’s expiration in mind. Of course, the equally important question you would face is: Should you write those calls in the money, at the money, or out of the money? 

If the stock was trading at $45, the $45 strike price would be at the money, $40 would be in the money, and $50 would be out of the money. In other words, in the money options have higher intrinsic value than their counterparts. 

Again, research shows a particular stock has recently made a significant move –- well ahead of the competition with the possibility to retrace more than the overall market and the competition -- writing the covered calls in the money is worthwhile, factoring in the potentially more significant pull-back. On the other hand, if the expected pull-back is in line with the market and the competition, writing at the money or out of the money covered calls will make more economic sense.

Either way, as market trends lower, dragging down the time value, one can always cover (buy back) the position at a fraction of the original selling price, repeating the process at the top of the next bull-run. Conversely, if research proves wrong and the market continues to trend up after the writing of the covered calls, the other unencumbered 50% position will participate in the market.

Always consult a licensed investment advisor before engaging in any options activity as it involves significant risks.

- Sid Som MBA, MIM

homequant@gmail.com

Link to the Book

Did Russell 2000 Outperform S&P 500 in 2019?

        Intended for New Graduates

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Emily, a new graduate with co-concentrations (Econ & Finance), is interviewing for Equity Analyst position. 

Question # 1
Interviewer: Explain to us the basic difference between these two indices. 

Emily: While the S&P 500 index measures the performance of 500 large-cap stocks, the Russell 2000 index measures the performance of 2000 small-cap stocks. S&P 500 is the most widely followed stock market index.

Question # 2
Interviewer: Is there a market definition of large-cap stock? Also, can you name a few large caps?

Emily: Typically, a large-cap company has a market value of at least $10 Billion. Microsoft, Apple, Amazon, Google and Facebook are examples of large-caps. 

Question # 3
Interviewer: Can S&P 500 include one such large-cap stock that is listed on Nikkei only?

Emily: No. S&P 500 comprises large-cap stocks that are listed on US Exchanges.     

Question # 4
Interviewer: The data table shows S&P 500 has higher volatility than Russell's. What "quick" metric did we use to arrive at these volatility figures? And why?

Emily: I believe the quick metric you used is the Coefficient of Variation (commonly known by its short form COV). COV is the ratio of standard deviation to mean. Since you are making inter-index comparisons, you used the "normalized" metric. 

Question # 5
Interviewer: By glossing over these two graphs, do you notice any similarity?

Emily: Yes, between August and December, they both produced linear growth. Spectacular growth, indeed!

Question # 6
Interviewer: Any striking dissimilarity, per se?

Emily: Yes, the correction in August was way more pronounced for Russell than that of S&P's. 

Question # 7
Interviewer: By looking at the data table, can you tell us how S&P outperformed Russell in terms of overall growth?

Emily: Because S&P produced 8% growth between January and August, whereas Russell remained on a slippery slope, failing to hang on to its gains. 

Question # 8
Interviewer: To take advantage of these indices, what investment vehicles would you recommend to our clients?

Emily: Index Funds, Index ETFs, S&P Futures and Options, etc.

Question # 9
Interviewer: Of these two indices, which one would you recommend to our conservative clients? Or, would you recommend both?

Emily: Russell 2000 would not be appropriate for them.

Good Luck!

-Sid Som, MBA, MIM
President, Homequant
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

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

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

Can Sector ETFs be used to construct Funds?

(Click on the image to enlarge)

ETF Sectors:
SPY=S&P 500; XLE=Energy; XLF=Financial; XLI=Industrial; XLK=Technology; XLP=Consumer Staples: XLU=Utilities; XLV=Healthcare; XLY=Consumer Discretionary

Laura is interviewing for the Hedge Fund Analyst position.

Question # 1

Interviewer: These graphics have been compiled off Standard and Poor's Exchange Traded Funds (ETF), reflecting daily closing prices between 07/01/2018 and 07/31/2019. Are you familiar with these ETFs?

Laura: Yes, I track and analyze them quite frequently. While SPY tracks the S&P 500 stock market index, the other ones are individual sector ETFs.

Question # 2

Interviewer: Use 5 sector ETFs to construct an aggressive (long only) fund. Weighting factors can range between 10% and 30%.

Laura: I would use XLF, XLI, XLK, XLP and XLY, equally weighted at 20% each. They are all highly correlated so they would move in tandem.     

Question # 3

Interviewer: How come you didn't select a hedge component while constructing the portfolio?

Laura: Because I was asked to construct an aggressive (long only) fund. An aggressive (long only) fund generally excludes hedges or negatively correlated components. 

Question # 4

Interviewer: In continuation of the prior fund construction, develop a weighted balanced fund where the dividend yields proxy fixed income assets. 

Laura: I would select the three equally-weighted stock ETFs, i.e., XLF, XLK and XLV with low multi-collinearity and the two equally-weighted high yield ones, XLP and XLU, surrogating fixed incomes. 

Question # 5

Interviewer: Why did you skip XLE despite yielding the highest dividend?

Laura: Since it has the highest beta, it's the most volatile one in the mix. Ideally, the balanced funds should try to minimize the use of highly volatile asset classes and components.  

Question # 6

Interviewer: Now, construct an income fund, with minimum volatility and maximum income. 

Laura: In constructing the income fund, I would use variable weights. My fund would include 30% XLU, 25% XLP, 20% XLF, 15% XLV and 10% XLK, respectively.  Again, though XLE has the highest yield, it is also the most volatile, hence skipped.

Question # 7

Interviewer: Is there an alternate use of these 3 funds?

Laura: Yes, as Fund of Funds; for example, for a low risk investor, the income and balance funds could be heavily weighted while the aggressive fund could contribute marginally. Similarly, for someone without any appetite for risk, the aggressive fund could be avoided altogether.

Question # 8

Interviewer: So, what's the use of these sector ETFs when SPY can represent them all?

Laura: SPY represents all the major sectors of the economy, so it's more or less an all of all index. The fund managers cannot use it to address clients' specific investment objectives or levels of risk tolerance. The sector ETFs can help achieve those goals.    

Question # 9

Interviewer: Finally, do you think ETFs have any special advantages over the competing Mutual Funds?

Laura: Yes, ETFs provide a number of advantages over the competing Mutual Funds. Here are the three most important ones: (a) ETFs have significantly lower expense ratios, e.g., all of these sector ETFs have under 0.15% expense ratios as compared to the usual 1-3% for Mutual Funds; (b) ETFs can be self-directed, while Mutual Funds are managed by dedicated managers; and (c) ETFs have no additional sales commissions, while all actively managed funds (generally sold by brokers and private managers) carry loads, making them quite expensive.

    

Interviewer: Did you learn all these at school?

Laura: No. My mom taught me. She is a consulting Economist.

"Well, that says it all."

Disclaimer - The author is not advocating the ETFs 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