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Statistical Precision

Statistics are broadly used to describe the characteristics and behavior of data. Investment professionals use a variety of statistics to describe the behavior of the assets which they manage. We use the percentage of change in market value to describe return on investment. We use the standard deviation of asset prices to describe volatility. There are four primary descriptive statistics commonly used in portfolio management, Beta, R2, Return, and Standard Deviation. We tend to think of these statistics as being somewhat static. For example, analysts will refer to the beta of a particular asset. The fact is asset betas change all the time based on overall market conditions. Asset betas in a highly volatile market are very different than those same assets in a calm market. In fact, all of the descriptive risk statistics mentioned above are in constant movement.


When we use statistics to describe assets and market events, we must be careful and thoughtful about the precision (the number of data points in the sample) of the statistics we employ. For example, if I told you that asset “A” had an annual return of 12% you would have a limited understanding of the asset's actual performance since I was using a long period to calculate the statistic. If I gave you quarterly returns you would understand that asset “A” had a 12% annual return but you would also understand more about how that 12% return was achieved. By increasing the precision from annual (one long observation) to quarterly (four shorter observations) you have been given more information.


Selecting the best precision (calculation period) is not an easy task. Historically statisticians want to use large swaths of data. In opinion sampling the more opinions you survey the more accurate your data is assumed to be. Financial organizations also tend to use large samples to develop the statistics used in the investment profession. Both MorningStar and Yahoo Financial use a minimum 3-year observation to develop their risk statistics (Beta, standard deviation, Sharpe ratio, etc.).


The time horizon of the statistical sample should match the time horizon with which you are concerned. It may be helpful to know at a “macro level” that an asset tends to move more or less than its index but that seems to be more informative than useful. What might be more useful is to know “how does this asset react in a correction?”. Using a long statistical calculation period, naturally loses details about the asset’s behavior. At the other extreme, if we calculate a weekly beta we end up with no discernible pattern to our analysis. Neither extreme is particularly descriptive.


Selecting the proper precision is somewhat like adjusting a telescope. Too far from or too close to the object we are observing obscures our ability to observe the characteristics and behavior in any meaningful manner. In this paper we will examine the four descriptive statistics as they relate behaviorally to the 2018 crash. If we select the proper precision for our calculations these four primary statistics should accurately portray the 2018 4th quarter crash. Understanding how statistics move in concert during various market conditions may provide additional insight into portfolio construction. It is akin to an MRI for the portfolio.


In this study we looked at 9 different portfolios. Four portfolios were constructed by wealth managers (LEVINE, IGROWTH, MODIII, and LAKE). Four portfolios were constructed by mutual fund portfolio managers (NBHIX, MVLVIX, ESGX and EGOIX (alias WFLCH)). One portfolio was constructed by Artificial Intelligence using IBM’s Watson, that portfolio is AIEQ.


To determine if we can actually "paint a picture" of the crash using the four primary statistics mentioned above, we used the (LAKE) portfolio as the subject of the study. We trace the un-weighted average portfolio return during the 2018 Q4 crash varying precision from 15 days to 90 days. This study illustrates that a precision of 30 provides the most descriptive picture of what actually took place.


Looking at the 2018 4th Quarter Crash


The 2018 crash provided an exceptional opportunity to examine statistical precision. We can witness the actual 2018 crash by observing the movement of the S&P 500 index.

Every market event has certain inflection-points which define the event. The 2018 crash began approximately 10/3/2018 and ended approximately 12/24/2018. We have identified eight inflection points during the crash.


1. On October 3 Chairman Powell made the following comment in a televised interview. “Interest rates are still accommodative, but we’re gradually moving to a place where they will be neutral,” he added. “We may go past neutral, but we’re a long way from neutral at this point, probably.” This raised the specter of an aggressive Federal Reserve and shook investor confidence. The market may have been able to shake that statement off if it were not for a plethora of existing market concerns:


Simultaneous concerns precipitating the 4th quarter crash

The Chairman’s comment on top of the list of concerns appeared to be the last straw.

2. On October 10th the market dropped 800 points.

3. On October 11th the market added an additional 500 points to the decline.

4. On the 13th the market tried to bounce back but could not hold.

5. On the 15th the S&P dropped 3.3% and broke key technical levels

6. In the week leading up to the G20 summit the market rebounded slightly in anticipation of a China truce.

7. On 12/24/2018 the DOW dropped 600 points and the S&P entered bear market territory

8. January 3rd 2019 the market began a rebound and by 1/18/2019 was up over 8% from the lows


There was no consensus on why the crash occurred. Here is one plausible theory. Once the comments by the Fed Chairman was assimilated by the market the 1,300-point two-day drop violated key technical levels on 10/15/2018. This triggered the “algos” to initiate sell programs. As the broader market began to understand what was happening and fear took hold people began to sell. Many of them held market index ETFs. When they sold shares of an ETF it required the ETF manager to sell a portion of all the shares contained in the ETF. This exacerbated the broader selling and added to fear. During December and managers undertook the process of “window dressing” which increased volatility in an already highly volatile environment. Finally, the revisions to the tax rules made it more beneficial to harvest losses and the tax loss harvesting which ensued only added to the turmoil. Had the event that precipitated the crash happened a month earlier the crash may not have been as bad.


The LAKE portfolio

Composition of our subject portfolio at the time of this analysis

The LAKE portfolio is a live portfolio designed by a local wealth manager


The S&P 500 During the 2018 4th Quarter Crash


Daily movement of the S&P 500 during the 4th quarter 2018 crash

Figure 1


If it is true that statistics can be used to describe the characteristics of investment events then the picture painted by the statistics during the event should be a realistic representation of observable facts as they occurred in the market and as depicted by the S&P 500 in figure 1. In fact, using a 30-day precision all of the portfolios we examined exhibited the same characteristics. (See Appendix D note included in this post)


Figures 2 through 4 apply varying degrees of precision to the un-weighted average portfolio Return statistic to test for the most descriptive precision. In each example the S&P 500 is presented on top of the returns for the LAKE portfolio. We tested precision at 15, 30, 45, 60, 75- and 90, day intervals to see which precision gave the most accurate depiction of actual results observed in the S&P 500.


Based on these tests the clearest picture was represented using a 30-day precision shown in figure 4.


S&P 500 (top) and our subject portfolio (bottom) 90 day precision

Figure 2


Figure 2 shows the S&P 500 (Top) and the Lake portfolio (Bottom) with a precision of 90 days. That is, each data point represents the average portfolio return calculated from 90 days prior to the data point. So, the data point represented by 10/3/2018 is calculated from 7/5/2018.


S&P 500 (top) and our subject portfolio (bottom) 15 day precision

Figure 3


Figure 3 uses a precision of 15 days. We can see four clear pattern matches with a positive uptick in January.


S&P 500 (top) and our subject portfolio (bottom) 30 day precision (Most Descriptive)

Figure 4


With precision at 30 days we can see six clear pattern matches. The right-hand side uptick on the chart is 6.7%. The actual uptick for the Lake portfolio was 8%. When we increase precision to 45 days and above, we lose the positive January uptick (see Appendix A not included in this post)


All Betas move to 1 in a Crisis


Daily Beta for the Lake Portfolio - Look at the impact of violating the 50 and 100 day Moving average on 10/15

Figure 5


There is an adage on Wall Street that “During a crisis all betas go to 1”. Adages like stereotypes exist because there is a kernel of truth in the statement. Beta measures how much a security moves in relationship to an index. In this study we used the SPY ETF as the benchmark. If during a crisis all betas move toward one then we would anticipate that the underlying securities in the LAKE portfolio would move in a very similar manner as the S&P 500. As soon as the S&P broke the 50 and 100-day moving average on 10/15/2018 Beta moved decisively. This behavior was exhibited by all 9 portfolios.


Beta movement all 9 portfolios during the crash

Correlation Matrix for Beta for all 9 portfolios

Figure 6 Correlation Matrix for Beta Q4 2018


Composition of the MODIII portfolio

Figure 7

Note that there was one exception to the pattern. MOD III was different from the other portfolios in two respects. First it had only 11 assets and more significantly those assets were all ETFs. ETFs appear to behave differently than a portfolio derived from equities. Portfolios derived from equities would likely have a high representation of the assets contained in the S&P 500. Accordingly, statistical movement should mimic the S&P 500 to the extent that there was asset commonality between the portfolio and the index. Of the top 20 assets in all portfolios in this study 19 were in the S&P 100.


Another reason for the dissimilarity may be that each ETF follows a specific investment “theme”. VHT tracks the health sector, and QQQ tracks technology. The concentration of thematic assets in each ETF could influence how the ETF moves relative to a diverse basket of equities.


The movement of Standard Deviation for all portfolios Q4 2018


Correlation Matrix for Standard Deviation for all portfolios

Figure 8 Correlation Matrix for Standard Deviation Q4 2018


Observations Conclusions, Questions and Opinions


1. The similarity in the movement pattern of un-weighted returns in all 9 portfolios was stunning.

2. The movement pattern of the S&P 500 was clearly reflected in all 9 portfolios un-weighted return movement.

3. Beta, R2, and Standard Deviation movement was highly correlated in all portfolios

4. ETFs appear to behave differently than equities (opinion)

5. The Wall Street adage about Beta moving to 1 in a crisis is demonstrably true

6. Shorter statistical calculations provide more granular information about the data being analyzed than longer calculation periods

7. Selecting the proper precision for statistical calculations is critical, one size does not fit all

8. In a crisis asset weighting is more important than specific asset selection (opinion)

9. The 2018 crash was an example of systemic risk. This study shows that diversification does little to mitigate systemic risk.

10. Standard Deviation peaks asynchronously with asset return

11.Beta is a less effective risk measure than standard deviation (opinion)


If you would like a copy of the full study including the appendices and raw data in spreadsheet format simply request paper 121.

I’ll be happy to send it to you no cost, no strings.

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© 2019 BovaMetrics Colossians 3:23

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