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An R-Squared Chart Taxonomy: Seeing is Not Believing
Thanks Investor- great article. Also very good commentary from respondents. I particularly liked:
• "Choosing what method and what numbers to look at can lead to a ‘truth’ that is meaningless."
• "Not everything worth evaluating can be measured by numbers."
I also was taken by the link to the Wickipedia article. Sometimes the longest and most heavily citation-laden posts here on MFO fail to consider these truths.
Thank you for posting this statistical education article. All investors need some familiarity with statistical terminology to better interpret financial data and charts, both their advantages and shortcomings.
Most MFO participants fully recognize the importance of understanding the benefits and limitations of such data in the investment decision making process; a few Luddites on this site do not.
One continuing problem for many investors is that the US educational system does a very poor job at preparing its students in the statistical arena. That deficiency does harm throughout a person’s lifecycle.
I congratulate you on your current attempt to partially erase that deficiency. Unfortunately, it is like running against a strong headwind. I’m sure you appreciate that I’ve been huffing and puffing against that same headwind for years now on both the Fund Alarm and MFO websites. I certainly need all the help offered; resistance is high and progress seems modest.
The referenced article’s objective is laudatory; its execution is somewhat perplexing. I suspect the author himself was discovering some of the not so subtle aspects of the R-squared formulation for the first time with his exploratory computer simulation charts.
Embedded within the text, the author mentioned that many of the charts were not real data. They were computer generated. That factoid deserves a special highlighted commentary. Stock market patterns that appear to be real world performance data can be absolutely simulated by a machine using a random draw program.
The takeaway from that observation is that the chart patterns that technical analyst diligently search-out and identify for investment opportunity are random events in nature. Charts merely are an excellent visual summary of history. So chartists must be skeptical when drawing straight lines into the future. Good luck on them possessing useful predictive powers.
One need not be mathematically proficient (although it would help) to extract insights from the R-squared term. Simply put, it measures the degree of goodness fit between two separate data sets. It statistically answers the question “How closely do these two data sets move in time-wise unison”. It is a general measure of togetherness.
R-squared (and its close companion “correlation coefficient” which is the square root of R-squared) has a total spectrum value range between plus One and minus One. A plus-One denotes perfect unison; a zero value indicates complete randomness of pricing action; a negative-One means perfectly out-of-sync contrarian price movement. Various intermediate valuations mean an orderly spectrum of imperfectly correlated activity.
If one seeks to assemble a diversified portfolio, then adding products that have low or negative R-squared or correlation coefficients should be the target. Historically bonds and stocks have values that are in the 0.3 to 0.5 range. Gold and stocks typically have lower levels of price movement R-squared values. It is difficult to find a pair of investment options that are negatively correlated.
Be aware that all these statistical measures of goodness of fit are time varying. Nothing remains constant.
Also be aware that the output statistical measure obviously depends upon the extensiveness of the data set used in the analysis. The longer that data set, the smoother the final output estimate of goodness. Short data strings produce spiky, unreliable estimates of performance just like daily stock pricing returns do the same. Short duration analysis only captures the randomness of the marketplace.
There is a significant shortcoming of the overall R-squared procedure that is far too infrequently mentioned. The methodology ASSUMES a linear relationship between the two parameters being explored. Economists and market wizards love the linear assumption, but complexity theory acknowledges that all interactions need not be linear. Feedback loops and nonlinearity exists in the real world. An R-squared analysis fails to capture any such added complexity.
One could argue that in the short run, a reasonable linearity will persist. For well designed systems that is likely true, but just remember the frequency of Black Swan events. So be warned that the linear assumption is an integral part of the method, and that limits its universal application.
Investor, I appreciate that you fully understood the article you just posted. My note is directed at those MFO members who are not on friendly ground when assessing statistical methods. My goal here was to offer them some triage.
You can judge by the meager readership numbers of your submittal that the topic is less than popular. Talking statistical methods and uses is an uphill battle, even among the informed, seasoned investment community. You show considerable courage in posting on this subject. Hope springs eternal for a sea change in that arena. The battle is joined.
Thanks also for the opportunity to further incite the Luddites, not so hidden among us.
Perhaps my wariness of economic pronouncements (usually presented with an air of infallibility) and statistical analysis of economic matters is influenced by the recent repeated failures of some of the best mathematical minds at large hedge funds and other major financial houses, and the subsequent need to expend our tax dollars to ameliorate some of the damage.
I did very much appreciate the link you provided, and the informative exposition of a need to be wary when interpreting charting or other statistical data. It was ignorant of me not to realize that it required courage on your part- I simple-mindedly thought that you were sharing an interesting perspective. My apologies for the oversight... please make allowances for potential Luddites.
Comments
• "Choosing what method and what numbers to look at can lead to a ‘truth’ that is meaningless."
• "Not everything worth evaluating can be measured by numbers."
I also was taken by the link to the Wickipedia article. Sometimes the longest and most heavily citation-laden posts here on MFO fail to consider these truths.
Thank you for posting this statistical education article. All investors need some familiarity with statistical terminology to better interpret financial data and charts, both their advantages and shortcomings.
Most MFO participants fully recognize the importance of understanding the benefits and limitations of such data in the investment decision making process; a few Luddites on this site do not.
One continuing problem for many investors is that the US educational system does a very poor job at preparing its students in the statistical arena. That deficiency does harm throughout a person’s lifecycle.
I congratulate you on your current attempt to partially erase that deficiency. Unfortunately, it is like running against a strong headwind. I’m sure you appreciate that I’ve been huffing and puffing against that same headwind for years now on both the Fund Alarm and MFO websites. I certainly need all the help offered; resistance is high and progress seems modest.
The referenced article’s objective is laudatory; its execution is somewhat perplexing. I suspect the author himself was discovering some of the not so subtle aspects of the R-squared formulation for the first time with his exploratory computer simulation charts.
Embedded within the text, the author mentioned that many of the charts were not real data. They were computer generated. That factoid deserves a special highlighted commentary. Stock market patterns that appear to be real world performance data can be absolutely simulated by a machine using a random draw program.
The takeaway from that observation is that the chart patterns that technical analyst diligently search-out and identify for investment opportunity are random events in nature. Charts merely are an excellent visual summary of history. So chartists must be skeptical when drawing straight lines into the future. Good luck on them possessing useful predictive powers.
One need not be mathematically proficient (although it would help) to extract insights from the R-squared term. Simply put, it measures the degree of goodness fit between two separate data sets. It statistically answers the question “How closely do these two data sets move in time-wise unison”. It is a general measure of togetherness.
R-squared (and its close companion “correlation coefficient” which is the square root of R-squared) has a total spectrum value range between plus One and minus One. A plus-One denotes perfect unison; a zero value indicates complete randomness of pricing action; a negative-One means perfectly out-of-sync contrarian price movement. Various intermediate valuations mean an orderly spectrum of imperfectly correlated activity.
If one seeks to assemble a diversified portfolio, then adding products that have low or negative R-squared or correlation coefficients should be the target. Historically bonds and stocks have values that are in the 0.3 to 0.5 range. Gold and stocks typically have lower levels of price movement R-squared values. It is difficult to find a pair of investment options that are negatively correlated.
Be aware that all these statistical measures of goodness of fit are time varying. Nothing remains constant.
Also be aware that the output statistical measure obviously depends upon the extensiveness of the data set used in the analysis. The longer that data set, the smoother the final output estimate of goodness. Short data strings produce spiky, unreliable estimates of performance just like daily stock pricing returns do the same. Short duration analysis only captures the randomness of the marketplace.
There is a significant shortcoming of the overall R-squared procedure that is far too infrequently mentioned. The methodology ASSUMES a linear relationship between the two parameters being explored. Economists and market wizards love the linear assumption, but complexity theory acknowledges that all interactions need not be linear. Feedback loops and nonlinearity exists in the real world. An R-squared analysis fails to capture any such added complexity.
One could argue that in the short run, a reasonable linearity will persist. For well designed systems that is likely true, but just remember the frequency of Black Swan events. So be warned that the linear assumption is an integral part of the method, and that limits its universal application.
Investor, I appreciate that you fully understood the article you just posted. My note is directed at those MFO members who are not on friendly ground when assessing statistical methods. My goal here was to offer them some triage.
You can judge by the meager readership numbers of your submittal that the topic is less than popular. Talking statistical methods and uses is an uphill battle, even among the informed, seasoned investment community. You show considerable courage in posting on this subject. Hope springs eternal for a sea change in that arena. The battle is joined.
Thanks also for the opportunity to further incite the Luddites, not so hidden among us.
Best Wishes.
Perhaps my wariness of economic pronouncements (usually presented with an air of infallibility) and statistical analysis of economic matters is influenced by the recent repeated failures of some of the best mathematical minds at large hedge funds and other major financial houses, and the subsequent need to expend our tax dollars to ameliorate some of the damage.
I did very much appreciate the link you provided, and the informative exposition of a need to be wary when interpreting charting or other statistical data. It was ignorant of me not to realize that it required courage on your part- I simple-mindedly thought that you were sharing an interesting perspective. My apologies for the oversight... please make allowances for potential Luddites.
Take care there in Austin-
OJ