I have always raised the fundamental questions for many years but given the monopoly of many factor based mangers and blind users of Least Square Regression Tools.
I had an idea of developing a scientific physics based strong theory with strong foundation to draw the financial variables trajectory based on sort of causal variables in financial/econometric space-time way back in 2010. Now I find some big institutions are possibly trying to work on some ideas like that in different way. I had proposed the idea to work in Non- Euclidean Econometric Space -Time to relate to Bankruptcy of a firm to other financial variables trajectory. There is a deep scientific mechanism out there like in Physics. Like Physical Space-time , there is Economic Space-Time Manifold as well. I had proposed the idea way back in 2010.
But the matter and issue is extremely serious. I have been talking and thinking about these points ,but others used not to take that seriously as it comes from Nobel class influential people (with due regards to them) on which the entire industry has been commercially set up and many have built their career on it over the decades. We can call it “intellectual intertia” to come out of the comfort zone of traditional econometricians to factor based investment managers.
Infact Factor type investment has become more of Marketing Exercise to attract funds rather some scientific exercise.
So, few points briefly here although we can go into more technical detail later.
Traditional Investing has been mostly built on associational terms not causal terms. It’s indeed deep.. Similarly Backtesting is also superficial associational things on different datasets historically which doesn’t answer “why” like we do in science. Entire industry is crazily and blindly relying on Backtesting using Random Trials without looking into the Causal mechanism. ( Recalling Reproducibility Crisis)
Bertrand Russell once told stated “ Physics is Mathematical because we know so little about it, we know only mathematical properties to find out the relationships”.
Similar problem is here with Econometrics/Factor Based investing in general. It is mostly tried to establish superficial association based on the data sets .but what is quite misunderstood is that they are following some causal mechanism in some different higher dimensional financial Space- time.
I had even had an idea to project financial trajectory and bankruptcy related scientific idea from physics long back on that (which was possibly first of its kind in the whole of financial literature to the best of my knowledge but had to drop as it was not taken seriously possibly due to lack of understanding and imagination by many round including traditional experts.
The one main root of all these is misunderstanding Least Square Based Regression Analysis as well.
Regression Analysis is one of the most conceptually misunderstood concept in this history of econometrics to finance to statistics which is affecting such a huge investment industry affecting day to day life of common people directly or indirectly.
Regression can be done on any two data say for example : Raining water level on Mars and Number of Cars on Earth , which has no logical interrelation or causation. It would definitely have some Beta.
It has become a Data Mining exercise without finding the proper logic and causal mechanism
Without going into much technicl detail that why we should take “ Least Square Approch”
Beta ,Residual error etc are indeed conceptually very less understood technically. Error shows the Randomness component as well and it’s generally ignored to establish deterministic associational relationship. But the study of that residual can tell a lot deeper aspects about the causation relationship and randomness component inherent as well.
By ignoring the nature of Residual error terms, One falsely tries to establish association based superficial relationship.
That doesn’t establish the causation between say X and Y variables. What actually needs to be done is rather than superficially establishing the associational relationship( which is like virtual shadow) ,one should try to search for the actual real causal mechanism in some other financial space-time. That’s the true logic, concept and science. This is because if that cause of why doesn’t exist, the entire relationship is just coincidence or misleading baseless product of regression analysis which can find out relationship in any two sets of variables randomly chosen. E.g. red colour of cars on Earth and water rainfall on Mars.
Moreover Least Square based Regression Analysis can produce vastly misleading Beta in the presence of some outliers and there ca be drawn multiple line of fit having different Beta values on the same data set.
That’s the reason while going forward, the regression based Prediction often fails in finance , particularly least square based approach.
This entire Least Square based Regression Analysis has Fundamental issue that needs to be relooked.
Moreover, RealWorld may not be always so deterministic as well. It has Randomness component as well .
RealWorld is more Random than Conventional Regression Analysis.
Residual part of Regression carrying huge information is often ignored to make the system falsely deterministic and establish association based results.
Time Asymmetricity of Regression Tool in Real World.
The deeper concept is ignoring the role of time dimension in mathematics/ statistics here contextually.
Data Mining Association Deduction in Backward Direction of Econometric Space-Time doesn’t necessarily hold true in Forward Direction of Space-Time. It is falsely assumed that symmetricity would exist while carrying out the Regression Analysis.
This is one of the key issue with statistical tools in econometrics/ finance.
If it’s really causal and not associational, True Regression Analysis should be conducted on Future Data in Forward direction of Space -Time not on Historical Data.
One can always find out different misleading associational relationship on past data points in backward direction of space-time but forward direction of time could be the real test of causation. If those variables indeed exhibit those regression type relationship in forward direction of space,-Time as well then that might possibly means causation.
But the case is not that. Factor enthusiasts or Least Square Regression enthusiasts perform these things on past data in backward direction of time which often doesn’t hold true in forward direction of space- time. This is extremely serious misleading aspect which is generally ignored and misunderstood by even best statisticians or financial minds. It’s not Time (T) symmetric here.
It is inherently presumed that the entire statistics here is time symmetric hence what association has been found out on past data in backward space time would hold true in forward direction as well. which often fails in real world.
This is indeed very serious problem with Statistical tools like Regression, Correlation etc.
The World does have some randomness component as well which exposes the traditional association to Black Swan Type of Risks because historical associational factors might not work in future space-time.
We should seriously worry that Factor based investing without proper scientific mechanism blindly relying on Least Square type Regression Analysis is vastly exposed to Black Swan Tail Risk .
So, unlike many associational factors that have been traditionally been used, we should really look forward to search the causation based confounding factors e.g. GDP, Inflation, Yield ,Supply – Demand related factors etc. which really helps to build the proper scientific theory with proper falsifiable mechanism which can be tested in multiple framework . But yes mechanism could vary time to time. There should be a proper scientific mechanism of “Why”and “How” X is affecting Y. Infact that can and should be done. The reason being that with the scientific mechanism approach can better handle the things in future whether through prediction or managing Uncertainty/Randomnes depending upon one’s relative stance.
So, in a nutshell, the factor based strategy needs to be revised to search for casual factors , not associational ones. Out of many factors, one should accept only causal ones and establish proper theory and reject others.If one wants to predict scientifically,it has to follow deeply scientific rather just superficial data mining exercise.
This indeed ushers a new era of financial science and we all must work on that together.
Happy to discuss in more detail and collaborate to work out on this research mission ahead,if any , to benefit the common people and investors are large...
Thank you.
Best wishes,
Pankaj Mani, CQF,FRM,
AIFI@NYU Tandon
RealWorldRisk
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