Alpha, Beta and Heisenberg Uncertainty
In physics, complementarity is a basic principle of quantum theory closely identified with the Copenhagen interpretation, and refers to effects such as “wave–particle duality,” in which different measurements made on a system reveal it to have either particle-like or wave-like properties.
Niels Bohr is usually associated with this concept, which he developed at Copenhagen with Heisenberg, as a philosophical adjunct to the recently developed mathematics of quantum mechanics and in particular the Heisenberg uncertainty principle. The Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known with precision. That is, the more precisely one property is known, the less precisely the other property can be known.
In Chinese philosophy, the concept of “yīn yang” is used to describe how polar or seemingly contrary forces are interconnected and interdependent in the natural world, and how they give rise to each other in turn. Yin yang are complementary opposites within a greater whole. Everything has both yin and yang aspects, although yin or yang elements may manifest more strongly in different objects or at different times. Yin yang constantly interacts, never existing in absolute stasis as symbolized by the Taijitu symbol.
A similar paradox exists within the CAPM paradigm involving the relationship between the concept of "beta," as determined by the market portfolio, and "alpha," which loosely represents "a proxy for manager skill". As suggested by our blog, "The CAPM Debate and the Search for 'True Beta'", the yin yang “whole” relates to the “True Beta” concept which Jagannathan and Wang (1996) theorized must encompass “the aggregate wealth portfolio of all agents in the economy”.
Schneeweis (1999) in his article, “Alpha, Alpha, Whose got the Alpha?,” writes about a related problem with respect to measuring “alpha” by raising the question of “how to define the expected risk of the manager’s investment position”. In other words, when marketing “alpha” portfolio managers often assume “the reference benchmark is the appropriate benchmark and that the strategy has the same leverage as the benchmark”. Further, “[w]ith the exception of a strategy that is designed to replicate the returns of the benchmark, the alpha generated by this approach is essentially meaningless”.
Schneeweis (1999) makes the case that investors often make the mistake of relying on a single-index model as a meaningful benchmark from which to gauge the factors “driving the return of the strategy” when often a “multi-factor model should be used to describe the various market factors that drive the return strategy”. The problem is that statistically it is “better to over-specify a model… than to under-specify. If the model is over-specified, many of the betas will simply be zero. However, if under-specified, there is the possibility of significant bias”.
Which brings us back to the Heisenberg uncertainty principle...
Just like the physical properties of position and momentum cannot both be known with precision, the properties of “alpha” and “beta” can also not be measured precisely. This statement has been interpreted in two different ways. According to Heisenberg its meaning is that it is impossible to determine simultaneously both properties with any great degree of accuracy or certainty. According Ballentine this is not a statement about the limitations of a researcher's ability to measure particular quantities of a system, but it is a statement about the nature of the system itself as described by the equations.
- Mack Frankfurter, Managing Director
Alpha Alpha Whose Got the Alpha - Schneeweis
References:
Schneeweis, Thomas. “Alpha, Alpha, Whose got the Alpha?” University of Massachusetts, School of Management (October 5, 1999).
Jagannathan, Ravi; McGrattan, Ellen R. (1995). “The CAPM Debate” Federal Reserve Bank of Minneapolis Quarterly Review, Vol. 19, No. 4, Fall 1995, pp. 2-17.
Bohr, Niels. Atomic Physics andHuman Knowledge, p. 38.
Heisenberg, W. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. In: Zeitschrift für Physik. 43 1927, S. 172–198.
Ballentine, L.E. The statistical interpretation of quantum mechanics, Rev. Mod. Phys. 42, 358–381 (1970).
Niels Bohr is usually associated with this concept, which he developed at Copenhagen with Heisenberg, as a philosophical adjunct to the recently developed mathematics of quantum mechanics and in particular the Heisenberg uncertainty principle. The Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known with precision. That is, the more precisely one property is known, the less precisely the other property can be known.
In Chinese philosophy, the concept of “yīn yang” is used to describe how polar or seemingly contrary forces are interconnected and interdependent in the natural world, and how they give rise to each other in turn. Yin yang are complementary opposites within a greater whole. Everything has both yin and yang aspects, although yin or yang elements may manifest more strongly in different objects or at different times. Yin yang constantly interacts, never existing in absolute stasis as symbolized by the Taijitu symbol.
A similar paradox exists within the CAPM paradigm involving the relationship between the concept of "beta," as determined by the market portfolio, and "alpha," which loosely represents "a proxy for manager skill". As suggested by our blog, "The CAPM Debate and the Search for 'True Beta'", the yin yang “whole” relates to the “True Beta” concept which Jagannathan and Wang (1996) theorized must encompass “the aggregate wealth portfolio of all agents in the economy”.
Schneeweis (1999) in his article, “Alpha, Alpha, Whose got the Alpha?,” writes about a related problem with respect to measuring “alpha” by raising the question of “how to define the expected risk of the manager’s investment position”. In other words, when marketing “alpha” portfolio managers often assume “the reference benchmark is the appropriate benchmark and that the strategy has the same leverage as the benchmark”. Further, “[w]ith the exception of a strategy that is designed to replicate the returns of the benchmark, the alpha generated by this approach is essentially meaningless”.
Schneeweis (1999) makes the case that investors often make the mistake of relying on a single-index model as a meaningful benchmark from which to gauge the factors “driving the return of the strategy” when often a “multi-factor model should be used to describe the various market factors that drive the return strategy”. The problem is that statistically it is “better to over-specify a model… than to under-specify. If the model is over-specified, many of the betas will simply be zero. However, if under-specified, there is the possibility of significant bias”.
Which brings us back to the Heisenberg uncertainty principle...
Just like the physical properties of position and momentum cannot both be known with precision, the properties of “alpha” and “beta” can also not be measured precisely. This statement has been interpreted in two different ways. According to Heisenberg its meaning is that it is impossible to determine simultaneously both properties with any great degree of accuracy or certainty. According Ballentine this is not a statement about the limitations of a researcher's ability to measure particular quantities of a system, but it is a statement about the nature of the system itself as described by the equations.
- Mack Frankfurter, Managing Director
Alpha Alpha Whose Got the Alpha - Schneeweis
References:
Schneeweis, Thomas. “Alpha, Alpha, Whose got the Alpha?” University of Massachusetts, School of Management (October 5, 1999).
Jagannathan, Ravi; McGrattan, Ellen R. (1995). “The CAPM Debate” Federal Reserve Bank of Minneapolis Quarterly Review, Vol. 19, No. 4, Fall 1995, pp. 2-17.
Bohr, Niels. Atomic Physics andHuman Knowledge, p. 38.
Heisenberg, W. Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. In: Zeitschrift für Physik. 43 1927, S. 172–198.
Ballentine, L.E. The statistical interpretation of quantum mechanics, Rev. Mod. Phys. 42, 358–381 (1970).
posted by Cervino Capital Management LLC at 1/09/2011
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