Efficient frontier analysis: Difference between revisions
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The efficient frontier is a [[w:convex hull]] of the a set of data points. | The efficient frontier is a [[w:convex hull]] of the a set of data points. | ||
It is a concept that has been in circulation for a long time, and has been used in a wide variety of disciplines. | It is a concept that has been in circulation for a long time, and has been used in a wide variety of disciplines. For this reason, it is known by many names, and many nomenclatures for describing its various intricacies. | ||
For this reason, it is known by many names, and many nomenclatures for describing its various intricacies. | |||
Efficient frontier analysis (EFA) is used to negotiate "optimal" compromises between "competing" objectives. | |||
Synonyms are numerous, and include: | Synonyms are numerous, and include: | ||
* efficiency frontier | * efficiency frontier | ||
* efficient set | * efficient set | ||
* Pareto optimal set | * [[Pareto optimal]] set | ||
* non-dominated set | * non-dominated set | ||
* convex hull | * convex hull | ||
* multiple objective optimization (MOO) | * multiple objective optimization (MOO) | ||
The classic textbook definition of EFA is found in [[financial]] textbooks and is based on the "tradeoff" between | The classic textbook definition of EFA is found in [[financial]] textbooks and is based on the "tradeoff" between | ||
risk (called "beta" or covariance between a given issue and "the rest of the market") and reward | risk (called "[[beta]]" or covariance between a given issue and "the rest of the market") and [[risk and reward|reward]] | ||
(called yield) expected from various available issues of financial paper (stocks, bonds etc.) | (called [[yield]]) expected from various available issues of financial paper (stocks, bonds etc.) | ||
In the textbook example, it is assumed that investors wish to minimize beta (i.e. risk) and maximize yield. | In the textbook example, it is assumed that investors wish to minimize beta (i.e. risk) and maximize yield. | ||
In such textbooks, beta is the abscissa (horizontal axis) and yield is the ordinate. | In such textbooks, beta is the abscissa (horizontal axis) and yield is the ordinate. ''This contrasts with the [[risk as regret]] style of analysis which relies on EFA only to average various mutually exclusive [[comprehensive outcome]]s modelled as scenarios - in that method, [[upside]] and [[downside]] are asymmetrical, as in [[behavioural finance]].'' | ||
== algorithm == | |||
The convex hull of the data points consists of those points that can't be enclosed by connecting other points (dots) with line segments. | The convex hull of the data points consists of those points that can't be enclosed by connecting other points (dots) with line segments. | ||
The portion of the convex hull that is of interest when one is interested in maximizing the vertical axis variable while minimizing the other | The portion of the convex hull that is of interest when one is interested in maximizing the vertical axis variable while minimizing the other | ||
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If the point is "non-dominated" within the larger set, | If the point is "non-dominated" within the larger set, | ||
then there will be no points in the fourth (southeast) quadrant after moving the origin in this way. | then there will be no points in the fourth (southeast) quadrant after moving the origin in this way. | ||
Think of "non-dominated" as the opposite of "dominated." | Think of "non-dominated" as the opposite of "dominated." | ||
If one candidate's parameters are "superior in every way" to another's, one might say the former "dominates" the latter. | If one candidate's parameters are "superior in every way" to another's, one might say the former "dominates" the latter. | ||
The EFA method applies to optimization problems in other fields, too. | The EFA method applies to optimization problems in other fields, too. | ||
A two variable EFA might define the efficient set as the upper right, lower right or lower left convex hull depending on which variables one wishes to minimize or maximize. | A two variable EFA might define the efficient set as the upper right, lower right or lower left convex hull depending on which variables one wishes to minimize or maximize. | ||
When negotiating between more than two objectives, of course, the number of efficiency frontiers is more than four. | When negotiating between more than two objectives, of course, the number of efficiency frontiers is more than four. | ||
== assumptions == | |||
Needless to say, EFA relies on a number of assumptions: | Needless to say, EFA relies on a number of assumptions: | ||
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The reasoning behind this seems to include a desire to emphasize an ethical agenda rather than ask | The reasoning behind this seems to include a desire to emphasize an ethical agenda rather than ask | ||
shallowly commercial questions such as "is the price of X commensurate with its 'specifications?'" | shallowly commercial questions such as "is the price of X commensurate with its 'specifications?'" | ||
== Consumerium objectives == | |||
[[User:N8chz|The present author]] has included this information on EFA in Consumerium's pages, anyway, because it seems reasonable to believe that | [[User:N8chz|The present author]] has included this information on EFA in Consumerium's pages, anyway, because it seems reasonable to believe that | ||
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For example, for research activities, one might wish to identify and patch "holes" in Consumerium's knowledge base. | For example, for research activities, one might wish to identify and patch "holes" in Consumerium's knowledge base. | ||
In such a case, an efficiency-based "queueing system" for picking factoids for further investigation, the "maybe" value might be prioritized above the other two. | In such a case, an efficiency-based "queueing system" for picking factoids for further investigation, the "maybe" value might be prioritized above the other two. | ||
A description of such a strategy is given in [[User:N8chz|my]] essay "efficient shopping lists:" | A description of such a strategy is given in [[User:N8chz|my]] essay "efficient shopping lists:" | ||
http://geocities.com/n8chz/esl.htm | http://geocities.com/n8chz/esl.htm | ||
== transparency == | |||
Another use Consumerium might have for EFA would concern information volunteered to Consumerium (or to the public domain at large) by entities, concerning their own products. | Another use Consumerium might have for EFA would concern information volunteered to Consumerium (or to the public domain at large) by entities, concerning their own products. | ||
In such a scheme (certainly in the public domain), which "variables" of interest are made public can vary between suppliers. | In such a scheme (certainly in the public domain), which "variables" of interest are made public can vary between suppliers. | ||
If Consumerium holds "transparency" as a "good" (as seems to be the case), supplied values should perhaps be preferred over unsupplied in some cases. | If Consumerium holds "transparency" as a "good" (as seems to be the case), supplied values should perhaps be preferred over unsupplied in some cases. | ||
In the previous sentence, the word "transparency" refers to a general preference for more (public and accurate) information over less. | In the previous sentence, the word "transparency" refers to a general preference for more (public and accurate) information over less. ''The [[Transparent Consumerium]] [[best cases]] are about making Consumerium's own internal processes fully inspectable and transparent as a good example, much as [[healthy buying infrastructure]] must itself be built from defensible parts.'' | ||
== distributed database == | |||
This is one reason why I think Consumerium should consider not running on wiki alone, but consider including a database facility. | This is one reason why I think Consumerium should consider not running on wiki alone, but consider including a database facility. | ||
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* possible opportunities to avoid having to deal with main$tream financiers to finance large projects within Consumerium, by simply keeping projects of the "server" type smallish. | * possible opportunities to avoid having to deal with main$tream financiers to finance large projects within Consumerium, by simply keeping projects of the "server" type smallish. | ||
* possible opportunities to leverage existing methods for [[file sharing]] and [[distributed computing]] à la Seti@Home. | * possible opportunities to leverage existing methods for [[file sharing]] and [[distributed computing]] à la Seti@Home. | ||
''See [[Distributed Consumerium]] for more on the architecture of this project.'' | |||