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Reviews of publications on Info-Gap decision theory

Review # 11 (Posted: June 15, 2009; Last update: August 13, 2009)

Reference: An info-gap approach to managing portfolios of assets with uncertain returns
Bryan Beresford-Smith and Colin J. Thompson
Journal of Risk Finance
10(3), 277-287, 2009.
Abstract Purpose
The purpose of this paper is to provide a quantitative methodology based on information-gap decision theory for dealing with (true) Knightian uncertainty in the management of portfolios of assets with uncertain returns.

Portfolio managers aim to maximize returns for given levels of risk. Since future returns on assets are uncertain the expected return on a portfolio of assets can be subject to significant uncertainty. Information-gap decision theory is used to construct portfolios that are robust against uncertainty.

Using the added dimensions of aspirational parameters and performance requirements in information-gap theory, the paper shows that one cannot simultaneously have two robust-optimal portfolios that outperform a specified return and a benchmark portfolio unless one of the portfolios has arbitrarily large long and short positions.

Research limitations/implications
The paper has considered only one uncertainty model and two performance requirements in an information-gap analysis over a particular time frame. Alternative uncertainty models could be introduced and benchmarking against proxy portfolios and competitors are examples of additional performance requirements that could be incorporated in an information-gap analysis.

Practical implications
An additional methodology for applying information-gap modeling to portfolio management has been provided.

Originality/value This paper provides a new and novel approach for managing portfolios in the face of uncertainties in future asset returns.

Keywords: Portfolio investment, Financial modelling, Uncertainty management, Information management

Paper type: Research paper.

Acknowledgement The authors are grateful to Yakov Ben-Haim for many illuminating discussions on info-gap theory and for a critical reading of an early version of this paper.
Scores TUIGF:100%

The main reason for my taking up this paper for review is to address a statement made by the authors about results reported on in my 2008 article, which was published in the same journal.

On page 278 of the Beresford-Smith Thompson's (2009) article we read (emphasis is mine):

The main problem with CAPM and related models is that they are based on expected future returns on assets that in principle are unknown and subject to considerable uncertainty. In such situations we are dealing with "true uncertainty" in the sense of Knight (1921) who was the first to distinguish between "risk" based on known probability distributions and true uncertainty when the underlying statistical distributions are unknown. Knight's ideas have been further developed by several authors over the years and in particular by Ben-Haim (2006) who has developed a quantitative formulation known as information-gap decision theory. This theory has recently been shown by Sniedovich (2008) to be formally equivalent to Wald's maximin model in classical decision theory (French, 1988).

This text addresses three prevailing myths about Info-Gap decision theory, namely:

In the quoted text the authors dispel Myth 1 and Myth 2 and continue to propagate Myth 3.

Some comments:

  1. To begin with, it cannot be emphasized enough that Info-Gap decision theory is, as a matter of principle, unable to deal with Knightian uncertainty. Indeed, adopting as it does a local approach to the treatment of uncertainty, hence to robustness against severe uncertainty, Info-Gap's robustness model constitutes the exact antithesis of what a proper/correct/sound treatment of Knightian uncertainty calls for.

    For, how can a theory even be expected to meet the challenges posed by severe uncertainty, especially "true" Knightian uncertainty, if it a priori fixes only on a wild guess and limits its entire robustness analysis to the immediate neighborhood of this wild guess?

    The answer is: it can't!

    The picture is this:

    No Man's LandûNo Man's Land
    <-------------- Complete region of uncertainty under consideration -------------->

    where û denotes the estimate of the parameter of interest, the black area represents the complete region of uncertainty under consideration, the red area around û represents the region of uncertainty that actually affects the results generated by Info-Gap's robustness analysis, and the vast No Man's Land represents that part of the complete region of uncertainty that has no impact whatsoever on the results generated by Info-Gap's robustness model.

    Clearly, how can one possibly expect Info-Gap decision theory — that as attested by this statement is designed to take on the severest uncertainty imaginable "True Knightian Uncertainty — to deal with Black Swans namely, extreme events that would fall under "True Knightian Uncertainty", if it cannot even handle plain, ordinary, "white swans" that occur in the vast No Man's Land.

    And what is the wonder that such a theory cannot possibly be expected to deal with this type of uncertainty?!

    After all, Info-Gap's uncertainty and robustness models were originally (Ben-Haim, 1996 ) put forward to deal with a relatively mild uncertainty and variability around given "nominal values". Yet, without the slightest modification having been made in these models to meet the challenges of severe uncertainty, precisely the same models, prescribing precisely the same treatment of uncertainty, were imported lock stock and barrel into the two more recent Info-Gap books (Ben-Haim, 2001, 2006) to offer an approach to decision under the severest uncertainty imaginable: "knightian" uncertainty.

    To repeat, how can one possibly expect that models designed for the treatment of a mild uncertainty will be suitable for the treatment of "true" Knightian uncertainty!

    Indeed, the obove picture speaks for itself. It gives a graphic depiction of the fact that Info-Gap decision theory does not even come close to tackling the severity of the uncertainty that it claims to manage. Info-Gap's formula for dealing with the ("True Knightian") uncertainty that it professes to take on is simply ... to ignore it. This is the effect of Info-Gap prescribing a robustness analysis that fixes only on a given wild guess of the true value of the parameter of interest and its immediate neighborhood, to the exclusion of practically the entire region of uncertainty!

    The robustness that one obtains then cannot possibly be declared robustness against severe uncertainty.

    All one can say is that the results yielded by the Info-Gap analysis provide a local robustness in the vicinity of a wild guess!

  2. And so while it is of course a fact that in his 2001 and 2006 books and in many of his articles, Ben-Haim makes constant reference to Knightian uncertainty, thus giving the impression that Info-Gap is practically tailored to handle this type of forbidding uncertainty; the truth is that Info-Gap constitutes the precise antithesis of what a theory for the treatment of severe uncertainty ought to be.

    Because, to repeat, the uncertainty and robustness models deployed by Info-Gap decision theory are the same models deployed in Ben-Haim's 1996 book where the uncertainty under consideration is not assumed to be severe, and where there is no mention of Knightian uncertainty.

  3. Regrettably, the statement describing the relationship between Ben-Haim's Info-Gap decision theory and Wald's Maximin model which is attributed to my 2008 paper is mistaken and therefore requires a major correction.

    In my 2008 paper I set out a detailed proof of a theorem showing that Info-Gap's robustness model is an instance of Wald's Maximin model. That is, I show that the generic Info-Gap robustness model, namely

    is a simple instance of Wald's generic Maximin model, namely of

    The proof is constructive: it shows that Info-Gap's robustness model is the simple instance of Wald's generic Maximin model specified by


    So, the point of this theorem is not that Info-Gap's robustness model is equivalent to Wald's Maximin model. Rather, the point of this theorem is that by virtue of its specific objective function and sets of admissible states, Info-Gap's robustness model constitutes a simple instance of the classical Maximin model. This means, of course, that like countless other instances of Wald's generic Maximin model, the Info-Gap model is subsumed by the Maximin model. The immediate implication is, of course, that Maximin is incomparably more general and powerful than Info-Gap's robustness model so that there can be no talk whatsoever of equivalence between the two models.

    Indeed, by analogy, the assertion that Info-Gap's robustness model is equivalent to Wald's Maximin model is as mistaken as the assertion that the family of polynomials specified by

    p(x) = 1 + αx2+βx4

    is equivalent to the family of polynomials specified by

    q(x) = a + bx + cx2+dx3+ex4+fx5+gx6+hx7

    or that the class of exponential distributions

      ,   λ > 0

    is equivalent to the class of Weibull distributions

      ,   λ > 0, k > 0

    All three assertions share a common feature: they are in error!

  4. On page 279 the authors formulate the Info-Gap robustness model for decision x, namely

    They then go on to argue that this expression shows that their " ... info-gap model is formally at least, equivalent to conventional max-min decision theoretic models (French, 2006) ..."

    But, this argument

    • Is mistaken. At best it indicates that this particular Info-Gap model is an instance of Wald's generic Maximin model.

    • Gives a distorted picture of how the Maximin/info-Gap connection is in fact treated in the Info-Gap decision literature.

    • Is far too simplistic to actually capture the kinship between the two models.

    To wit:

    • Wald's Maximin model is far more general than this Info-Gap model. Indeed, this model is but an instance of Info-Gap's generic robustness model, which in turn is just a simple instance of Wald's generic Maximin model. So how can this model possibly be equivalent to Wald's generic Maximin model??!?!?! It cannot be, and is definitely not, equivalent to Wald's Maximin model.

    • There is no reference whatsoever to the fact that Ben-Haim — the Father of Info-Gap — continues to stick to his guns, maintaining his denials that Info-Gap's robustness model is a Maximin model. These denials are made not only in a paper published in the same journal — cited in my 2008 paper — but in other writings and presentations to date, where this question is raised. This includes, among other publications, Ben-Haim's two books on Info-Gap, and his compilation of FAQs about Info-Gap. Also see Review 5 and Review 12.

      So, if — as claimed by the authors — the above conclusion follows so directly from the expression describing the above Info-Gap model, shouldn't they have addressed Ben-Haim's persistent claims that Info-Gap's robustness model is not a Maximin model?

    • The fact that a "max" and a "min" occur in the formulation of a model does not automatically render this model a Wald's Maximin model. Indeed, to formally show that the above model is a Maximin model it is necessary to reformulate the elements of the model, eg. incorporate the constraint in the objective function of the Maximin model, as done in my 2008 paper.

      To illustrate,

      is not a Maximin model, and

      is a Maximin model.

      In fact, it is not essential for a model to have an "inner" max or min to be a Maximin model. For instance,

      is a perfectly kosher Maximin model.

      These subtle modeling issues are discussed and explained in Wikipedia. Also, see my discussion on math formulations of the Maximin model.

  5. But, more than anything else, in view of their contention that Info-Gap "is equivalent" to Wald's maximin model, shouldn't the authors have given us at least some indication as to the rationale behind their proposition to use Info-Gap in the first place?!

    Shouldn't they have made it clear why, in their view, is there any point, merit, or advantage to turn to Info-Gap rather than stick with the old warhorse Wald's Maximin model, which, one need hardly point out, is the most prevalent model used in the field of "Robust Optimization" and in "Robust portfolio optimization"?!

  6. It is no less regrettable that the authors do not address the other fundamental flaws in Info-Gap decision theory — flaws that are described and criticized in detail in my 2007 paper — particularly because these flaws bear directly on the validity of the analysis and results presented in the article.

    Specifically, because my arguments (proof and analysis) show that Info-Gap's robustness model fails to tackle the severity posed by the "true" Knightian uncertainty considered in the article — the implications for their analysis and results are obvious.

On the brighter side, though, the authors' statement is a major breakthrough for my Info-Gap campaign. For, after more than three years of hammering this fact, I finally succeeded to convince two dedicated Info-Gap adherents that Ben-Haim's repeated assertions that Info-Gap's robustness model is not a Maximin model are erroneous! (see Review 5).

It is interesting that Ben-Haim still claims that Info-Gap's robustness model is not a Maximin model (see Review 12).

To learn more about the Maximin/Info-Gap connection and Info-Gap's flawed implementation of its Maximin robustness model go to the compilation of FAQs about Info-Gap.

Other Reviews

  1. Ben-Haim (2001, 2006): Info-Gap Decision Theory: decisions under severe uncertainty.

  2. Regan et al (2005): Robust decision-making under severe uncertainty for conservation management.

  3. Moilanen et al (2006): Planning for robust reserve networks using uncertainty analysis.

  4. Burgman (2008): Shakespeare, Wald and decision making under severe uncertainty.

  5. Ben-Haim and Demertzis (2008): Confidence in monetary policy.

  6. Hall and Harvey (2009): Decision making under severe uncertainty for flood risk management: a case study of info-gap robustness analysis.

  7. Ben-Haim (2009): Info-gap forecasting and the advantage of sub-optimal models.

  8. Yokomizo et al (2009): Managing the impact of invasive species: the value of knowing the density-impact curve.

  9. Davidovitch et al (2009): Info-gap theory and robust design of surveillance for invasive species: The case study of Barrow Island.

  10. Ben-Haim et al (2009): Do we know how to set decision thresholds for diabetes?

  11. Beresford and Thompson (2009): An info-gap approach to managing portfolios of assets with uncertain returns

  12. Ben-Haim, Dacso, Carrasco, and Rajan (2009): Heterogeneous uncertainties in cholesterol management

  13. Rout, Thompson, and McCarthy (2009): Robust decisions for declaring eradication of invasive species

  14. Ben-Haim (2010): Info-Gap Economics: An Operational Introduction

  15. Hine and Hall (2010): Information gap analysis of flood model uncertainties and regional frequency analysis

  16. Ben-Haim (2010): Interpreting Null Results from Measurements with Uncertain Correlations: An Info-Gap Approach

  17. Wintle et al. (2010): Allocating monitoring effort in the face of unknown unknowns

  18. Moffitt et al. (2010): Securing the Border from Invasives: Robust Inspections under Severe Uncertainty

  19. Yemshanov et al. (2010): Robustness of Risk Maps and Survey Networks to Knowledge Gaps About a New Invasive Pest

  20. Davidovitch and Ben-Haim (2010): Robust satisficing voting: why are uncertain voters biased towards sincerity?

  21. Schwartz et al. (2010): What Makes a Good Decision? Robust Satisficing as a Normative Standard of Rational Decision Making

  22. Arkadeb Ghosal et al. (2010): Computing Robustness of FlexRay Schedules to Uncertainties in Design Parameters

  23. Hemez et al. (2002): Info-gap robustness for the correlation of tests and simulations of a non-linear transient

  24. Hemez et al. (2003): Applying information-gap reasoning to the predictive accuracy assessment of transient dynamics simulations

  25. Hemez, F.M. and Ben-Haim, Y. (2004): Info-gap robustness for the correlation of tests and simulations of a non-linear transient

  26. Ben-Haim, Y. (2007): Frequently asked questions about info-gap decision theory

  27. Sprenger, J. (2011): The Precautionary Approach and the Role of Scientists in Environmental Decision-Making

  28. Sprenger, J. (2011): Precaution with the Precautionary Principle: How does it help in making decisions

  29. Hall et al. (2011): Robust climate policies under uncertainty: A comparison of Info-­-Gap and RDM methods

  30. Ben-Haim and Cogan (2011) : Linear bounds on an uncertain non-linear oscillator: an info-gap approach

  31. Van der Burg and Tyre (2011) : Integrating info-gap decision theory with robust population management: a case study using the Mountain Plover

  32. Hildebrandt and Knoke (2011) : Investment decisions under uncertainty --- A methodological review on forest science studies.

  33. Wintle et al. (2011) : Ecological-economic optimization of biodiversity conservation under climate change.

  34. Ranger et al. (2011) : Adaptation in the UK: a decision-making process.

Recent Articles, Working Papers, Notes

Also, see my complete list of articles
    Moshe's new book!
  • Sniedovich, M. (2012) Fooled by local robustness, Risk Analysis, in press.

  • Sniedovich, M. (2012) Black swans, new Nostradamuses, voodoo decision theories and the science of decision-making in the face of severe uncertainty, International Transactions in Operational Research, in press.

  • Sniedovich, M. (2011) A classic decision theoretic perspective on worst-case analysis, Applications of Mathematics, 56(5), 499-509.

  • Sniedovich, M. (2011) Dynamic programming: introductory concepts, in Wiley Encyclopedia of Operations Research and Management Science (EORMS), Wiley.

  • Caserta, M., Voss, S., Sniedovich, M. (2011) Applying the corridor method to a blocks relocation problem, OR Spectrum, 33(4), 815-929, 2011.

  • Sniedovich, M. (2011) Dynamic Programming: Foundations and Principles, Second Edition, Taylor & Francis.

  • Sniedovich, M. (2010) A bird's view of Info-Gap decision theory, Journal of Risk Finance, 11(3), 268-283.

  • Sniedovich M. (2009) Modeling of robustness against severe uncertainty, pp. 33- 42, Proceedings of the 10th International Symposium on Operational Research, SOR'09, Nova Gorica, Slovenia, September 23-25, 2009.

  • Sniedovich M. (2009) A Critique of Info-Gap Robustness Model. In: Martorell et al. (eds), Safety, Reliability and Risk Analysis: Theory, Methods and Applications, pp. 2071-2079, Taylor and Francis Group, London.
  • .
  • Sniedovich M. (2009) A Classical Decision Theoretic Perspective on Worst-Case Analysis, Working Paper No. MS-03-09, Department of Mathematics and Statistics, The University of Melbourne.(PDF File)

  • Caserta, M., Voss, S., Sniedovich, M. (2008) The corridor method - A general solution concept with application to the blocks relocation problem. In: A. Bruzzone, F. Longo, Y. Merkuriev, G. Mirabelli and M.A. Piera (eds.), 11th International Workshop on Harbour, Maritime and Multimodal Logistics Modeling and Simulation, DIPTEM, Genova, 89-94.

  • Sniedovich, M. (2008) FAQS about Info-Gap Decision Theory, Working Paper No. MS-12-08, Department of Mathematics and Statistics, The University of Melbourne, (PDF File)

  • Sniedovich, M. (2008) A Call for the Reassessment of the Use and Promotion of Info-Gap Decision Theory in Australia (PDF File)

  • Sniedovich, M. (2008) Info-Gap decision theory and the small applied world of environmental decision-making, Working Paper No. MS-11-08
    This is a response to comments made by Mark Burgman on my criticism of Info-Gap (PDF file )

  • Sniedovich, M. (2008) A call for the reassessment of Info-Gap decision theory, Decision Point, 24, 10.

  • Sniedovich, M. (2008) From Shakespeare to Wald: modeling wors-case analysis in the face of severe uncertainty, Decision Point, 22, 8-9.

  • Sniedovich, M. (2008) Wald's Maximin model: a treasure in disguise!, Journal of Risk Finance, 9(3), 287-291.

  • Sniedovich, M. (2008) Anatomy of a Misguided Maximin formulation of Info-Gap's Robustness Model (PDF File)
    In this paper I explain, again, the misconceptions that Info-Gap proponents seem to have regarding the relationship between Info-Gap's robustness model and Wald's Maximin model.

  • Sniedovich. M. (2008) The Mighty Maximin! (PDF File)
    This paper is dedicated to the modeling aspects of Maximin and robust optimization.

  • Sniedovich, M. (2007) The art and science of modeling decision-making under severe uncertainty, Decision Making in Manufacturing and Services, 1-2, 111-136. (PDF File) .

  • Sniedovich, M. (2007) Crystal-Clear Answers to Two FAQs about Info-Gap (PDF File)
    In this paper I examine the two fundamental flaws in Info-Gap decision theory, and the flawed attempts to shrug off my criticism of Info-Gap decision theory.

  • My reply (PDF File) to Ben-Haim's response to one of my papers. (April 22, 2007)

    This is an exciting development!

    • Ben-Haim's response confirms my assessment of Info-Gap. It is clear that Info-Gap is fundamentally flawed and therefore unsuitable for decision-making under severe uncertainty.

    • Ben-Haim is not familiar with the fundamental concept point estimate. He does not realize that a function can be a point estimate of another function.

      So when you read my papers make sure that you do not misinterpret the notion point estimate. The phrase "A is a point estimate of B" simply means that A is an element of the same topological space that B belongs to. Thus, if B is say a probability density function and A is a point estimate of B, then A is a probability density function belonging to the same (assumed) set (family) of probability density functions.

      Ben-Haim mistakenly assumes that a point estimate is a point in a Euclidean space and therefore a point estimate cannot be say a function. This is incredible!

  • A formal proof that Info-Gap is Wald's Maximin Principle in disguise. (December 31, 2006)
    This is a very short article entitled Eureka! Info-Gap is Worst Case (maximin) in Disguise! (PDF File)
    It shows that Info-Gap is not a new theory but rather a simple instance of Wald's famous Maximin Principle dating back to 1945, which in turn goes back to von Neumann's work on Maximin problems in the context of Game Theory (1928).

  • A proof that Info-Gap's uncertainty model is fundamentally flawed. (December 31, 2006)
    This is a very short article entitled The Fundamental Flaw in Info-Gap's Uncertainty Model (PDF File) .
    It shows that because Info-Gap deploys a single point estimate under severe uncertainty, there is no reason to believe that the solutions it generates are likely to be robust.

  • A math-free explanation of the flaw in Info-Gap. ( December 31, 2006)
    This is a very short article entitled The GAP in Info-Gap (PDF File) .
    It is a math-free version of the paper above. Read it if you are allergic to math.

  • A long essay entitled What's Wrong with Info-Gap? An Operations Research Perspective (PDF File) (December 31, 2006).
    This is a paper that I presented at the ASOR Recent Advances in Operations Research (PDF File) mini-conference (December 1, 2006, Melbourne, Australia).

Recent Lectures, Seminars, Presentations

If your organization is promoting Info-Gap, I suggest that you invite me for a seminar at your place. I promise to deliver a lively, informative, entertaining and convincing presentation explaining why it is not a good idea to use — let alone promote — Info-Gap as a decision-making tool.

Here is a list of relevant lectures/seminars on this topic that I gave in the last two years.

Disclaimer: This page, its contents and style, are the responsibility of the author (Moshe Sniedovich) and do not represent the views, policies or opinions of the organizations he is associated/affiliated with.

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