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The Efficient Frontier Is Not Real: A Case for Lottery-like Assets

• Understanding the assumptions of even the most foundational frameworks is necessary for effective asset allocation and client solutions.

• Lottery-like assets, such as venture capital or cryptocurrency, can play an important part in certain wealth management paradigms.

A Nuanced Paradigm

In a domain overwhelmed by numbers, semantics have a profound effect on how financial concepts are understood and applied (hence Two Minute Tuesdays!).

Let’s start with the first word of the cornerstone of modern portfolio theory – THE efficient frontier1. As a reminder, the efficient frontier is the mix of assets that theoretically maximizes portfolio return for given levels of risk. Seems pedantic, yet it implies that there is only one. We particularly like Robert Michaud’s characterization of the issue2:

20220920-chart-1Due to uncertainty and estimation error, we can easily depict different experiences of returns and risk while using the same inputs. The graphic illustrates this by plotting different “efficient frontiers” (in blue) simulated from the same assets as the traditional frontier (in red). The implications can be non-trivial, especially if one of these lines becomes gospel for a given strategy or client. This leads us to be more open-minded about solutions labeled as “suboptimal” based on a proposed efficient frontier because the efficient frontier is unknown and based on future returns.

An Effective Frontier

Michaud’s explanation is also somewhat problematic. Not only do we need to have the correct inputs, but we should make sure we also have the correct definitions and understandings – specifically of risk. Typically, volatility of an asset or portfolio is assumed as a proxy for risk, but in certain circumstances, like goals-based investing, the definition of risk is the probability of not attaining a goal3. Said differently, a highly volatile asset could be less risky in the sense it helps increase the probability of achieving an investor’s goal. In that type of paradigm, we are looking for an effective frontier, not necessarily an efficient one.

20220920-chart-2A thoughtful example involves allocating to an investor’s most aspirational goals with “lottery-like” assets4, such as venture capital or cryptocurrency. In a traditional framework, highly volatile assets are penalized and constrained away while goals that require a return beyond a stated efficient frontier are deemed “infeasible”. However, as the illustration shows, the high-variance asset has a greater probability of achieving the required return if it “pays off” (red line above blue at goal return).

In the context of a client’s specific situation and goals, a case can be made for allocations to these types of assets, albeit small, as long as it does not materially reduce the overall expected achievement of other goals, due to the consequential elevated expected downside.


Modern portfolio theory, efficient frontiers and balancing return and volatility are invaluable tools that we as a multi-asset research team use extensively, but with increased nuance and understanding of their inherent assumptions. Franklin Parker, a practitioner and thought-leader of goals-based management, summarizes this well: “Capturing portfolio efficiency is important, after all, but to the extent that having quality tools is important—it is not ultimate3.”

Important Disclosures & Definitions

1 Modern Portfolio Theory, 1950 to Date, Journal of Banking & Finance, Volume 21, Issues 11-2, December 1997.

2 Estimation Error and Portfolio Optimization: A Resampling Solution, New Frontier Advisors, LLC, 2007.

3 Portfolio Selection in a Goal-Based Setting, The Journal of Wealth Management, Fall 2016.

4 Allocation of Wealth Both Within and Across Goals: A Practitioner’s Guide, The Journal of Wealth Management, Summer 2020.

Standard Deviation: a statistical measure that indicates the extent of deviation for a group as a whole.

Suboptimal: a solution or outcome that is below the best possible level or standard.

Performance data quoted represents past performance. Past performance is no guarantee of future results; current performance may be higher or lower than performance quoted.

ALPS Advisors, Inc. is affiliated with ALPS Portfolio Solutions Distributor, Inc.

ALPS Portfolio Solutions Distributor, Inc., FINRA Member.

APS002112 11/30/2023

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