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Advanced Thought Leadership for Your Money®

  • Writer's pictureAaron Kolkman

Mean Variance Optimization Part IV

Take the Day off and Aggregate

To appreciate the value of aggregate Mean Variance Optimization (MVO), the investor must first recognize that the vast majority of portfolio theory achievements (and therefore current literature) relate to security-level analysis, not portfolio-level analysis. These achievements include work by talented researchers and investors such as Benjamin Graham, Sir John Templeton, Warren Buffet, Kenneth French and Eugene Fama – all of whom focused their work on the analysis of individual holdings. One notable contrast to this group is the “Wizard of Wharton” – renowned professor Jeremy Siegel – who inches closer to measuring aggregate portfolios with a focus on asset class behavior. Siegel’s work is primarily focused on areas of the marketplace compared to each other in terms of their risk/reward characteristics (e.g., stocks versus bonds versus gold). Despite the many achievements of all the aforementioned individuals, there remains a shortage of information and practice around portfolio-level analysis. Importantly, this “aggregate” analysis is requisite to any portfolio supporting a family’s financial plan or a company’s strategic plan. Any technically-drafted financial or strategic plan relies on aggregate portfolio assumptions, in order for the plan to function as intended. Therefore, more precise assumptions mean greater predictability during the planning process, and often, better long-term funding for the plan.

During this series on MVO, I have intentionally bypassed portfolio diversification techniques, and treated portfolios as sufficiently diversified. That is, diversifiable (non-market) risk was assumed to be managed. Also, I assumed the portfolio was sufficiently correlated to its relevant indices (aka the “blended benchmark”) and was therefore exhibiting risk/reward characteristics reflective of the blended benchmark. Further, I have implied (and will continue to assume) that the portfolio’s total risks (i.e., non-market and market) are sufficiently managed. Recall that Parts II and III of this series suggested 1) using the standard deviation-based Sharpe Ratio to measure aggregate risk/reward, and 2) comparing the portfolio’s Sharpe Ratio to that of the blended benchmark – different from the direct portfolio-to-market comparison made with Alphas and Betas, related only to market risk.

The reason for assuming the portfolio is healthy overall? Good portfolio advice is readily available from technical advisors doing the hard work of portfolio construction, asset allocation, and asset location. After this work is complete, aggregate MVO can begin. The purpose of this edition of The Risk Manager is to provide a process for aggregate portfolio MVO, after traditional portfolio management techniques have been executed.

To illustrate this optimization process, consider a recent case study that explains how aggregate MVO works.

Portfolio Optimization – Carrie’s Project

Carrie was recently introduced to our firm, through her accounting office. Carrie is a wife, mother, and successful realtor in her early 50’s. Throughout her career, Carrie has built a total portfolio of approximately $1MM across 7 total accounts. To begin the project, Carrie’s portfolio was aggregated: the 7 accounts were combined, then measured against a relevant, blended benchmark for moderate investors. Next, the aggregate results were compared to an optimized model for moderate investors.

NOTE: Advisory fees for the current portfolio were not available at the onset of the project. All data are shown without the impact of advisory fees.

For Carrie’s current portfolio, the aggregated risk/reward data were as follows:

Risk and Return Statistics - 5 Yr.

As of Date 09/30/2015

Portfolio Benchmark

Standard Deviation 7.72 7.57

Mean Return 6.84 6.52

Sharpe Ratio 0.89 0.87

All data provided by Morningstar, Inc.

For an optimized moderate model, the aggregated risk/reward data were as follows:

Risk and Return Statistics - 5 Yr.

As of Date 09/30/2015

Portfolio Benchmark

Standard Deviation 6.62 7.57

Mean Return 7.66 6.52

Sharpe Ratio 1.14 0.87

All data provided by Morningstar, Inc.

Aggregate Risk/Reward Findings: we can observe from these data an Alpha of 1.27 and Beta of .85 (on an R-squared of 70.14) meaning Carrie’s portfolio was well-diversified, and actually achieved superior results when compared directly with the relevant, blended benchmark. Her 6.84%/year return versus the 6.52%/year return for the benchmark clearly demonstrates this reality, and suggests that traditional portfolio management techniques have been implemented (either per account or on the aggregate, or both).

Optimization Findings: comparing the aggregate portfolio to an optimized model for the 5-year rolling period through 09/30/15, a different theme emerged. During the period, risk could have been slightly lower, and return slightly higher. Consequently, the Sharpe Ratio of .89 could have been 1.14, for a moderate investor. Further, comparing the aggregate with an optimized model from a pure return standpoint, the portfolio lagged .82% per year. That’s .82% per year – every year for 5 years - or 4.1% cumulative. For Carrie, this 4.1% on $1MM invested (assuming a constant value) totaled approximately $41,000 in lost opportunity.


Unfortunately, many investors will continue to miss the opportunity to optimize their portfolios, often unknowingly impacting their overall financial or strategic plans. For those who pursue portfolio optimization, the process is very straightforward, but requires an initial time commitment ranging from a few hours to a full day. To create focused time, many investors choose to Take the Day Off and Aggregate.

Aggregation means pulling the portfolio into a common view for analysis as “one” investment plan.

Aggregation generally involves 4 steps:

  1. Gathering statements showing holdings and quantities (shares or units) of holdings

  2. Integrating the holdings and quantities

  3. Evaluating the correlation among holdings

  4. Comparing the aggregate data to a relevant, blended benchmark

Once aggregation is complete, the portfolio can be optimized. Optimization can happen in just two steps:

  1. Measuring aggregate risk/reward against optimized models

  2. Adjusting the portfolio accordingly

Part I of this series demonstrated that a consistent portfolio-level measurement methodology is the centerpiece of aggregate Mean Variance Optimization (MVO). The opening paragraph of this current edition articulated a lack of research in portfolio-level MVO, meaning a lack of available measurement techniques. From a theoretical standpoint, this void represents an important opportunity for academic research. As a practical matter, the only interim answer to optimizing an entire portfolio is to approach the measurement process consistently. To begin, the investor and/or professional advisor(s) need to aggregate. Then the aggregate portfolio can be optimized and adjusted as needed. Without aggregation and optimization, the investor may be completely unaware of the substantial missed opportunity to add value to the overall plan. Far worse, the overall plan may suffer from invalid assumptions, a lack of long-term funding, or both.

In upcoming releases of The Risk Manager, additional attention will be given to the relative unimportance of indexing vs. active management of portfolio holdings, and the point at which advisory fees matter.

To inquire about your portfolio optimization project, contact Chris Gerber, CFA at: (833) 234-3373 xt. 301, or

The Risk Manager delivers intelligent, actionable content related to managing primary financial risks throughout the Life Cycle of Wealth. It can assist the reader in applying advanced financial concepts to a given situation with a well-informed and financially conservative viewpoint. The ultimate purpose of this work is to bring the reader less uncertainty and a greater ability to achieve life goals.

For more information, visit or call (833) 2-FIDERE.

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