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  • Writer's pictureAaron Kolkman

Mean Variance Optimization: II and III

MVO Part II: A Tale of Two Portfolios

MVO Part III: Getting the Score

To revisit Part I of this Series (Q1, 2015) on Mean Variance Optimization (MVO), recall that using Sharpe Ratios can provide a complete view of total risk/reward for a portfolio – that is risk/reward measurement encompassing diversifiable (aka “business” or “unsystematic”) risk, and non-diversifiable (aka “market” or “systematic”) risk/reward, the latter of which is often measured against a relevant benchmark, using Beta/Alpha. The distinction between total risk/reward measurement and market risk/reward measurement is especially clear when asset prices fall (1973-1974, 1987, 1991, 2000-2002, 2007-2009, etc.), with entire asset classes (and their benchmarks) in flux. Therefore, using market-based measurements of risk/reward – particularly when discussing aggregate portfolios – is at best a volatile proposition. By contrast, Part I of this series also established that employing Sharpe Ratio to measure an aggregate portfolio can be effective when comparing to the Sharpe Ratio of a relevant (strongly and positively correlated) benchmark. Importantly, the comparison between two Sharpe Ratios does not mean comparing the portfolio to the benchmark directly. In short, remember the goals of MVO stated in Part I of this series: “[a] formula for measuring Aggregate MVO should quantify the success or failure of achieving this risk-adjusted (net of fees) outperformance.” Probably the best way to apply these points is through the use of real examples – stories of those who have undergone an MVO process, and their results.

A Tale of Two Portfolios

Portfolio #1 –Tom and Sally

During one recent engagement, my firm provided analysis for approximately $3MM of investable assets. The investors involved were convinced their holdings were strong, having generated consistent double-digit returns over the recent 5-year period measured. They were right. Based upon a rolling 5-year history, of June 30, 2015, their portfolio results according to Morningstar were as follows:

Risk and Return Statistics - 5 Yr


Portfolio Benchmark

Standard Deviation 7.45 5.42

Mean Return 10.47 7.04

Sharpe Ratio 1.37 1.27

What do we know from this analysis? We know that Tom and Sally’s 5-year historical Mean Return reported is substantially higher than the relevant benchmark return (using a benchmark with a correlation co-efficient of 85.14 over the same period). We also know that the portfolio variance (i.e., total risk) was substantially higher, based upon its Standard Deviation. The combination of these two points provides a return premium (or discount) for total risk taken – the Sharpe Ratio. Clearly, the risk premium achieved by Tom and Sally was inadequate compared to the Sharpe Ratio available to them in relevant areas of the marketplace. This is all helpful information for Sally and Tom, and provides evidence that risk is too high for the return achieved, when compared to other relevant options available to them. The argument for indexing stops here, and asserts that Tom and Sally should “buy the relevant index(es)” through low-cost investing and achieve the same total risk/reward as the benchmark itself. This method of improvement is both accurate and viable for Sally and Tom. However, it does little to explain the efficiency of their portfolio. Enter MVO scoring. Using a proprietary scoring method to measure portfolio efficiency can establish whether or not the aggregate portfolio (measured above) offers a more efficient risk-adjusted result versus the benchmark or other relevant alternatives. Specifically, Sally and Tom can know whether or not their portfolio achieved better or worse than an aggregated portfolio risk/reward continuum known as the “Capital Market Line” (CML), and what adjustments they can make to optimize their overall investable assets.

In this example, Tom and Sally’s MVO Score was: (1.62) or -1.62. This score indicates the investors’ portfolio was less efficient when compared to the CML. Note that the CML represents the intersection of risk and reward, so itself is perfectly efficient (it cannot be more or less efficient than itself). We therefore assign the CML score an MVO score of zero. As such, a relevant indexing strategy would carry a portfolio MVO score of zero, less the internal costs of the vehicle used (Mutual fund, ETF, etc.). In Sally and Tom’s case, a negative MVO score indicates either excess risk, insufficient reward, or both. Other than investing their entire portfolio in an indexed fashion, what else can Sally and Tom do to achieve a more optimal aggregate portfolio? Let’s look at another example.

Portfolio #2 – Mark and Sara

Another recent engagement my firm accepted included an MVO analysis for a family with approximately $4.5MM of investable assets, approximately $1.5MM of which was highly-concentrated stock in a U.S. blue-chip company. For comparison purposes, we will set aside this stock position, and focus on the other $3MM in assets. Similar to the previous case, the investors were proud of the results of their holdings over the 5-year rolling period, as follows (according to Morningstar):

Risk and Return Statistics - 5 Yr


Portfolio Benchmark

Standard Deviation 10.04 5.42

Mean Return 11.42 7.04

Sharpe Ratio 1.12 1.27

In this case, the benchmark correlation coefficient was 89.11 over the period measured, indicating a strong positive correlation, and therefore a relevant comparison point. Once again, when the index itself is inserted into the CML formula will again render an MVO score of zero, being neither less efficient nor more efficient than itself. Sara and Mark’s portfolio MVO score was the focus of this project, and was: .79 or +.79. This score indicates the portfolio measured was superior over the period measured, when compared to the CML (previously defined as the intersection between risk and reward for the entire portfolio). What does this mean for Mark and Sara? It means they received reward in excess of the risk taken – at the aggregate level. How did they achieve this? The interactions between portfolio holdings (i.e., covariance) allowed them to “elevate” their results beyond that of the index or any individual holding.

Not unlike a competent college basketball coach identifying which player(s) contribute to and detract from overall results (when viewing the overall team on the court), a competent portfolio manager can create a portfolio MVO attribution analysis, which measures the contribution of each asset class (and even each holding) to the overall MVO score and can thereby isolate and remove poor MVO contribution.

Getting the Score

In conclusion, no matter how your assets are managed (or by whom), and no matter how you feel about the results, an MVO analysis can provide necessary insight into the assets in the portfolio mix, their interplay, and their combined efficiency. In the two cases discussed, both couples held different types of vehicles with different levels of underlying fees (advisory fees were not applied). Also, both couples felt confident with their results, and were generally comfortable with the direction of their asset base.

The MVO scoring process gave both households an added dimension of clarity, and necessarily, a starting point from which to work with their advisors on the underlying cause of any inefficiency identified. Whether or not Boulevard Wealth Management handles part or all of your entire portfolio, whether or not you choose to index with your assets, and whether or not you have the ideal underlying fee structure, consider measuring the efficiency of the aggregate first. If you have an MVO score, you can better decide how to proceed with any remaining analysis.

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

To inquire or schedule your MVO scoring project, contact Chris Gerber at (833) 234-3373 xt. 301, or

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