**Investment Risk Glossary**

**Alpha** is a measure of the difference between a fund’s actual returns and its expected performance, given its level of risk (as measured by beta). Alpha grades an investment’s return scaled to the return expected by its benchmark. The amount of Alpha delineates the amount by which the investment has outperformed or underperformed its benchmark.

**Ambient Dimensionality (AD)** is the scientific name for the diversification metric that measures the total numerical count of risk assets(only) held in a portfolio and is one of the 3 quantity factors used to measure diversification.

**Beta** is the measure of an investment’s sensitivity to market movements. The beta of the benchmark is 1.00, so a fund with a 1.10 beta is expected to perform 10% better than its benchmark index in up markets and 10% worse in down markets. Conversely, a beta of .85 indicates that the fund is expected to perform 15% worse than the benchmark index in up markets and 15% better in down markets.

**Commonality** is the common name for Intrinsic Dimensionality (listed below), one of the 3 quantity factors used to measure a portfolio’s diversification.

**Compensated Investment Risk** is unavoidable. It is the inherent risk assumed when making any investment. Compensated risk is also known as “un-diversifiable risk,” “market risk,” or “systematic risk” because it affects all investments, and is not limited to a particular investmenttype, security, industry, etc. and investors expect higher returns when assuming more of it. As a result, every participant in the investment market is exposed to it. This compensated risk is both unpredictable and unavoidable. It cannot be changed or diversified away. It changes only when market conditions change. It is considered to be the “price of admission” paid by everyone who becomes a market participant. Compensated risk is approximately 1/3 of total risk.

**Concentration** is the common name for Spanning Dimensionality (listed below), one of the 3 quantity factors used to measure a portfolio’s diversification.

**Correlation** compares the direction only (not the amount) of a portfolio’s movement in relation to its benchmark. A correlation coefficient of +1 implies that as a benchmark moves either up or down, the portfolio will move in lockstep, in the same direction. Alternatively, a perfectly negative correlation of -1 means that if either the portfolio or benchmark moves one way the other will move in the opposite direction. If the correlation is 0, the movements of the portfolio and index are said to have no correlation; they are completely random.

**Count** is the common name for Ambient Dimensionality (see above), one of the 3 quantity factors used to measure a portfolio’s diversification.

**Cross-Correlation % (Reciprocal)** is a stand-alone, holistic metric that measures the correlation composition of all interrelationships within a given portfolio. It quantifies the degree to which the securities held inside the portfolio are expected to move in the same direction and is an academically accepted measure of a portfolio’s systematic risk.

**Down-Market Capture** ratio is the statistical measure of an investment portfolio’s overall performance in down- markets. Portfolios that display a down-market capture of greater than 100% have underperformed their benchmark during periods when the benchmark decreased in value by the percentage amount in excess of 100%.

**Diversification Return (Estimated).** In Diversification Returns and Asset Contributions, Eugene Fama and David Booth (1992) proved how diversification yielded additive portfolio returns, naming the phenomenon “diversification returns.” They reasoned that if the correlation of all a portfolio’s assets equaled 1, then the weighted average asset variance would equal the portfolio variance. They went on to prove how more diversification increased this incremental return and was a function of the amount of variance reduction, not the actual level of portfolio variance. They estimated a portfolio’s “diversification returns” equaled half the variance reduction caused by diversification (e.g. I f you start with a portfolio made up entirely of low-volatility assets, their covariance can only reduce the portfolio’s standard deviation by a small amount — causing smaller variance reduction and reduced diversification returns). Prudent uncompensated risk management requires focusing on correlations, not standard deviations.

**Fixed-income security** is a security that pays an unchanging rate of interest. Fixed-income securities include bonds and money market instruments.

**Intrinsic Dimensionality (ID)** is the scientific name for the companion Diversification Metric to SD and is used to quantify the number of diversification elements available for removal of uncompensated risk from a portfolio. ID is a necessary metric because SD, alone, cannot differentiate between assets that are highly correlated (e.g. a portfolio holding 5 different S&P 500 Index ETFs at 20% each will have a SD of 5, but an ID of 1). The I D metric measures the number of sufficiently asymmetrical and equally weighted equivalent elements that are present in a portfolio. The more of these elements present in a portfolio; the greater is the ability for each element to perform independently, and independent performance by more elements is the hallmark of diversification.

**Maximum drawdown** is a portfolio’s peak to trough performance measured from the high point reached prior to the decline’s inception until a new high is reached. The drawdown is determined upon completion of the entire cycle, which cannot be known until a new high is reached. Once reached the percentage decline from the old high to the lowest interim point of that cycle is the drawdown. Maximum drawdown is the drawdown having the largest decline during the period examined. It is a metric that measures risk.

**R–Squared (R2)** is the percentageof the portfolio’s performance explained by the behavior of the assigned benchmark. R- Squared values range between 0 and 100, where 0 represents the least correlation and 100 represents full correlation. The R-Squared of a portfolio indicates whether the index being used to analyze beta is an appropriate benchmark. If a portfolio’s R-Squared value is close to 100,the beta of the investment can be trusted. On the other hand, an R-Squared value that is less than 75 indicates that the beta is not particularlyuseful because the portfolio is being compared to an inappropriate benchmark.

**Risk** refers to an investment’s vulnerability to fluctuations in value relative to changing economic or market conditions. Risk is used to define all uncertainty relating to the outcome. The level of risk incurred by a fund varies from fund to fund, depending primarily on the types of securities in which a fundinvests.

**Semi-Deviation** is a measure of dispersion for the values of a data-set falling below the observed mean or target value. Semi- Deviation is the square root of semi-variance, which is found by averaging the deviations of observed values that have a result that is below the mean.

**Sharpe Ratio** measures the portfolio’s excess return over the risk-free rate divided by the standard deviation of the excess return. It is a measure of the absolute rate of return per one unit of risk. The better an investment’s risk- adjusted performance has been, the higher its Sharpe ratio will score. A negative Sharpe ratio indicates that a risk-less asset would have performed better than the investment being analyzed.

**Spanning Dimensionality (SD)** is the companion Diversification Metric to AD. It is the scientific name for the number of equally- weighted equivalent risk assets present in a portfolio. Equally weighted portfolios have maximum SD possible for the given number of total portfolio assets, and represent the smallest possible concentration structure. Decreases in the SD metric indicate increases to portfolio concentration and less diversification. Real life portfolios are almost never equally weighted, thereby encompassing varying degrees of unknown concentration. Using the SD metric to learn a portfolio’s equally weighted equivalent asset count is an important step in accurate diversification measurement.

**Standard Deviation** is a statistical measure of portfolio risk measured by the variability of the portfolio’s return around its average over a specific time period. Unlike alpha, beta, and R-squared which are relative to a benchmark index, standard deviation is an absolute measure. In general, the higher the standard deviation is, the greater the volatility or risk is.

**Systemic Risk**, in finance, is the risk of collapse of an entire financial system or entire market, as opposed to risk associated with any one individual entity, group or component of a system that can be contained therein without harming the entire system. It refers to the risks imposed by inter-linkages and inter-dependencies where the failure of a single entity or cluster of entities can cause a cascading failure, which could potentially bankrupt or bring down the entire system or market. Normally systemic risk is not a great factor, but when it is it becomes a tsunami it overruns all other factors in the marketplace.

**Important Note:** “systemic” (8 letters) risk is sometimes erroneously referred to as “systematic” (10 letters) risk (compensated risk).

**Tracking Error** measures the divergence between the price behavior of the listed portfolio and the price behavior of the benchmark. Tracking error shows how well the movement of each portfolio tracks the benchmark over the period of time being measured. Even portfolios that display high R-squared values to their benchmark usually behave differently than the benchmark during shorter periods of time within the overall measurement period, Tracking error quantifies this difference.

**Ulcer Index (UI)** is a technical indicator that measures downside risk in terms of both the depth and duration of a portfolio’s short-termmarket value declines. The index increases in value as the value moves farther away from a recent high and falls as the value rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown an investor can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a portfolio to get back to its formerhigh.

**Uncompensated Risk** is a risk that can be eliminated with diversification and unlike compensated or systematic risk investors cannot expect added return for assuming more uncompensated risk. Uncompensated risk is also referred to as unsystematic risk and can be reduced by methodically re-balancing the portfolio. Uncompensated risk represents approximately 2/3 of total risk.

**Uncompensated Risk Not Removed from Portfolio.** Although uncompensated risk measurement is defined by both quantity and quality factors, we use only quantity factors for this metric. Because cross correlations can vary greatly over time and as such are not suitable measures to constrain portfolio construction, incorporating quality factors in a single statistic could prove misleading. For this metric, it is assumed that the Intrinsic Dimension or Fiduciary Score achieved by the MAX DIVERSIFICATION UCR portfolio equals 0.00% remaining uncompensated risk. Each portfolio’s Intrinsic Dimensions when divided by the MAX Diversification UCR portfolio’s Intrinsic Dimensions represents the percentage of uncompensated risk not removed from that portfolio.

**Up-Market Capture** ratio is the statistical measure of the investment portfolio’s overall performance in up- markets. Portfolios that display an up-market capture of greater than 100 have outperformed their benchmark during periods when the benchmark increased in value by the percentage amount in excess of 100.

**Variance** is a measurement of the spread between numbers in a data set. It measures how far each number in the set is from the mean and is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set. Variance is a key parameter in diversification management. Along with correlation, the variance of asset returns helps investors prudently manage the risk/return trade-off in investment portfolios. The square root of variance is standard deviation

**Variance Gap.** According to Restatement (3rd) of Trusts “…a portfolio’s risk is less than the weighted average of the risk of its individual holdings.” The variance gap equals the sum of the weighted average variances of the portfolio’s individual asset holdings less the portfolio’s overall variance. The greater the variance gap, the greater the diversification benefit.

**Volatility** is a statistical measure of the dispersion of returns for a given security, a portfolio, or market index. Volatility can either bemeasured by using the standard deviation or variance between returns from that same security, portfolio, or market index. Usually, the higher the volatility is, the riskier the portfolio is.

**Assumptions, Limiting Conditions, & Disclaimers**

The information contained in an analysis report is intended to provide limited diversification information on how the analyzed portfolios would have performed during the period being analyzed, under circumstances where all positions held at the start of the year were held throughout the year ended on the same month and day in 2019, and no changes occurred in number of shares held in any of the portfolios throughout the year. The optimized portfolios provide a more detailed diversification information with similar assumptions. Accordingly, all the portfolios used for analysis and optimization are hypothetical.

Data is furnished by others and such information and data have been accepted as reliable. None of the information or data prepared by outside sources was independently verified for accuracy or completeness. Accordingly, no responsibility is assumed for information prepared and/or furnished by others.

We did not independently verify any of the historical financial data prepared by third parties for accuracy or completeness, and therefore, do not express an opinion or any other form of assurance regarding the historical financial data used in a report.

References made to any specific securities do not constitute an offer to buy or sell securities. The past performance of an ETF, mutual fund, individual security, or investment/diversification strategy cannot guarantee its future outcome or performance.

When unlisted collective investments are present in a portfolio, listed ETF and mutual fund proxies are substituted for the unlisted collective investment positions. Selection criteria for each proxy are based on estimated similarities to the investment purpose and risk profile of the collective investment being replaced.

All the ETF, mutual fund, and individual security symbols used in a report are a proxy for their related asset class, sector, sub-sector, industry, country index, etc. and were chosen based on their estimated similarities to the investment purpose and risk profile of the related investment being replaced.