Diversification Meter
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Simple Explanation
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Bigger is Better. Strive to achieve the highest score possible.
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The Diversification Meter produces a simplified visual indication of how much diversification
exists in a portfolio. Increased diversification among traditional investments like
stocks, mutual funds and bonds reduces the volatility of a portfolio and provides
improved returns across full market cycles.
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"It’s interesting; we’ve recently discovered that diversification provides a free
lunch. Recent research performed between the University of Denver and Gravity Investments
shows no material relationship between diversification and returns during a bull
market, however in a bear market it’s a different story. For every incremental percent
increase of IPC achieved, a .98% increase in returns is realized. This correlation
asymmetry of diversification and returns is not reciprocated when examining the
relationship of risk and return. Accordingly, diversification warrants the focus
of asset allocation and portfolio optimization."
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James E. Damschroder - Inventor of Gsphere and True Diversification®
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Advanced Explanation
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The Diversification Meter represents one of 3 measures that comprise the overall
True Diversification® score. The 3 components that influence True Diversification®
are:
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1. Total Diversification - AKA Portfolio Dimensionality
More Portfolio Dimensions = Better.
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Portfolio Dimensionality represents the Total Diversification of the portfolio and
accounts for the Total Diversification effect. More dimensions enable the portfolio
to perform in a greater number of independent and simultaneous directions. Since
behaving independently is the essence of diversification, Portfolio Dimensionality
defines the total level of diversification present in the portfolio.
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In mathematics, dimensions are inherently unrelated to one another. The weighted
time series or correlation matrix of the assets begins with a dimensionality equal
to the number of holdings, but due to the overlap, unequal weightings and other
redundancy, the actual information of the portfolio can be represented in fewer
dimensions. The dimensions are associated with confidence intervals and the measure
provided represents the total dimensionality of the portfolio at the 75% confidence
interval. This is a lower confidence interval than commonly used in statistics,
but due to the nature of financial data having non-Gaussian distributions the more
stringent 75% confidence interval is appropriate as the measured dimension will
better withstand crisis, providing a stable and more consistent diversification
value. The measure is patent pending.
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Generally, a portfolio with exclusively individual assets should seek a minimum
score of 7, while a portfolio containing at least some level of aggregated accounts
(Mutual Funds, ETF's, etc...) should seek a minimum score of 4-6. It is acceptable
for portfolios with mutual fund type accounts to have less Portfolio Dimensions.
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2. Intra-Portfolio Correlation (IPC)
Higher IPC = Better.
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The greater the percentage IPC the less correlated the portfolio. Generally, 50%
or higher represents adequate diversification with regards to IPC. IPC measures
the amount of Systematic Diversification that exists in a portfolio. It is a means
to quantify diversification. The meter shows the amount of market risk eliminated.
A value of 100% or -1 represents perfect diversification and a value of 0% or 1
represents no diversification between the holdings in a portfolio. In the case of
aggregated accounts such as mutual funds, the IPC provides a very useful measure
since the relationship of the fund as a whole to other assets in the portfolio will
directly impact the performance characteristics of the overall portfolio.
We actually use a weighted average intra-portfolio correlation. This statistic is
calculated as follows:
Where Q is the intra-portfolio correlation
Xi is the fraction invested in asset i
Xj is the fraction invested in asset j
Pij is the correlation between assets i and j
The expression is computed when i ≠ j
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Intra-Portfolio-Correlation (IPC%)
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% of diversifiable risk removed
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1.00
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0.00%
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0.75
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12.50%
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0.50
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25.00%
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0.25
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37.50%
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0.00
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50.00%
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-0.25
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62.50%
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-0.50
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75%
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-0.75
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87.5%
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-1.00
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100%
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3. Concentration Coefficient (CC)* - AKA Equal Weight Equivalent
Higher CC = Better.
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The greater the CC, the less concentrated the portfolio.
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The CC is a measure of portfolio concentration and represents the non-systematic diversification
in a portfolio. CC is equal to the number of assets if equally weighted. The number is proportionally
less as concentration increases. For example, if a portfolio consists of 2 assets that are equally
weighted (50% each), the concentration coefficient is 2. If a portfolio consists of 2 assets where
these assets are weighted 99% and 1%, the CC is 1.02. If two assets in a given portfolio are weighted
75% and 25% the CC is 1.6.
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The CC is an important measure of diversification when we consider the significance that asset
weighting has a contributing factor to diversification of a portfolio. In other words, it would
be inaccurate to assume that a portfolio consisting of 20 non-correlated assets is well diversified
without knowing their respective weightings. In this case, 19 assets could make up 1% of the portfolio
and the remaining asset 99%. The CC will help identify these potential issues.
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*CC is a measurement created by The Brandes Institute, San Diego, CA.
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