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For Professional Use Only
Construction Rules for the Morningstar® US Market Factor Tilt
IndexSM
Morningstar Indexes
December 2015
Overview
The Morningstar US Market Factor Tilt Index measures the performance of U.S. equity markets with
increased exposure toward small- and micro-capitalization and value stocks. It is designed to take
Contents
1
Overview
2 Index Construction
2.1 Assigning Stocks to the Index
2.2 Index Weighting
3 Index Maintenance and Calculation
3.1 Index Maintenance and Corporate
Action Treatment
3.2 Index Calculation and Price Data
4
Methodology Review and Index
Cessation Policy
5 Data Correction and Precision
5.1 Intraday Index Data Corrections
5.2 Index-Related Data and Divisor
Corrections
5.3 Computational and Reporting
Precision
6 Appendixes
6.1 Glossary
6.2 Modification to Rulebook
7
About Morningstar
advantage of the market anomalies—the small-cap and value-oriented stocks tend to outperform over
the long term. The index seeks to capture both a value and size premium to achieve what the efficientmarket camp refers to as systematic exposure to undiversifiable risk. Stocks that are deemed to be smallcapitalization or value have an overweighting in the index compared with their weight in a corresponding
market-capitalization-weighted index. Likewise, stocks designated as large or growth stocks have
underweighting compared with a standard market-capitalization weighting.
Index Inception Date and Performance Inception Date
The inception date of the Index is September 14, 2011, and the performance inception date of the index
is June 30, 1997, when the first back-tested index value was calculated.
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Index Construction
Exhibit 1 Morningstar US Market Factor Tilt Index Construction Process
Selection Universe
Morningstar® US
Security Selection
Market Factor Tilt
IndexSM
× Securities from the U.S.
equity universe.
× Securities with more than
10 nontrading days in prior
quarter are excluded.
× Select top 75% of securities
based on liquidity score.
× Security must have a
known investment style.
× Select top 99.5% of
market capitalization.
× Categorize stocks by
market cap and style.
× Tilt portfolio toward
small-/micro-cap and
value.
For additional details, refer to the "Assigning Stocks to the Index" section.
Assigning Stocks to the Index
Selection Universe
At each reconstitution, securities for the index are derived from U.S. equity universe. To qualify for
Morningstar's U.S. equity universe, a security must meet the following criteria:
× Security must be a common stock, REIT, or tracking stocks
× Security must trade on one of the three major U.S. exchanges: the New York Stock Exchange, the
Nasdaq, or the NYSE Market LLC.
× A company is classified in the U.S. universe if its primary stock market activities are carried
out in the U.S. and any of the following conditions are met: It is incorporated in the U.S. or
the following U.S. territories - Guam, Puerto Rico, or U.S. Virgin Islands
× It is incorporated in any other country but it files a Form 10-K/10-Q or equivalents and its
primary business activities as measured by the geographic distribution of revenue and assets
are conducted in the U.S. For cases where the distribution of revenue and assets is not
exclusive to the U.S., the Morningstar Index Committee will determine a company's eligibility.
Companies that remain unclassified at the end of the exercise are ineligible from the equity
universe.
× The following security types do not qualify:
× American depository receipts and American depository shares
× Fixed-dividend shares
× Convertible notes, warrants, and rights
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× Limited partnership/master limited partnership and limited liability companies
× Business development companies
× Pooled investment vehicles
× Royalty and statutory trusts
Security Selection
To be eligible for the index, all constituents must meet the following criteria in sequence:
× Securities that have more than 10 nontrading days in the prior quarter are excluded.
× Securities must be among the top 75% of the companies in the investable universe based on their
liquidity score. A security’s liquidity score is the average of its ranks on each of the following measures:
× The average monthly trading volume in U.S. dollars during the six calendar months
immediately before reconstitution or, in the case of corporate entities younger than six
months, since the security was first issued (partial month periods are prorated by number of
trading days in the month).
× The lowest two months’ total trading volume during the six calendar months immediately
before reconstitution (the months need not be sequential).
× The liquidity criterion is waived for corporate takeovers, spin-offs, or other corporate actions where the
successor entity issues one or more securities that meet the following criteria:
× The new entity qualifies for index membership in either the mid-cap or the large-cap band.
× The new entity’s float value is greater than or equal to the smallest float in the mid-cap band.
× To qualify for the Total US Market Index, a security must have a known investment style,
based on the procedures described in the "Assigning Stocks to the Style Factor Index"
section.
Companies with Multiple Share Classes
For companies with multiple share classes of equity securities, the following general rules apply:
× All trading classes that meet the general eligibility criteria are considered for inclusion.
× The market capitalization of a company is determined by aggregating all listed share classes.
This aggregate market capitalization is used to assign companies to market capitalization
bands, which is described in detail in the following section.
× The weight contribution of a share class in a given index is based on the free-float market
capitalization of that share class.
Morningstar US Market Factor Tilt Index
Each security that meets the general criteria above is considered for the US Market Index covering top
97% market capitalization as presented below by categorized the stocks in one of three cap bands: large,
mid, small.
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Assigning Large-Cap Band Constituents
× The stocks in the investable universe that meet eligibility criteria are ordered by market-cap size in
descending order.
× Selecting by size in descending order, the stocks that, in aggregate, account for 69% of the total market
capitalization of the investable universe are assigned to the large-cap band.
× Among the stocks that fall between 69% and 70% of the capitalization of the investable universe (the
upper end of the large-cap/mid-cap buffer zone), those that were classified as mid-cap or small cap and
ranked below 70% of the capitalization of the investable universe at the previous reconstitution date are
assigned to the mid-cap band. The rest are assigned to the large-cap band.
Assigning Mid-Cap Band Constituents
× Among the stocks that fall between 70% and 71% of the investable universe (the lower end of the large-
cap/mid-cap buffer zone), those that were classified as large cap and ranked within the top 70% of the
capitalization of the U.S. equity market at the previous reconstitution date are reassigned to the large-cap
band. The rest are assigned to the mid-cap band.
× Selecting from the remaining stocks by size in descending order, the stocks that fall between 71% and
89.5% of the investable universe are assigned to the mid-cap band.
× Among the stocks that fall between 89.5% and 90% of the capitalization of the investable universe (the
upper end of the mid-cap/small-cap buffer zone), those that were classified as small cap and ranked
below 90% of the capitalization of the investable universe at the previous reconstitution date are
reassigned to the small-cap band. The rest are assigned to the mid-cap band.
Assigning Small-Cap Band Constituents
× Among the stocks that fall between 90% and 90.5% of the investable universe (the lower end of the mid-
cap/small-cap buffer zone), those that were classified as mid cap or large cap and were ranked within
the top 90% of the capitalization of the U.S. equity market at the previous reconstitution date are
assigned to the mid-cap band. The rest are assigned to the small-cap band.
× Selecting from the remaining stocks by size in descending order, the stocks that fall between 90.5% and
96.75% of the capitalization of the investable universe are assigned to the small-cap band.
× Among the stocks that fall between 96.75% and 97% of the capitalization of the investable universe (the
upper end of the small-cap/micro-cap buffer zone), those that were classified as small cap and ranked
below 97% of the capitalization of the investable universe at the previous reconstitution date are
reassigned to the small-cap band. The rest are assigned to the micro-cap band.
Assigning Micro-Cap Band Constituents
× Among the stocks that fall between 97% and 97.25% of the investable universe (the lower end of the
small-cap/micro-cap buffer zone), those that were classified as small cap, mid-cap. or large cap and were
ranked within the top 97% of the capitalization of the U.S. equity market at the previous reconstitution
date are assigned to the small-cap band. The rest are assigned to the micro-cap band.
× Selecting from the remaining stocks by size in descending order, the stocks that fall between 97.25% and
99.45% of the capitalization of the investable universe are assigned to the micro-cap band.
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× Among the stocks that fall between 99.45% and 99.5% of the capitalization of the investable universe
(the lower micro-cap buffer zone), those that were excluded from the Total U.S. Market and ranked lower
than 99.5% of the capitalization of the investable universe at the previous reconstitution date, are
excluded from the micro-cap band. The rest are assigned to the micro-cap band.
Assigning Stocks to a Style Factor
Assigning Large-Cap Stocks to a Style Factor
Each index constituent within the Large Cap Index is assigned to the Large Factor Value, the Large Factor
Core, or the Large Factor Growth index. Style assignment is based on the stock's style orientation score
and the threshold levels between value and core and core and growth.
Determining a Stock’s Style Factor Orientation Score
Each stock is assigned a value orientation between zero and 100. See the "Style Methodology" section
for how stock style is scored.
Determining Threshold Levels
Value, core, and growth factor indexes are each targeted to account for one third of the total
capitalization of each capitalization group. This is referred to as the Target Weight.
Within each capitalization group, the value thresholds are calculated as follows:
× Rank stocks within the Large Cap Index by their value orientation score in ascending order.
× Calculate cumulative free-float market cap for stocks in the Large Cap Index.
× The value threshold is equal to the stock’s value score where cumulative free-float market cap is equal to
or just greater than the target weight for the Large Factor Value Index
× The growth threshold is equal to the stock’s style score where the cumulative free float market cap is
equal to or just greater than the target weight for Large Factor Value Index + target weight for Large
Factor Core Index.
Style Assignment and Buffering
× The constituents of the Large Cap Index are ordered by their value orientation score in ascending order.
× The percentage of total cap index free float represented by stocks with a score less than or equal to the
value threshold amount is calculated. This percentage is the current value threshold, or CVT.
× The percentage of total cap index free float represented by stocks with a score less than or equal to the
growth threshold amount is calculated. This is the current growth threshold, or CGT.
× Selecting by value score in ascending order, the stocks that, in aggregate, account for the CVT-5% of the
free float of the cap index are assigned to the Large Factor Value Index.
× Selecting by score in ascending order, the stocks that fall between CVT-5% and CVT are classified as
either value or core. Among these, stocks that were classified as large core and fell between the CVT and
the CGT or stocks that were classified as large growth at the previous reconstitution date are reassigned
to the Large Core Index. The rest are assigned to the Large Factor Value Index.
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× Selecting by score in ascending order, the stocks that fall between CVT and CVT+5% are classified as
either value or core. Among these, stocks that were classified as large value and fell below the CVT at
the previous reconstitution date are reassigned to the Large Value Index. The rest are assigned to the
Large Factor Core Index.
× Selecting by score in ascending order, the stocks that fall between CVT+5% and CGT-5% are assigned to
the Large Factor Core Index.
× Selecting by score in ascending order, the stocks that fall between CGT-5% and CGT are classified as
either core or growth. Among these, stocks that were classified as large growth and fell above the CGT at
the previous reconstitution date are reassigned to the Large Factor Growth Index. The rest are assigned
to the Large Factor Core Index.
× Selecting by score in ascending order, the stocks that fall between CGT and CGT+5% are classified as
either core or growth. Among these, stocks that were classified as large core and fell between the CVT
and the CGT or stocks that were classified as large value at the previous reconstitution date are
reassigned to the Large Factor Core Index. The rest are assigned to the Large Factor Growth Index.
× Selecting by score in ascending order, the stocks that fall beyond the CGT+5% are assigned to the Large
Factor Growth Index.
Assigning Mid-, Small-, and Micro-Cap Stocks to a Style Factor Index
The process described above for assigning stocks to large style factor index is also used for mid-, small,
and micro -aps.
Determining Value and Size Tilts
Factor Tilt
Weights of each constituent in a given index are tilted toward small/micro-cap and value, a part of the
market that has historically outperformed the total U.S. market over long periods of time. The weight
adjustment factors are determined as follows:
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Let:
𝑊𝐴𝐵 = the market weight of style index AB as a fraction of the Morningstar Total U.S. Market, A = L, M,
S; or Micro; B = V. C, or G. By definition:
∑
∑
𝑊𝐴𝐵 = 1
𝐵∈{𝐿,𝐶,𝐺}
𝐴∈{𝐿,𝑀,𝑆,𝑀𝑖𝑐𝑟𝑜}
For A = L, M, S, and Micro, is defined:
𝑊𝐴 = ∑
𝐵∈{𝑉,𝐶,𝐺}
Similarly, for B = V, C, and G, is defined:
𝑾𝑩 = ∑
𝑊𝐴𝐵
𝑾𝑨𝑩
𝑨∈{𝑳,𝑴,𝑺,𝑴𝒊𝒄𝒓𝒐}
The market is divided into asymmetric quadrants as follows:
𝑊𝐼 = 𝑊𝐿𝐶 + 𝑊𝐿𝐺 + 𝑊𝑀𝐶 + 𝑊𝑀𝐺
𝑊ΙΙ = 𝑊𝐿𝑉 + 𝑊𝑀𝑉
𝑊ΙΙΙ = 𝑊𝑆𝑉 + 𝑊𝑀𝑖𝑐𝑟𝑜𝑉
𝑊Ι𝑉 = 𝑊𝑆𝐶 + 𝑊𝑆𝐺 + 𝑊𝑀𝑖𝑐𝑟𝑜𝐶 + 𝑊𝑀𝑖𝑐𝑟𝑜𝐺
A parallel notation is used for the portfolio by replacing uppercase W with lowercase w. For example,
𝑊𝑀𝐶 is the allocation to the Mid-Cap Core Index, 𝑊𝑀 is the mid-cap allocation, and 𝑊𝐼 is the allocation
to quadrant I.
The value tilt is defined as a number between 0 and 1 that represents how much the portfolio is tilted
toward value. The formula for the value tilt is:
𝝋𝒀 = 𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 −
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐
𝑾𝑳
𝑾𝑳
Problem and Solution
Value and size tilt targets are denoted as X and Y, respectively. To reach these targets, weight is
allocated across the quadrants. It is assumed that within each quadrant, relative market weighting is
maintained. Therefore:
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𝑾𝑳𝑽 =
𝑾𝑳𝑽
𝑾
𝑾𝚰𝚰 𝚰𝚰
𝑾𝑳𝑪 =
𝑾𝑳𝑪
𝑾
𝑾𝜤 𝜤
𝑾𝑳𝑮 =
𝑾𝑳𝑮
𝑾
𝑾𝜤 𝜤
𝑾𝑴𝑽 =
𝑾𝑴𝑽
𝑾
𝑾𝜤𝜤 𝜤𝜤
𝑾𝑴𝑪 =
𝑾𝑴𝑪
𝑾𝜤
𝑾𝜤
𝑾𝑴𝑮 =
𝑾𝑴𝑮
𝑾𝜤
𝑾𝜤
𝑾𝑺𝑽 =
𝑾𝑺𝑽
𝑾
𝑾𝜤𝜤𝚰 𝜤𝜤𝚰
𝑾𝑺𝑪 =
𝑾𝑺𝑪
𝑾
𝑾𝜤𝑽 𝜤𝑽
𝑾𝑺𝑮 =
𝑾𝑺𝑮
𝑾
𝑾𝜤𝑽 𝜤𝑽
𝑾𝑴𝒊𝒄𝒓𝒐𝑽 =
𝑾𝑴𝒊𝒄𝒓𝒐𝑽
𝑾𝜤𝚰𝚰
𝑾𝜤𝜤𝜤
𝑾𝑴𝒊𝒄𝒓𝒐𝑪 =
𝑾𝑴𝒊𝒄𝒓𝒐𝑪
𝑾𝜤𝑽
𝑾𝜤𝑽
𝑾𝑴𝒊𝒄𝒓𝒐𝑮 =
𝑾𝑴𝒊𝒄𝒓𝒐𝑮
𝑾𝑽𝜤
𝑾𝜤𝑽
Four values are determined; namely, 𝑾𝜤 , 𝑾𝜤𝜤 , 𝑾𝜤𝜤𝜤 and 𝑾𝜤𝐕 and three conditions are imposed:
The quadrant weights must sum to one:
∑
𝑊𝑄 = 1
𝑄𝑒 (Ι,ΙΙ,ΙΙΙ,Ι𝑉)
The value tilt target must be met: 𝜑𝑋 = 𝜃𝑋
The size tilt target must be met: 𝜑𝑌 = 𝜃𝑌
Because the three conditions are linear, three of the quadrant weights can be expressed as a linear
function of the remaining one. Express 𝑾𝜤𝜤 and 𝑾𝜤𝑽 as functions of 𝑾𝜤𝜤𝜤 as follows:
𝑊ΙΙ = 𝛼ΙΙ + 𝛽ΙΙ 𝑊ΙΙΙ
𝑊𝛪𝑉 = 𝛼𝛪𝑉 + 𝛽𝛪𝑉 𝑊𝛪𝛪𝛪
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Where𝛼𝛪Ι , 𝛽𝛪𝛪 , 𝛼𝛪𝑉 , and 𝛽𝛪𝑉 are coefficients to be determined.
Since the quadrant weights must sum to 1:
𝑊Ι = 1 − 𝑊ΙΙ − 𝑊ΙΙΙ − 𝑊Ι𝑉
Restated as:
𝑾𝚰 = 𝜶𝚰 + 𝜷𝚰 𝑾𝚰𝚰𝚰
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Where:
𝜶𝚰 = 𝟏 − 𝜶𝚰𝚰 − 𝜶𝚰𝑽
𝜷𝚰 = −(𝜷𝚰𝚰 + 𝟏 + 𝜷𝚰𝑽 )
For completeness, is defined:
𝜶𝚰𝚰𝚰 =0
𝜷𝚰𝚰𝚰 = 1
From conditions (1), (2), and (3), the following pair of linear equations is derived in 𝑊ΙΙ 𝑎𝑛𝑑 𝑊Ι𝑉
𝒂𝟏𝟏 𝑾𝚰𝚰 + 𝒂𝟏𝟐 𝑾𝚰𝑽 = 𝜽𝒀 +
− (𝟏 +
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
𝑾𝑳
𝑾𝚰
𝑾𝑺 +𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
) 𝑾𝚰𝚰𝚰
𝑾𝑳
𝑾𝚰
𝒂𝟐𝟏 𝑾𝚰𝚰 + 𝒂𝟐𝟐 𝑾𝚰𝑽 = 𝜽𝑿 +
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
− (𝟏 +
) 𝑾𝚰𝚰𝚰
𝑾𝑮
𝑾𝚰
𝑾𝑮
𝑾𝚰
Where:
𝒂𝟏𝟏 =
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮 𝑾𝑳𝑽
(
−
)
𝑾𝑳
𝑾𝚰
𝑾𝚰𝚰
𝒂𝟏𝟐 =
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
+𝟏
𝑾𝑳
𝑾𝚰
𝒂𝟐𝟏 =
𝒂𝟐𝟐 =
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
+𝟏
𝑾𝑮
𝑾𝚰
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮 𝑾𝑺𝑮 + 𝑾𝑴𝒊𝒄𝒓𝒐𝑮
(
−
)
𝑾𝑮
𝑾𝚰
𝑾𝚰𝑽
The solution to this pair of equations is:
𝑾𝚰𝚰 = 𝑨𝟏𝟏 (𝜽𝒀 +
− [𝑨𝟏𝟏 (𝟏 +
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
) + 𝑨𝟏𝟐 (𝜽𝑿 +
)
𝑾𝑳
𝑾𝚰
𝑾𝑮
𝑾𝜤
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
) + 𝑨𝟏𝟐 (𝟏 +
)] 𝑾𝚰𝚰𝚰
𝑾𝑳
𝑾𝜤
𝑾𝑮
𝑾𝜤
𝑾𝜤𝑽 = 𝑨𝟐𝟏 (𝜽𝒀 +
− [𝑨𝟐𝟏 (𝟏 +
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
) + 𝑨𝟐𝟐 (𝜽𝑿 +
)
𝑾𝑳
𝑾𝜤
𝑾𝑮
𝑾𝜤
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
) + 𝑨𝟐𝟐 (𝟏 +
)] 𝑾𝜤𝜤𝜤
𝑾𝑳
𝑾𝜤
𝑾𝑮
𝑾𝜤
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Construction Rules for the Morningstar US Market Factor Tilt Index | December 2015
Page 11 of 16
Healthcare Observer | 1 July 2016
Where:
𝑨𝟏𝟏 =
𝒂𝟐𝟐
𝒂𝟏𝟏 𝒂𝟐𝟐 − 𝒂𝟐𝟏 𝒂𝟐𝟐
𝑨𝟏𝟐 = −
𝒂𝟏𝟐
𝒂𝟏𝟏 𝒂𝟐𝟐 − 𝒂𝟐𝟏 𝒂𝟐𝟐
𝑨𝟐𝟏 = −
𝒂𝟐𝟏
𝒂𝟏𝟏 𝒂𝟐𝟐 − 𝒂𝟐𝟏 𝒂𝟐𝟐
𝑨𝟐𝟐 =
𝒂𝟏𝟏
𝒂𝟏𝟏 𝒂𝟐𝟐 − 𝒂𝟐𝟏 𝒂𝟐𝟐
It follows that:
𝜶𝚰𝚰 = 𝑨𝟏𝟏 (𝜽𝒀 +
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
) + 𝑨𝟏𝟐 (𝜽𝑿 +
)
𝑾𝑳
𝑾𝜤
𝑾𝑮
𝑾𝜤
𝜷𝜤𝜤 = − [𝑨𝟏𝟏 (𝟏 +
𝜶𝚰𝐕 = 𝑨𝟐𝟏 (𝜽𝒀 +
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
) + 𝑨𝟏𝟐 (𝟏 +
)]
𝑾𝑳
𝑾𝜤
𝑾𝑮
𝑾𝜤
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
) + 𝑨𝟐𝟐 (𝜽𝑿 +
)
𝑾𝑳
𝑾𝜤
𝑾𝑮
𝑾𝜤
𝜷𝜤𝑽 = − [𝑨𝟐𝟏 (𝟏 +
𝑾𝑺 + 𝑾𝑴𝒊𝒄𝒓𝒐 𝑾𝑳𝑪 + 𝑾𝑳𝑮
𝑾𝑽 𝑾𝑴𝑮 + 𝑾𝑳𝑮
) + 𝑨𝟐𝟐 (𝟏 +
)]
𝑾𝑳
𝑾𝜤
𝑾𝑮
𝑾𝜤
𝑳𝑸 = 𝐦𝐢𝐧 (
−𝜶𝑸 𝟏 − 𝜶𝑸
,
)
𝜷𝑸
𝜷𝑸
𝑯𝑸 = 𝐦𝐚𝐱 (
−𝜶𝑸 𝟏 − 𝜶𝑸
,
)
𝜷𝑸
𝜷𝑸
Then calculate:
𝑾𝒎𝒊𝒏
𝚰𝚰𝚰 =
𝑾𝒎𝒂𝒙
𝜤𝜤𝜤 =
𝒎𝒂𝒙
𝑸𝝐{𝚰,𝚰𝚰,𝚰𝚰𝚰,𝚰𝑽 }𝑳𝑸
𝒎𝒊𝒏
𝑸𝝐{𝜤,𝜤𝜤,𝜤𝜤𝜤,𝜤𝑽 }𝑯𝑸
The first candidate for 𝑊ΙΙΙ is the one that minimizes the Euclidean distance between the investor’s
quadrant allocations to the market quadrant allocations. The problem is:
𝐦𝐢𝐧
𝑊𝚰𝚰𝚰
∑
𝑄𝜖{𝛪,𝛪𝛪,𝛪𝛪𝛪,𝛪𝑉}
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2
(𝜶𝑸 +𝜷𝑸 𝑤𝜤𝜤𝜤 −𝑾𝑸 )
Page 12 of 16
Construction Rules for the Morningstar US Market Factor Tilt Index | December 2015
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Healthcare Observer | 1 July 2016
The solution to this problem is:
𝒘
̂ 𝚰𝚰𝚰 =
∑𝑸𝝐{𝜤,𝜤𝜤,𝜤𝜤𝜤,𝜤𝑽} (𝑾𝑸 − 𝜶𝑸 ) 𝜷𝑸
∑𝑸𝝐{𝜤,𝜤𝜤,𝜤𝜤𝜤,𝜤𝑽} (𝜷𝑸 )
𝟐
If
𝑚𝑖𝑛
𝑚𝑎𝑥
𝑤ΙΙΙ
≤ 𝑤
̂𝛪Ι𝛪 ≤ 𝑤ΙΙΙ
𝑚𝑖𝑛
𝑚𝑎𝑥
the problem is solved. Otherwise, there are two remaining candidates; namely 𝑤𝛪𝛪𝛪
and 𝑤𝛪𝛪𝛪
. Each
candidate is evaluated by the Euclidean distance between the resulting portfolio and to the marketweighted portfolio of the nonzero quadrants of the candidate solution.
Value and size tilt targets are denoted as X and Y, respectively
To determine the size and value target tilt factors, 𝜃𝑋 and 𝜃𝑌 the Fama and French three-factor model
(FF3) is used. The three factors are the excess return on the market portfolio; SMB, which is the
difference between the returns of a small-cap and a large-cap portfolio; and HML, which is the difference
in returns between a high book/market and low book/market portfolio. Through this context a Bayesian
statistical model estimates the time varying beta exposures for each of 25 distinct portfolios where the
size and value tilt factors are each incremented from 0.1 to 0.5. Recall that a size and value tilt of 0
results in no tilt, i.e. a float market cap weighted portfolio. At each reconstitution, we then select from
the 25 candidate portfolios the one that has beta exposures closest to the target of SMB=0.14 and
HML=0.16. These coefficients are selected as the optimal strategy for a U.S. market portfolio tilted
toward small and value.
Number of Stocks
The number of stocks in the index is subject to the selection and eligibility criteria at the time of
reconstitution.
Index Weighting
The index is float market capitalization weighted adjusted for tilt. For more details, refer to the
Morningstar Indexes Calculation Methodology rulebook.
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Page 13 of 16
Construction Rules for the Morningstar US Market Factor Tilt Index | December 2015
Page 13 of 16
Healthcare Observer | 1 July 2016
Index Maintenance and Calculation
Scheduled Maintenance
The index is reconstituted semiannually and implemented after the close of business on the third Friday
of June and December and is effective the following Monday. If Monday is a holiday, reconstitution is
effective on the immediate following business day. The market data used for reconstitution is as of the
last trading day of May and November.
The index is rebalanced quarterly and implemented after the close of business on the third Friday of
March, June, September, and December and is effective the following Monday. If Monday is a holiday,
rebalance is effective on the immediate following business day. The market data used for rebalance is as
of the last trading day of February, May, August, and November.
Refer to Appendix 1 for details on reconstitution and rebalancing.
Corporate Action
The treatment of corporate actions can be found in the Morningstar Indexes Corporate Actions
Methodology rulebook.
Index Calculation and Price Data
Details about index calculations and price data can be found in their respective rulebooks: Morningstar
Indexes Calculation Methodology and Equity Closing Prices Used for Index Calculation.
Methodology Review and Index Cessation Policy
The index methodology is continually reviewed to ensure it achieves all stated objectives. These reviews
take into account corporate action treatment, selection, and maintenance procedures. Subscribers to the
index will be notified before any methodology changes are made. For more details, refer to the
Morningstar Index Methodology Change Process.
Morningstar also notifies all subscribers and stakeholders of the index that circumstances might arise
that require a material change to the index, or a possible cessation of the index. Circumstances that
could lead to an index cessation include, but are not limited to, market structure change, product
definition change, inadequate supply of data, insufficient revenue associated with the index, insufficient
number of clients using the index, and/or other external factors beyond the control of the Morningstar
Index Committee.
Because the cessation of the index or benchmark index could disrupt subscriber products that reference
this index, all subscribers are encouraged to have robust fallback procedures if an index is terminated.
For more details, refer to the Morningstar Index Cessation Process.
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Page 14 of 16
Construction Rules for the Morningstar US Market Factor Tilt Index | December 2015
Page 14 of 16
Healthcare Observer | 1 July 2016
Data Correction and Precision
Intraday Index Data Corrections
Commercially reasonable efforts are made to ensure the accuracy of data used in real-time index
calculations. If incorrect price or corporate action data affect index daily highs or lows, they are corrected
retroactively as soon as is feasible.
Index-Related Data and Divisor Corrections
Incorrect pricing and corporate action data for individual issues in the database will be corrected upon
detection. In addition, an incorrect divisor of an index, if discovered within five days of its occurrence, will
always be fixed retroactively on the day it is discovered to prevent an error from being carried forward.
Commercially reasonable efforts are made to correct an older error subject to its significance and
feasibility.
For more details, refer to the Recalculation Guidelines.
Computational and Reporting Precision
For reporting purposes, index values are rounded to two decimal places and divisors are rounded to
appropriate decimal places.
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Page 15 of 16
Construction Rules for the Morningstar US Market Factor Tilt Index | December 2015
Page 15 of 16
Healthcare Observer | 1 July 2016
Appendixes
Appendix 1: Glossary
Terms
Description
Reconstitution
Each reconstitution involves the following:
• Updating the global market investable equity universe.
• Reviewing the economic segment- and country-level size segment breakpoints.
• Assigning companies to capitalization bands taking into account the buffer zones.
• Changes in index shares (free float, total shares outstanding, index-specific adjustment factor) of each
constituent.
Each rebalancing involves the following:
• Changes in index shares (free float, total shares outstanding, index-specific adjustment factor) of each
Constituent.
• Addition of U.S. spin-offs/IPOs to the global markets index (exclude for ex-U.S. index rulebooks).
Rebalance
Appendix 2: Modification to Rulebook
Section
Description
Update Date
Multiple share
classes
All eligible trading share classes are considered for the index from December 2015
reconstitution.
December 2015
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Construction Rules for the Morningstar US Market Factor Tilt Index | December 2015
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Healthcare Observer | 1 July 2016
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Any matter arising from undocumented events will be resolved at the discretion of Morningstar Index Committee. The information
in this document is the property of Morningstar, Inc. Reproduction or transcription by any means, in whole or part, without the prior
written consent of Morningstar, Inc., is prohibited. While data contained in this report are gathered from reliable sources, accuracy
and completeness cannot be guaranteed. All data, information, and opinions are subject to change without notice. This document
may contain back-tested or simulated performances and the subsequent results achieved by the investment strategy may be
materially different.
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