Whitepaper
Equity Factor Risk Models
Version #1.1 · 31st of July 2020
www.bitadata.com
LOG OF AMENDMENTS
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Introduction and Background
General Information
Literature Review on Factor Models
Factor Structure Overview 1. Estimation Universe 2. Sector Factors 3. Style Factors
3.1. STYLE FACTORS DEFINITIONS
Methodology 1. Security and Portfolio Level Factor Exposures
1.1. Style Factor Exposures
1.2. Binary Factor Exposures
2. Factor Returns Estimation 3. Risk Estimation
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Summary and Conclusions 16
References
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CONTACT
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1) 06.05.2020
- Version #1.0. First publication of this whitepaper. 2) 31.07.2020
- Version #1.1. General edits.
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About the BITA Equity Risk Model
Equity Risk modeling is a powerful tool that provides insights for risk management, performance attribution,
and portfolio construction. In this document, we provide the methodology, and the implementation process
of the BITA Global Equity Risk Model, a fundamental multi-factor model developed by BITA for the
identification of sources of a portfolio’s risk. Combined with some other tools, the BITA Equity Risk Model is
used by investors to evaluate quantitative investment strategies within the BITACore environment.
About BITA
BITA is a Germany-based Fintech that provides enterprise-grade indexes, data, and infrastructure to
institutions operating in the passive and quantitative investment space. Thanks to BITA’s innovative index
software, designed to outperform other existing solutions in terms of flexibility and speed, BITA is able to
provide independent, methodologically-sound indexes that both are investable and replicable by customers
and stakeholders. All of BITA’s methodologies and processes are completely transparent and available
publicly.
About this Document
This document is published to serve as a guidebook of the methodology adopted in the construction,
calculation and management of the BITA Equity Risk Model.
Any methodological changes or alterations to this document are performed by the BITA Data Management
Board and authorized by the BITA Oversight Function, following the directives of the Regulation (EU)
2016/2011 “Benchmark Regulation” (BMR). The BITA Equity Risk Model outputs are owned, calculated,
administered and disseminated by BITA GmbH.
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The BITA Global Equity Risk Model and the closely related Single country, and Regional Models are tools to
understand and manage sources of performance and risk in diversified global (or single market) portfolios.
Additionally, the models can be paired with a portfolio optimizer, such as the BITA Index Optimizer, to build
risk/return optimized investment strategies. Global coverage demands balancing ubiquity and granularity. Factors that capture the behavior of one
industry or market might fail on another. To address this issue, we could be joining many specialized models.
However, accuracy in the linkages is poor, and the interpretation of the exposures to a large set of
redundant factors might be unclear. Alternatively, a huge set of factors has high in-sample explanatory
power but blunders on the dynamic future. The BITA Global Equity Risk Model is built to capture risks affecting diversified global portfolios. Portfolios
invested in a Single market or specific Region are best served by a model covering solely that market.
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One of the main objectives of multiple factor models is to describe asset returns and their covariance matrix
as a function of a finite number of risk attributes. These kinds of models are based on one of the basic
principles of financial theory: there is no reward without risk. The Capital Asset Pricing Model (CAPM), first
presented by Sharpe (1964), uses stock beta as the only relevant risk measure, meaning that the market can
be considered as the first and most important equity factor. The Arbitrage Pricing Theory, presented by
Ross (1976), postulates a more general multiple factor structure for the generation of returns. However, it
neither specifies the nature, nor the number of these factors. In general, a factor can be defined as any characteristic relating a group of securities that is relevant in
explaining their returns and risk. Beyond the market factor, researchers generally look for factors that are
persistent over time and have strong explanatory power over a broad range of stocks. Because factors
cannot be directly observed, there is a keen debate about their definition and estimation. Currently, there are
three main categories of factors: macroeconomic, statistical, and fundamental. Macroeconomic factors
include measures such as surprises in inflation or GDP, surprises in the yield curve, and other measures of
the macro economy. Statistical factor models identify factors using statistical techniques such as principal
components analysis (PCA).
Nowadays, fundamental factors are the mostly widely used factors in the industry. According to this
approach, the sources of risk premia are linked to stock characteristics such as industry membership,
country membership, valuation ratios, and technical indicators. Rosenberg and Marathe (1976) showed the
relevance of these factors in explaining stock returns. Fama-French (1992) found price to book value ratio
and market capitalization to have significant influence on stock returns. Furthermore, a widely range of
studies has shown that industry, country, currency and style factors contribute significantly to active return
of actively managed funds. Style factors that have been proposed and explored include momentum (Carhart
1997), quality (Sloan, 1996), Volatility (Ang et al., 2006), dividend yield (Litzenberger and Ramaswamy, 1979)
and liquidity (Amihud, 2002). Nowadays, multiple factor models have been applied early in investment
practice, mainly because they allow a differentiated and intuitive risk-return analysis decomposition. The BITA Equity Risk Model is a multi-factor risk model which seeks to decompose each asset’s returns
across a set of 18 individual fundamental factors. The 18 factors in the model consist of 11 sector factors
and 7 style factors.
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1. Estimation Universe
The estimation universe is the set of stocks that is used to estimate the risk model. In order to ensure the
soundness of the model, we must look for representation, liquidity and stability when selecting these
securities. A well-constructed equity index must address these criteria, and therefore serves as an excellent
foundation for the estimation universe. In the following table, we present the estimation universes we use in the different BITA Equity Risk model
variants we offer:
Equity Risk Model Variant
Estimation Universe
BITA Global Fundamental Model (BITA RMGLF1)
BITA Global Universe
Europe Fundamental Model (BITA RMEUF1)
BITA Europe Universe
US Fundamental Model (BITA RMUSF1)
BITA US Universe
As of 2020, the models cover over 14,000 securities in more than 60 countries. Market returns,
capitalizations, and fundamental data are obtained from S&P Capital IQ. BITA’s Equity Risk Models use point-in-time fundamental data, which allows us to address look-ahead bias in
back-tests, and enable more timely updates. We use historical data from January 2008 onwards, and we
update the model on a daily basis.
2. Sector Factors
Sector classification is an important source of common factor risk and accounts for a great deal of
similarities observed in securities behavior.
Sector factors are based on the GICS industry classification:
- Consumer Discretionary
- Consumer Staples
- Energy
- Financials
- Health Care
- Industrials
- Information Technology
- Materials
- Real State
- Communication Services
- Utilities
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3. Style Factors
Style factors are drivers of return within an asset class; they have historically delivered a return premium
over the long term – capturing a specific risk premium, behavioral anomaly, or structural market impediment. BITA’s Equity Risk Model includes seven factors: Momentum, Size, Value, Quality, Volatility, Liquidity and
dividend Yield. Each factor is the result of a combination of descriptors, which are quantities and ratios
calculated from fundamental and market data. The following is a summary of the structure of each factor
and the descriptors used.
STYLE FACTOR
CLASSIFICATION
Momentum
Momentum (100%)
Size
Size (100%)
Value
Book to Price Ratio (20%)
Cash Flow to Price Ratio (20%)
EBITDA to Enterprise Value Ratio (20%)
Earnings to Price Ratio (20%)
Sales to Enterprise Value Ratio (20%)
Quality
Earnings Variability (34%)
Profitability (33%)
Leverage (31%)
Low Volatility
1/ VLRT: Inverse of volatility return over the
last year (100%)
Liquidity
Liquidity (100%)
Dividend Yield
Dividend Yield (100%)
3.1. STYLE FACTORS DEFINITIONS
This section gives detailed definitions of the descriptors which underlie the style factors in the BITA’s Equity
Risk Model. The method of combining these descriptors into style factors is proprietary to BITA.
a) Momentum:
The momentum exposure is calculated as the local 12-month total returns, after excluding the most recent
month (Return).
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b) Value:
The Value metric of asset i, Value on day t is calculated as a composite based on the following formula:
Where:
is the Book to Price ratio,
is the Cash Flow to Price ratio,
is the Earnings to Price ratio,
is the EBITDA to Enterprise Value ratio, and
is the Sales to Enterprise Value ratio.
c) Size:
The size metric of an asset, Size on day t is computed by calculating the log of its company's market
capitalization. The formula is:
d) Quality:
Quality is a composite of Profitability and Leverage measures. These measures are based on quarterly data.
Therefore, the quality exposure only changes from quarter to quarter, and we extend such calculations on a
daily basis.
where:
d.1. Profitability We calculate this descriptor as a composite of the following financial ratios:
Where ROE is the Return on Equity (ROE), ROA is the Return on Assets (ROA), and EBITDA Margin is the
Earnings before interests, taxes, depreciation, and amortization divided by revenues.
d.2. Earnings Variability
We calculate this descriptor as the standard deviation of year-on year Earnings per Share (EPS) growth in
the last five fiscal years.
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Where:
is the EPS growth
is the average EPS growth over the last five fiscal years
denotes the number EPS growth data points, e.g. 4 in the case of earnings variability
d.3. Leverage This descriptor is calculated as a composite of several leverage measures: where BLev is the Book Value of Leverage, Mlev is the Market Value of Leverage and
Total Assets Ratio.
is the Debt to
e) Low Volatility:
This factor exposure captures market risk that cannot be explained by the market factor, and is calculated
as follows:
Where:
is the return volatility over the last year.
f) Liquidity:
The liquidity factor exposure is calculated using the 3-month average daily volume divided by the shares
outstanding of the instrument in its primary exchange.
g) Yield:
For non-dividend paying stocks, this factor exposure is still calculated, and it will set to be 0.
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1. Security and Portfolio Level Factor Exposures
1.1. Style Factor Exposures
Style Factors are types of factors related to securities’ fundamental characteristics. Each style factor
consists of one or multiple “atomic” descriptors, which represent the features of an investment. The
advantages of using multiple descriptors are more robust calculations of factor exposure and better
explanatory power. This figure illustrates the factor exposures’ calculation process. Factor returns from the covariance matrix
are used for risk attribution analysis. Specific risk is estimated separately.
If Descriptor
Generate Descriptors
Winsorization
Generate Factors
Standarization
If Factor
Factor Exposures
Data Flow for Factor Exposures Calculation
All style factors in the BITA Global Equity Risk Model and other BITA fundamental equity factor models are
constructed base on the following steps. First, we calculate the descriptors, this can be done using
arithmetic operations of some fundamental values to get a ratio or applying a real function, such as taking
the logarithm of market capitalization. In some cases, this step involves more complex calculations like
estimating the CAPM beta through a time-series regression model. Next, we weight each descriptor with its corresponding market capitalization and winsorize the remaining
values to be within two standard deviations from the mean. After winsorizing, we standardize the descriptors
to have a cap-weighted mean of zero and a standard deviation of 1. Stocks with scores less than minus
three are set to minus three and those with scores greater than three are set to three. The scores are then
recalculated. This process is repeated iteratively until the market-cap-weighted mean of zero and the
standard deviation converge to zeros and one numerically. Thereafter, we linearly combine the standardized scores of the descriptors for the calculation of the factor
exposures. After removing outliers and winsorizing, we re-standardize each factor exposure to have a
market-cap-weighted mean of zero and unit standard deviation. This completes the standardization process.
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The formula for standardization is:
where Xnk denotes the nth security’s exposure towards factor k , and wn denotes the weight of the nth
security in the underlying universe. Moreover, uk denotes the cross-sectional cap-weighted average of
factor exposure k and sigma the cross-sectional standard deviation of factor exposure k. .
1.2. Binary Factor Exposures
In addition to the aforementioned “style” factors, security’s risk and return are also function of its industry,
currency and country. The matrix of each of these exposures is a set of binary values.
Country: Each security in this universe has a unit exposure to its own country, and 0 exposure to all other
countries.
Sector: In order to calculate the sector exposures, we assign an exposure value of 1 if a security belongs to
the sector and zero to all other sector. Currency: The currency exposures of each security are also binary variable, which equal to one if the share
is denominated in that currency and zero otherwise.
2. Factor Returns Estimation
The most general return attribution model can be written as: appreciation of the asset in local currency
and the repatriation of the asset value back to the base currency of the investor:
where xm represents the exposure to source (in our case, factor) m, and gm the return of the source
(factor).
BITA’s approach to multi-currency attribution starts with the decomposition of asset returns into these
fundamental sources. Once decomposed, the components can be aggregated to the portfolio level and
attributed separately. As a concrete example, consider an investment in a stock from the point of view of a US portfolio manager.
Let
denote the local return of asset in currency .. If currency appreciates by an amount relative
to the numeraire, then the base return of the asset is given by the standard formula:
(1)
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The cross-term is typically minute and can be safely ignored for risk purposes. The exchange-rate return
depends on the fluctuations of the sport rate over the investment horizon. The exchange rate return of
currency k from time to is given by:
(2)
where Sk(tf) is the spot price in base currency of one unit of currency at time .
Omitting the cross term, and using the equation (1), the base return can be decomposed in an equity
component and a currency component:
(3)
The equity component is the local return of the stock, for which we adopt a multi-factor framework. More
specifically, we propose that the local returns are driven by a relatively small number
of global equity
factors, plus an idiosyncratic component unique to the particular stock,
(4)
Here,
represents the local return of the nth security,
the exposure of the nth security to
towards factor ,
the return of the factor , and un given by the residuals of the cross-sectional
regression, the specific return. The factor exposures are known at the start of each period, and the factor
returns are estimated via cross-sectional regression.
Suppose that there are
currencies in the model. Ordering the currencies after the equity factors, we can
express the currency returns as:
(5)
Where
is the exposure of stock nto currency k, and
is the return of the currency with
respect to US dollar. We take the currency exposures xnk to be equal to 1 if k corresponds to the local
currency of stock , and 0 otherwise.
Combining equations (3), (4), and (5), we obtain
Where K=KE+KC
is the total number of combined equity and currency factors.
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The factor returns over the period are obtained via a cross-sectional regression of asset excess returns on
their associated factor exposures. We estimate the factor returns on a daily basis using the following
multi-factor fundamental model:
With the following constraints to avoid collinearity between the country and sector factors and the common
factor:
where w_{i,t}E_i^is the cap weight of each stock of the estimation universe in country c, and w_{i,t}E_i^{is the
corresponding weight in sector ..These constraints remove the exact collinearities from the factor exposure
matrix, without reducing the explanatory power of the model.
Given the security exposures are given, we run a weighted least squares model to get the factor returns
daily. The model uses regression weights proportional to the square root of market capitalization.
Finally, the resulting factor returns are robust estimates which can be used to calculate a factor covariance
matrix to be used in the remaining model estimation steps.
We do not mean to convey any sense of causality in this model structure. The factors may or may not be the
basic driving forces for security returns. In our view, they are merely dimensions along which to analyze risk.
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3. Risk Estimation
Factor and specific contributions can be rolled up to the portfolio level. That is, the portfolio active return
can be defined as:
where x_k^ represents the active exposure of factor k., and w_n the active weight.
Following the X-Sigma-Rho framework, we calculate the corresponding risk of the portfolio using the
following formula:
where \sigm iis the factor volatility, \rho(f_k,Ris the correlation between the factor return and the active
return, \sigmais the specific volatility of stock n, and \rho(u_n,Ris the correlation between the specific return
and the active portfolio. The first sum is the total risk due to factors, while the second sum gives the total
specific risk contribution.
We set a rolling window of 30 days in order to forecast risk, that is, every day we calculate volatilities and
correlations over a 30 days period. The factor contribution to risk is then calculated as:
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BITA’s Equity Risk Model is a tool to help investors understand and manage the risk in diversified global
investment strategies. We use classical techniques in finance to compute risk exposures to each relevant
factor for global equities. The risk model factors loadings and factor returns are fully available, for free,
within the BITACore environment. Further research is to come on common factors that could be useful in
international markets.
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Ang, A., R. Hodrick, Y. Xing, and X. Zhang (2006). “The cross-section of volatility and expected returns,” The
Journal of Finance, 61(1), 259–299.
Axioma, Inc. (2011) Axioma Robust Risk Model Handbook. Axioma, Inc.
Carhart, M. M. (1997). “On Persistence in Mutual Fund Performance". The Journal of Finance. 52 (1): 57–82
Fama, E., and R. French, (1992). “The Cross-Section of Expected Stock Returns,” Journal of Finance, 47(2),
427-465.
Fama, E., and R. French. (1993). “Common risk factors in the returns on stocks and bonds,” Journal of
Financial Economics 3-56.
Grinold, R., and R. Kahn, (2000). “Active Portfolio Management,” New York, NY: McGraw Hill.
Litzenberger, R. H. and K. Ramaswamy, (1979, “Tbe effects of personal taxes and dividends on capital asset
prices: tbeory and empirical evidence,” Journal of Financial Economics, 7,163-195
Menchero, J., Morozov, A., and P. Shepard, (2010). “Global Equity Risk Modeling,” in J. Guerard, Ed., The
Handbook of Portfolio Construction: Contemporary Applications of Markowitz Techniques, Springer.
Menchero, J., (2010). “Characteristics of Factor Portfolios,” MSCI Barra Research Insight. MSCI Barra
Fundamental Data Methodology Handbook, 2008.
Ross, S. A. (1976). "The Arbitrage Theory of Capital Asset Pricing." Journal of Economic Theory 341-360.
Sharpe, W. F. (1964). “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The
Journal of Finance 425-442.
Sloan, R., (1996) “Do stock prices fully reflect information in accruals and cash flows about future earnings?
The Accounting Review 71, 289-315.
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whitepaper or concepts:
BITA GmbH
Karlstrasse 12, Frankfurt am Main,
Hessen 60329 - Germany
info@bitadata.com