In this Research Insight, we present a framework for evaluating the relative accuracy of beta forecasts. We consider naive betas, historical betas, and predicted betas. Our technique relies on observing the residual returns of a large universe of stocks over various time periods. We find that the expected residual volatility decreases as the beta estimates become more accurate. We also demonstrate residual volatilities can be translated into beta estimation errors. We find that across the...

In this Global Market Report, we examine the latest developments in emerging markets through the lens of the Barra Emerging Markets Equity Model (EMM1), a risk model tailored for this specific investment universe. We examine whether there has been a change recently in the strength of industries and countries. We are also able to gauge how the inclusion of style factors modified the overall picture.

In this Research Insight, we use the Barra Emerging Markets Model (EMM1) and the Barra Global Equity Model (GEM3) to attribute the returns of a representative set of emerging market portfolios.  We show that by aligning the estimation universe with the investment universe, the EMM1 model provides a more accurate and meaningful description of emerging market portfolios.

In this Research Insight, we present a methodology for efficiently combining multiple sources of alpha when constructing a portfolio. The first part of our study shows that the most efficient implementation for a single source of alpha is the minimum-volatility factor portfolio, which has the lowest risk for a given level of expected return and, therefore, the maximum expected information ratio.  &In the second part of our study, we examine how to efficiently combine multiple sources...

In this Research Insight, we present a methodology for attributing the predicted beta of an asset or portfolio to an underlying set of factors. This provides investors with important insights into the drivers of predicted beta for a particular portfolio. We also present a technique for decomposing the cross-sectional dispersion of stock-level predicted betas. This analysis provides useful insight into how changing factor volatilities and correlations affect cross-sectional differences in the...

In the MSCI Japan Equity Model (JPE4), we include some well-known Systematic Equity Strategies as risk factors (SES factors, for short). Incorporating these SES factors can help identify and measure risk in investment strategies typically used by fundamental and quantitative managers.  In this paper, we find that models including the SES factors produced more accurate risk forecasts for portfolios tilted toward those investment strategies. Furthermore, for optimized portfolios tilting on...

In this Research Insight, we examine Marginal Contribution to Risk and define two alternative versions of this measure: Marginal Contribution to Active Risk (MCAR), and Marginal Contribution to Tracking Error (MCTE). Since most industry practitioners regard “active risk” and “tracking error” as synonymous, this nomenclature has sometimes generated confusion. In this paper, we explain the similarities and differences between MCAR and MCTE and offer insights from our...

The benchmark misfit effect arises when the policy benchmark and the manager benchmark are not aligned. Unless this effect is specifically modeled, it is not possible to determine how the active risk of an individual manager contributes to the risk of the overall fund. In this Research Insight, we showed how the classic Brinson model could be extended to account for benchmark misfit. We also demonstrated how to properly attribute overall portfolio risk to the active risk from an individual...

In this Europe Market Report, we investigate the relative importance of industries and countries in Developed Europe, using a case study with the EUE4 Model. In particular, we explore whether the recent sovereign-debt crisis had altered the relative importance of these two sets of variables.  We find that since the late 1990s, industries have dominated countries in Developed Europe. As the sovereign-debt crisis unfolded in 2011, the gap between the two narrowed, although countries never...

In this Model Insight, we investigate whether statistical models can capture sources of risk that are missing from a fundamental factor model. We also study whether statistical models are more effective at detecting missing factors during periods of market turmoil.  We conclude that the statistical model effectively identified sources of risk that were missing from a fundamental model. Furthermore, we show that the strength of these missing factors peaked during times of market...

Pure factor portfolios have unit exposure to the particular factor, and zero exposure to all other factors. Such portfolios, however, are not uniquely specified because they depend on the regression weighting scheme used for their construction. In this Research Insight, we investigate the risk and return characteristics of pure factor portfolios under several different regression weighting schemes.

Predicting risk at short horizons requires a delicate balance between two effects. On the one hand, it is best to give more weight to recent observations, as these contain the most relevant data; on the other hand, giving too much weight to recent observations can lead to increases in sampling error. In this paper, we study how to optimally balance these two effects through appropriate model calibration. Central to this challenge is the identification of a reliable measure of risk forecasting...

In this paper, we show how Barra models capture the risk and return characteristics of mid-cap stocks using the Non-Linear Size factor. This factor describes the return difference between mid-cap stocks and the overall market, net other factors. We show that since the global financial crisis of 2008, the impressive performance of global mid-caps was attributed, in large part, to their exposure to Non-Linear Size. Monitoring the exposure to this factor provides investors with a view of...

Global Equity Market Watch is a monthly publication that looks at global equity markets through the lens of the factors in the Barra Global Equity Model (GEM2). In each issue, we examine the various sources of global equity returns and risk - including the World factor, countries, industries, styles, currencies, and stock-specific sources - and monitor returns, volatilities, and correlations for those sources over the trailing 1-12 months. We also examine how the explanatory power and...

The Markowitz mean-variance framework is the foundation of modern portfolio theory. One problem with this approach, however, is how sample covariance matrices tend to underestimate risk. Since the biases of optimized portfolios are closely related to eigenfactor portfolios, we present a methodology for estimating biases in eigenfactor volatilities, and for adjusting the covariance matrix to remove such biases. By removing the biases of the eigenfactors, we remove the biases of optimized...

Research from MSCI’s Jose Menchero was recently published in the Journal of Performance Measurement. This paper provides an intuitive foundation for understanding and interpreting factor models. It shows every factor can be represented by a factor-mimicking portfolio, whose return exactly replicates the payoff to the factor. Pure factors provide a way of placing surgical bets and disentangling the often confounding effects of multi-collinearity.

While performance analysis is typically conducted on a benchmark-relative basis, risk analysis is often presented on an absolute-return basis. This mismatch between sources of risk and return leads to the pitfall that active management decisions cannot be evaluated on a risk-adjusted basis. In particular, usage of absolute return sources in risk attribution may lead to non-intuitive marginal contributions to risk and flagging aggressive positions as risk reducing. These pitfalls can be...

Cross-sectional volatility is given by the standard deviation of a set of asset returns over a single time period.  CSV is critical because it represents the opportunity to outperform a benchmark.  In this Research Insight, we present an exact methodology for decomposing CSV into contributions from individual factors.  Our approach treats countries, industries, and style factors on an equal basis.  We employ our framework to investigate several relevant questions in the...

In this paper we examine three approaches for capturing equity risk premia. In the 'simple' approach, the manager goes long stocks with positive exposure and shorts stocks with negative exposure, but makes no effort to control for other exposures or to minimize risk. In the 'pure' approach, the manager selectively retains only exposure to the desired factor, while hedging all other exposures.  In the 'optimized' approach, the manager constructs the minimum-risk portfolio with unit...

Risk analysis involves gaining deeper insight into the sources of risk, and evaluating whether these risks accurately reflect the views of the portfolio manager. In this paper, we show how to extend standard volatility analytics to shortfall, a measure of extreme risk. Using two examples, we show how shortfall provides a more complete and intuitive picture of risk than value at risk. In two subsequent examples we illustrate the additional perspective offered by analyzing shortfall and...

Brinson sector-based attribution explains active return in terms of intuitive allocation and selection decisions. However, it cannot easily disentangle competing industry and style effects. We introduce a special type of factor model with five defining characteristics that exactly replicates the classic Brinson model. We show that this “Brinson-replicating” factor model easily extends to explain more general types of investment processes. In this extension,...

A key to deeper understanding of factor models lies in the concept of factor-mimicking portfolios, whose returns exactly replicate the payoffs to the factors.  Simple factor portfolios are obtained by considering each factor in isolation, whereas pure factor portfolios are constructed by treating all factors jointly.  In this paper, we derive the holdings of simple factors portfolios for the World factor, as well as for countries, industries, and styles.  We also discuss the...

The two main drivers of global investment performance are local asset returns and currency exchange rate returns. These two sources represent distinct investment decisions, and should be attributed independently, as argued by Singer and Karnosky. This article presents a refined and generalized version of the Singer-Karnosky model  for multi-currency attribution.

This Research Insight introduces a general risk attribution framework known as the x-sigma-rho methodology.  Given any return attribution scheme, this approach attributes the corresponding risk as a product of exposure, volatility, and correlation.  Several examples are provided to illustrate application of the technique.

In this Model Insight, we present the volatilities and cumulative returns for every factor and currency in the GEM2 global equity model.  The analysis period runs from January 1997 through August 2009.

We compare the accuracy of risk forecasts from single-country models and GEM2 for portfolios concentrated in single countries.  We find that single-country models provide more accurate risk forecasts, consistent with intuition.  This demonstrates the importance of local factor structure for modeling intra-market risk.

This document contains research notes for three new Barra single country equity models: the Kuwait Equity Model (KWE1), the Qatar Equity Model (QAE1), and the United Arab Emirates (UAE) Equity Model (AEE1). Assets in these markets are included in the latest version of Barra Integrated Model (BIM207), via these new models. Along with our existing single country models for Bahrain, Oman, and Saudi Arabia, these new models complete our coverage of equities in the six Gulf Cooperation Council...

Quantitative risk management relies on a constellation of tools that are used to analyze portfolio risk. We develop the standard toolkit, which includes betas, risk budgets and correlations, in a general, coherent, mnemonic framework centered around marginal risk contributions. We apply these tools to generate side-by-side analyses of volatility and expected shortfall, which is a measure of average portfolio excess of value-at-risk. We focus on two examples whose importance is highlighted by...

This report introduces the Multiple-Horizon Australia Equity Model, available in two versions, shortterm (AUE3S) and long-term (AUE3L). This model has been constructed explicitly to meet the needs of near-term (several-month) and long-term (annual) investors. Both versions employ daily returns data and account for serial correlations in aggregating daily factor returns to longer horizons. Daily data provide denser and more detailed intra-horizon volatility information than monthly returns...

This document describes the new Barra Global Equity Model, GEM2, and provides an in-depth comparison with the model it replaces, the Global Equity Model (GEM). With GEM, originally released in 1989, Barra pioneered the use of factor models for the forecasting of global equity portfolio risk. In the nearly 20 years since the launch of GEM, changes have occurred that warrant the introduction of a completely new model. These changes fall into two categories.First, additional data sources are...