# Global Earnings Forecasting Efficiency

#### August 1, 2010

*Abstract/Overview*

*Designing equity investment portfolios by modeling momentum and earnings expectation data is believed to be a viable strategy that will outperform the market. We put that belief to the test in this study which addresses several aspects of selecting equity securities in risk optimized portfolios. McKinley Capital’s research and analysis revealed continued support for composite modeling using these sources of data from 1998-2009. *

*Momentum and analysts’ forecasts are used to create mean-variance and equally active weighted portfolios for U.S., Non-U.S., and global stock markets during the 1998-2009 period. Knowledge of earnings forecasts, revisions, and breadth is an important consideration to the stock selection and portfolio construction process. Momentum has long been associated with excess returns in stock selection models. Analysts’ earnings per share forecasts, their revisions, and breadth are all associated with excess returns. The combination of analysts’ revisions and price momentum is explored in this analysis. *

*Section I explores the notion that individual investors demand compensation for bearing risk, so the risk of a security should be directly linked to its rate of return. Investors will either secure the maximum return for a given level of risk, or the minimum risk for a given level of return. The concept of risk-return analysis is known as the Efficient Frontier. In this analysis we create portfolios using a statistically-based principal component analysis model and attribute portfolio excess returns according to a fundamentally-based multi-factor risk model. *

*Section II explores the benefits of combining fundamental value-based factors with momentum investing. Investing in portfolios based on price-to-earnings began in the 1930’s and evolved over the years with the availability of data through the use of better technology. The result is the ability to predict how price and earnings move together by using equity analysts’ forecasted earnings yield, earnings revisions, and breadth. Combining this with a price momentum variable with the optimal look-back time frame creates a more efficient portfolio i.e., a better risk/return trade-off. *

*Section III highlights the benefits of actively weighting a portfolio equally as opposed to pure optimization. This is known as equal active weighting (EAW). We conclude that investing with equity analysts’ earnings expectations data and momentum variables is a good investment strategy over the long term.*

♦ As presented by Dr. John B. Guerard, Jr., Director of Research, McKinley Capital Management LLC, at the 30th International Symposium on Forecasting, June 20-22, 2010, San Diego, CA.

**I: Understanding Risk and Portfolio Construction**

The Efficient Frontier portfolio construction approach endeavors to identify the point at which returns are maximized for a given level of risk, or risk is minimized for a given level of return. The portfolio expected return, E(Rp), is calculated by taking the sum of the security weights multiplied by their respective expected returns (See Formula 1, page 17).

The portfolio standard deviation is the sum of the weighted covariances (See Formula 2, page 17). The risk of a portfolio is measured as standard deviation, which is a measure of dispersion. Investors seek to minimize total risk with the assumption that expected returns are held constant. Implicit in the development of the Capital Asset Pricing Model (CAPM) is that investors are compensated for bearing market risk, or systematic risk, as measured by a stock’s beta. Systematic risk cannot be diversified away, as opposed to firm-specific risk, or unsystematic risk. An investor is not compensated for bearing risk that may be diversified away from the portfolio. The beta is the slope of the market model in which the stock return is regressed as a function of the market return. The CAPM holds that the return of a security is a function of the security’s beta (See Formula 3, page 17). The estimation of the CAPM beta (the measure of systematic risk) involves an ordinary least squares regression of the form (See Formula 4, page 17). The security beta is the linear relationship between the security return and market return. The difficulty of measuring beta and its corresponding security market line gives rise to extra market measures of risk.

**Barra Model Origin**

The Barra risk model is the industry standard for multifactor risk modeling (See Formulas 5 and 6, page 17). From 1966 to 1974 the industry saw a move towards this standard with the multifactor modeling of industries. Security returns were analyzed by estimating the covariance matrix of security total returns. The Barra risk model addressed the sources of co-movement in security returns. The covariance matrix was decomposed into the variances of security specific returns and estimates of common sources of variation.

As a multifactor model (MFM), the Barra risk model builds on single-factor models by including and describing the interrelationships among factors or characteristics. Following are the financial characteristics statistically associated with beta between 1954 and 1970:

• Latest annual proportional change in earnings per share

• Liquidity, as measured by the quick ratio

• Leverage, as measured by the senior debt-to-total assets ratio

• Growth measure of earnings per share

• Book-to-price ratio

• Historic beta

• Logarithm of stock price

• Standard deviation of earnings per share growth

• Gross plant per dollar of total assets

• Share turnover

In 1974 security specific risk was modeled as a function of financial descriptors, or known financial characteristics of the firm. This work was expanded upon in the late 1970’s with the following thirteen sources of factor, or systematic exposures we use today:

• Volatility

• Momentum

• Size

• Size non-linearity

• Trading activity

• Growth

• Earnings yield

• Value

• Earnings variation

• Leverage

• Currency sensitivity

• Dividend yield

• Non-estimation universe

**II: Expected Returns Modeling and Stock Selection
**

Expected, or future, returns on assets are not completely explained by only using historical mean returns and standard deviations of markets. Practitioners have traditionally used additional inputs such as reported financial data, momentum data, and earnings expectations data to estimate stock selection models and expected returns for individual securities. The earliest approaches to security analysis and stock selection involved the use of valuation techniques using reported earnings and other financial data. Strategies that purchase stocks on the basis of a low price-earnings (P/E) ratio have been studied since 1934. Evidence also exists that taking this strategy a step further by using other fundamental variables, such as book value, cash flow, and sales, enhances returns. The fundamental ratios can be divided by their five-year average of monthly ratios to create respective relative variables that further enhance the ability to choose a given company’s shares that will outperform. Please note that value-based strategies are not considered in this analysis.

**E ‘
**

Earnings forecasting enhances returns relative to using only reported financial data and valuation ratios. In 1975, a database of earnings per share (EPS) forecasts was created by a New York brokerage firm, called Lynch, Jones & Ryan, by collecting and publishing the consensus statistics of one-year and two-year EPS forecasts. The database evolved to become known as the Institutional Brokerage Estimation Service (I/B/E/S) database. There is extensive literature regarding the effectiveness of analysts’ earnings forecasts, earnings revisions, earnings forecast variability, and breadth of earnings forecast revisions, which finds that the use of earnings forecasts do not increase stockholder wealth. This is especially true given that reported earnings follow a random walk with a drift process, where analysts are rarely more accurate than a no-change model in forecasting earnings per share. Studies show that analysts become more accurate as time passes during the year as quarterly data is reported, thus causing analyst revisions to be statistically correlated with stockholder returns during any given year. In 1994, a strategy was developed that resulted in statistically significant excess returns known as the breadth strategy which is defined as the number of upward analyst forecast revisions less the number of downward forecast revisions, divided by the total number of estimates. Accordingly, McKinley Capital uses a composite earnings variable (E ) which is calculated using equally-weighted revisions, forecasted earnings yields, and breadth of one-year and two-year earnings forecasts.

Studies show that adding I/B/E/S variables to value ratios produces more than 2.5 percent of additional annualized return. The finding of significant predictive performance value for I/B/E/S variables indicates that analyst forecast information has value beyond purely statistical extrapolation of past value and growth measures. Possible reasons for the additional performance benefit could be that analysts’ forecasts and forecast revisions reflect information in other return-pertinent variables, reflect discontinuities from past data, or serve as a quality screen on otherwise out-of-favor stocks. The quality screen idea would confirm the argument that value ratios should be used in the context of the many qualitative and quantitative factors that arguably are essential to informed investing. To test the risk-corrected performance value of the forecasts, a 1997 study formed quarterly portfolios with risk calculated using a four-factor Arbitrage Pricing Theory (APT) model (created using five years of past monthly data). The portfolios’ quarterly returns averaged 6.18 percent before correcting for risks and transaction costs with excess returns of 3.6 percent after correcting for risk and 2.6 percent quarterly after subtracting 100 basis points to reflect an estimate of two-way transactions costs.

**PM**

Momentum investing was studied by academics at about the same time that earnings forecasting studies were being published. Several studies found that the short-term (three-month) financial predictability of a naïve monthly price momentum model was as statistically significant in identifying under-priced securities as using the alpha of the market model adjusted for the security beta. Thus beta adjustments slightly enhanced the predictive power in the six to twelve month periods. The vast majority of the studies conducted on momentum in the 1990s and 2000s found that the use of three, six, and twelve month price momentum variables, often defined as intermediate term variables, are statistically significant and associated with excess returns. Further, the quarterly information coefficient (IC) of the three-month price momentum variable exceeds its monthly IC, .073 versus .053. A stock selection model (MQ) which combined momentum (PM) and analysts’ forecasts, revisions, and breadth, denoted CTEF (defined initially as the consensus earnings forecasting effectiveness measure), and often referred to as E in a composite model. One of the differences in this analysis is that the price momentum variable was separated into distinct price momentum and standard deviation variables and produce an enhanced (proprietary) MQ model, denoted MQS. The MQS variable is McKinley Capital’s proprietary model composed of a price momentum variable, PM, defined as the price one-month ago divided by the price seven-months ago, E’, and the stock standard deviation.

**III. Efficient Portfolio Construction**

The MQS model results can be input into the APT system to create optimized portfolios. By varying the tolerance or risk-aversion, or lambda, the efficient frontier is created. The MQ model is McKinley Capital’s approximation of the expected return, or the forecast active return, α, of the portfolio. Industry researchers typically apply the mean/variance framework to active management.

Here α is the forecast active return (relative to a benchmark which can be cash), ω is the active risk, and h is the active holding (the holding relative to the benchmark holding). The Efficient Frontier can be created in the APT model by varying the lambda (λ), which captures the risk aversion parameter individual investor preference (See Formula 7, page 17). There are several criteria to be used in portfolio construction. As a portfolio construction objective, the geometric mean, Sharpe Ratio, and information ratio (IR) is to be maximized. IR is a measurement of residual return to residual risk (See Formula 8, page 17).

*In this analysis, we created portfolios that maximize the geometric mean, Sharpe Ratio, and information ratio.*

McKinley Capital constructed an Equal Active Weighting (EAW) Efficient Frontier varying the risk-aversion levels. The EAW process allows security weights in the portfolio to deviate no more than two percent from the benchmark weights, a process based on Markowitz’s Enhanced Index Tracking procedure. The portfolio construction process uses eight percent monthly turnover, after the initial portfolio is created, and 150 basis points of transactions costs each way. The MQS optimized portfolios outperform the U.S. market (Russell 3000 Growth [R3G] Index) and the Global Market (Morgan Stanley Capital International [MSCI] All Country World Growth [ACWG] Index) (See Chart 1). *(The Global Market includes the U.S. Growth and MSCI Europe, Australasia, Far East (EAFE) Growth Index securities.)*

The inefficiencies of the international and global markets, relative to the U.S. market, are illustrated in Chart 1 in the increased returns relative to the risk of investing in other markets. In Chart 1, the “B” denotes the universe benchmark.

The analyst-covered stocks in the U.S. market are ranked on monthly MQS-based criteria from January 1998 – December 2009. The sources of the MQS enhanced excess returns are exposures to size (buying smaller-capitalized securities), earnings yield, financial leverage, value, momentum risk indexes, and asset selection (See Tables 1 and 2). Asset selection is statistically significant at the 10 percent level in the Russell 3000 Growth universe for the 1998-2009 time period for a lambda of 500 estimation.

The analyst-covered stocks in the Global market are ranked on monthly MQS-based criteria from January 1998 – December 2009. The sources of the MQS enhanced excess returns are exposures to size (buying smaller-capitalized securities), success and value risk indexes, and asset selection (See Tables 3 and 4) for a lambda of 500 estimation.

(* McKinley Capital is aware of the Menchero et. al. (2010) GEM2 Model introduced in 2009 to create global portfolios and access global performance. The attribution model, used in Tables 3 and 4, was the MSCI Barra Global Equity Model, GEM model, because the GEM model existed at the time the McKinley Capital global portfolio management and research was conducted.*)

Efficient Frontier is estimated by varying the lambda, the measure of risk-aversion. As lambda increases, so does the riskiness of the portfolio. In the case of the MQS variable, smaller-capitalized stocks tend to produce potentially higher asset selection and total returns. The smaller stocks have more exposures to momentum (success in the Barra GEM model). The lambda = 500 portfolios maximize the geometric mean, asset selection, and total active return, in the MQS variable in domestic and global universes.

Asset selection of the MQS model is statistically significant at the five percent level in the ACWG universe in the January 1998 – December 2009 time period and exceeds the asset selection of the MQS model in the R3G universe. Global markets have historically been more inefficient than the U.S. markets.

In summary, the MQS selection model produces asset selection of 269 basis points (statistically-significant at the 10 percent level) in the U.S. market and 590 basis points in the Global market (statistically-significant at the 5 percent level). During the November 2000- December 2009 time period, Emerging Markets (EM) became an investable universe for many investors and EM expanded the riskreturn trade-off of McKinley Capital investors. In Chart 2, the “B” denotes the universe benchmark.

**Conclusions**

Investments with a strategy that utilizes a combination of earnings expectations data and momentum variables is a good investment strategy over the long term. Additional evidence supports the use of multifactor models for portfolio construction and risk control. Support exists for the use of tracking error in risk estimation procedures. While perfection cannot be achieved in portfolio creation and modeling, the MQ and MQS processes pass a data mining corrections test.

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**DISCLAIMER STATEMENT**

All information contained herein is believed to be acquired from reliable sources but accuracy cannot be guaranteed. This presentation is for informational purposes only, was prepared for academics and financially sophisticated and institutional audiences, and is not intended to represent specific financial services or recommendations for any targeted investment purposes. McKinley Capital Management, LLC (“McKinley Capital”) is a registered investment adviser under the Securities and Exchange Commission Investment Advisers Act of 1940. This material may contain confidential and/or proprietary information and may only be relied upon for this report. The data is unaudited and may not correspond to calculated performance for any specific client or investor in referenced disciplines. McKinley Capital, nor its employees, makes any representations or warranties as to the appropriateness or merit of this analysis for individual use. Investors must seek individualized professional financial advice before investing.

Investments and commentary were based on information available at the time and are subject to change without notice. Any references to specific indexes or securities are for informational purposes only, may or may not have been owned by McKinley Capital in the past, may or may not be owned by McKinley Capital in the future and may or may not be profitable. UNo single security, discipline, or process is profitable all of the time and there is always the potential for loss. Past performance is not indicative of future returns.

All returns are gross of investment management fees, broker commissions, taxes, and all other fees, costs and expenses associated with client account trading and custodial services, and therefore individual returns may be materially negatively affected. Returns do include the reinvestment of gains, dividends and other income. Global investing also carries additional risks and/or costs including but not limited to, political, economic, financial market, currency exchange, liquidity, accounting, and trading capability risks. Shorting and derivatives may materially increase overall risk and costs which could negatively affect returns. McKinley Capital’s proprietary investment process considers accompanying factors such as additional guidelines, restrictions, weightings, allocations, and market conditions. Thus, returns may at times materially differ from the stated benchmark. Future investments may be made under different economic conditions, in different securities and using different investment strategies.

Charts, graphs and other visual presentations and text information are provided for illustrative purposes, derived from internal, proprietary, and/or service vendor technology sources and/or may have been extracted from other firm data bases. As a result, the tabulation of certain reports may not precisely match other published data. Certain data may have originated from various third-party, and/or sources including but not limited to Bloomberg, FactSet, Clarifi, MSCI/Barra, Russell, FTSE, broker research, and/or other systems and programs. Neither McKinley Capital nor its employees may use and/or rely on specific index names, other financial data and certain analysis without the infringement of copyright materials. However, recipients of this information may not assume those same rights are transferrable. With regards to any materials accredited to MSCI/Barra: Neither MSCI nor any other party involved in or related to compiling, computing or creating the MSCI data makes any express or implied warranties or representations with respect to such data (or the results to be obtained by the use thereof), and all such parties hereby expressly disclaim all warranties of originality, accuracy, completeness, merchantability or fitness for a particular purpose with respect to any of such data. Without limiting any of the foregoing, in no event shall MSCI, any of its affiliates or any third party involved in or related to compiling, computing or creating the data have any liability for any direct, indirect, special, punitive, consequential or any other damages (including lost profits) even if notified of the possibility of such damages. No further distribution or dissemination of the MSCI data is permitted without MSCI’s express written consent. Please refer to the specific service provider’s website for complete details on all indices.

A list of referenced sources is included at the end of the presentation for additional details and information. McKinley Capital makes no representation or endorsement concerning the accuracy or proprietary of information received from any other third party. To receive a copy of the McKinley Capital Form ADV Part II, please contact the firm at 3301 C Street, Suite 500, Anchorage, Alaska 99503, 1.907.563.4488 or visit the firm’s website at HUwww.mckinleycapital.comUH to request one.