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Using Statistical-Based Risk Models to Generate Alpha

Feb 17, 2015

By John Guerard, Director of Quantitative Research, McKinley Capital Management, LLC

Expected returns on assets are not completely explained by using only historical means (and standard deviations). One can estimate models of expected return by using earnings expectations data, price momentum variables, and reported financial data. In this analysis, we construct and estimate a global stock selection model by using earnings expectations data, price momentum, and reported financial data for the period from January 1997 to December 2011. Earnings expectations information has been rewarded in the global stocks for the past 15 or so years. We find earnings expectations information to be the primary variable driving global stocks.

There are many approaches to security valuation and the creation of expected returns. One creates portfolios with inputs of expected returns, risk models, and constraints. (The reader is referred to Bloch, Guerard, Markowitz, Todd and Xu (1993) for a general description of the portfolio creation process.) One seeks to select expected returns inputs that are statistically associated with stock returns. We add an earnings forecasting variable, CTEF, and a price momentum variable, PM, to the original Bloch et al. (1993) model to create an Global Expected Returns Model, GLER. We test the GLER model in three levels: 

  1. The correlation coefficient between the strategy and subsequent returns is referred to as the information coefficient, IC.
  2. A complete Markowitz mean-variance efficient frontier to identify potential excess returns.
  3. Employ the Markowitz-Xu (1994) Data Mining Corrections test to reject the null hypothesis that our model returns are not statistically different from a “random” financial model.


EP = [earnings per share]/[price per share] = earnings-price ratio;

BP = [book value per share]/[price per share] = book-price ratio;

CP = [cash flow per share]/[price per share] = cash flow-price ratio;

SP = [net sales per share]/[price per share] = sales-price ratio;

REP = [current EP ratio]/[average EP ratio over the past five years];

RBP = [current BP ratio]/[average BP ratio over the past five years];

RCP = [current CP ratio]/[average CP ratio over the past five years];

RSP = [current SP ratio]/[average SP ratio over the past five years];

CTEF = consensus earnings-per-share I/B/E/S forecast, revisions and breadth,

PM = Price Momentum; and

e = randomly distributed error term.

How does one develop, estimate, and test a global stock selection model? We use the Guerard, Rachev, and Shao (2013) database of Global stocks included on FactSet (hence FSGLER) during the January 1997–December 2011 period. The universe was restricted to global stocks covered by at least two analysts, reducing the number to approximately 7000-8000 stocks. We estimate one-month IC in this analysis. There is strong support for the earnings expectations variables and fundamental variables (particularly earnings and cash flow). An objective examination of the reported ICs, shown in Table 1, leads one to identify CTEF, EP, and CP as leading variables for inclusion in stock selection models.

The consensus earnings forecasting variable, CTEF, dominates the top/bottom (one and three) decile spreads.

Let us examine the use of the Sungard APT model to create monthly portfolios using the GLER stock selection model, the APT world risk model, 150 basis points of transactions cost each way, and 8% monthly turnover for the 1997-2011 time frame. As lambda rises, the expected return of the portfolio rises and the number securities in the portfolio declines.

Guerard, Rachev, and Shao (2013) reported that the portfolio active returns, or excess returns, of 1093 basis points were highly statistically significant (with a t-statistic was 3.85), and was composed of factor contributions (701 basis points, corresponding t-statistic is 3.31) and specific return (391 basis points, with a t-statistic of 2.07) over the 1999-2011 period.

Several practitioners decided to perform a postmortem analysis of the Mean-Variance portfolios, attempted to understand the reasons for the deviation of ex-post performance from ex-ante targets, and used their analysis to suggest enhancements to Markowitz’s original approach. Lee and Stefek (2008) and Saxena and Stubbs (2012) worked on optimization models to “restore” a better relationship between ex-ante and ex-post risk model estimates. We report the effectiveness of the Saxena and Stubbs (2012) Alpha Alignment Factor (AAF) to establish a “better” Markowitz efficient frontier (it is “pushed out”). Moreover, if we use only the earnings forecasting variable, then we report higher Sharpe Ratios and Information Ratios on the CTEF variable than on the GLER model. We use the Axioma Fundamental and Statistical risk models, and the Statistical risk model with a constraint on the number of holdings. In Table 4, we report higher Sharpe Ratios and Information Ratios with the Axioma Statistical risk model than the Axioma fundament risk model. As the Tracking Errors rise, the Sharpe Ratios generally rise. The number of names constraint makes the portfolios more suitable for investment.

Investing with analysts’ expectations, fundamental data, and momentum variables is a good investment strategy over the long-run. Stock selection models often use momentum, analysts’ expectations, and fundamental data. We find additional evidence to support the use of APT and Axioma multi-factor models for portfolio construction and risk control. The anomalies literature can be applied in real-world global portfolio construction.

This research note is based on Guerard, Markowitz, and Xu, entitled Earnings Forecasting in a Global Stock Selection Model and Efficient Portfolio Construction and Management, forthcoming, in the International Journal of Forecasting.

John Guerard at the FactSet Symposium

FactSet is delighted to welcome back John Guerard, Director of Quantitative Research, McKinley Capital Management, to the FactSet Investment Process Symposium, March 29-31, 2015 in Washington D.C.

John's session, Using Statistical-Based Risk Models to Generate Alpha, will expand on the research above, showing that composite model incorporating earnings forecasted acceleration, price momentum, and valuation measures can be effectively used in stock selection models.

View the Symposium agenda and register >>

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