Executive Summary:



Univariate and Multivariate Factor Screens on the US Equity Market

May 1987 through January 2003

January 2003 through March 2004

Joe Kippels

April 27, 2004

Executive Summary:

Univariate and Multivariate factor screens were used to evaluate previous U.S. equity performance. The screens reset on a monthly basis and each stock within the universe was placed in one of ten tiers based on its ranking within the screen. The returns were based on fundamental and technical data with returns being measured on both an equal weighted and value weighted basis. The FACTSET data system was used to perform the screens and the returns referred to in this paper are those given through the FACTSET system.

Data:

The FACTSET system used connects through to the COMPUSTAT Database. The same dates that were run in a previous study by Kevin Stoll and Campbell Harvey were used in this study. These dates are from May 1987 through January 2003. Some data sets were not available dating back to May 1987 and when this was the case all available data was used. Time periods are marked on the results. Additional runs of the data were generated for the full year 2003 through March 2004.

The minimum market value used for the companies in the screens was $500 million kept constant throughout the screen. The only exception to this rule was the screen based on the market capitalization of the companies in the screen. In this screen the minimum market capitalization of the company was $15 million in order to take into account micro cap companies.

The number of eligible companies for the screen increases as time goes by. In 1987 slightly over 500 companies were included in the screen per month while there were close to 2000 companies in 2003. This is partly due to the eligible market cap staying constant through time at $500 million.

Univariate Factors Used:

Earnings Yield - Monthly

Stocks were tiered based on the earnings yield as of month-end for the dates requested. This is calculated as Latest Twelve Months EPS divided by Price, multiplied by 100. The data was lagged by 90 days to account for the amount of time it takes individual companies to disclose earnings to the market.

Return on Average Total Equity

This returns the annual return on average total equity as of the fiscal year-end for the dates requested. This is calculated as Net Income Before Extraordinary Items divided by the one-year average of Total Stockholders Equity, multiplied by 100. The data was lagged by 90 days to account for the amount of time it takes individual companies to disclose earnings to the market.

Earnings Momentum - 1 Year Annual Growth

This is calculated as the Current Earnings Per Share divided by Last Year's Earnings Per Share minus one multiplied by one hundred. The data was lagged by 90 days to account for the amount of time it takes individual companies to disclose earnings to the market.

Price Momentum 3-Year Price Change

This measurement calculates the actual percentage change that has taken place over three years.

Price Momentum 1-Year Price Change

This calculates the actual percentage change that has taken place over one year.

Price Momentum – Monthly Percent Change

This returns the month over month change in price as of month-end for the dates requested. This is calculated by taking the month over month percent change.

Price Momentum – One Year Minus One Month Price Momentum

This ranks stocks based on their one year percentage gain, minus their one month percentage gains. Stocks in the first tier of this category are those whose positive difference between their previous year’s percentage gain and their previous month’s percentage gain is the greatest.

Market Value - Monthly

The tiers are based on the market value as of the month-end. This is calculated as Price multiplied by Common Shares Outstanding. For this specific screen the minimum Market Capitalization was lowered from $500 million to $15 million to be able to capture the returns of small and micro cap companies.

Total Debt as a Percent of Total Equity

The tiers are based on the quarterly total debt as a percent of total equity as of the fiscal quarter-end. This is calculated as the sum of Total Long-Term Debt and Total Short-Term Debt, divided by Total Stockholder's Equity.

Price to Book Value

This returns the price to book ratio as of the month-end. This is calculated as Price divided by Book Value per Share. The stocks are tiered in reverse order, to give values based on book to price, where those stocks with higher book values relative their prices are ranking in the first tiers.

Price to Cash Flow

This is based on the latest twelve months of the quarterly price to cash flow ratio for the fiscal quarter for the dates requested. This is calculated as Price divided by latest twelve months of Net Cash Flow from Operations per Share. The lower the price to cash flow ratio, the closer to the first tier the stock will be.

Dividend Yield

This is the dividend yield as of the month-end for the date(s) requested. This is calculated as the Annualized Dividend Rate divided by Price, multiplied by 100.

Reinvestment Rate - LTM

Stocks are tiered based on the latest twelve months of the quarterly reinvestment rate as of the fiscal quarter-end for the date(s) requested. This is calculated as the sum of the latest four quarters of net income minus the sum of the latest four quarters calculation of common and preferred dividends. The result is divided by stockholders equity.

Multi-Factor Model:

A final screen was performed using 4 factors to determine the tiers. The factors used were: Earnings Yield, Return on Equity, 1 Year minus 1 Month Price Momentum, and Cash Flow Yield. Scoring was as follows:

For Earnings Yield, stocks in the first three tiers were given scores of 3, 2, and 1 respectively and stocks in the last decile were given a score of -2.

For ROE, stocks in the first two tiers were given scores of 2 and 1, and stocks in the last tier received a score of -3.

For 1 Year minus 1 Month Price Momentum, stocks in the first two tiers received a score of 4 and 3, and stocks in the last two tiers received scores of -1 and -3.

For Cash Flow Yield stocks in the first three tiers received scores of 4, 4, and 3 respectively, and stocks in the last tier received a score of -4.

Overview of Findings:

The strongest correlations between univariate factor specific variables and equity performance were found in Cash Flow to Price, Reinvestment Rate, Price Momentum, Return on Equity, and the Earnings Yield. In a portfolio consisting of a long position in the top 10% of stocks relative to the specific variable and a short position in the bottom 10% of stocks relative to the specific variables, monthly alphas relative to the S&P 500 of 1.7, 1.46, 1.14, and .92 were found from the initial dates tested from May 1987 through January 2003.

Alphas and Betas are calculated through FACTSET. The alpha value of each fractile’s constituent is the intercept of the regression line drawn for the S&P500 returns versus those of the fractile. The Beta Value for each fractile’s constituents is the slope of the regression line of the S&P500 returns versus those of the model.

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EARNINGS YIELD

Results indicate that there is a positive correlation to earnings yield and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the earnings yield and short positions in the 10% of stocks with the lowest earnings yield would have given the returns depicted in the graph below.

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Earnings Yield 2003-2004 results

These results have not held constant from January 2003 through March of 2004. Over the 15 months in an equally weighted portfolio stocks in the top 10% of earnings yield have gained a geometric average of 3.95% per month while those in the bottom 10% have gained a geometric average of 5.06%. A similar portfolio during this period would have yielded the following monthly returns:

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RETURN ON EQUITY

Results indicate that there is a positive correlation to Return on Equity and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the greatest Return on Equity and short positions in the 10% of stocks with the worst Return on Equity would have given the returns depicted in the graph below.

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2003-2004 results

These results have not held constant from January 2003 through March of 2004. Over the 15 months, stocks in the top 10% of year over year earnings momentum have gained a geometric average of 2.93% per month in an equally weighted portfolio while those in the bottom 10% have gained a geometric average of 4.41%. A similar portfolio during this period would have yielded the following returns:

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EANINGS MOMENTUM

Results indicate that there is virtually no correlation to earnings momentum and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the greatest year over year percent increases in earnings and short positions in the 10% of stocks with the worst year over year percent increases in earnings would have given the returns depicted in the graph below.

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2003-2004 results

Over the 15 months from January 2003 through March of 2004, stocks in the top 10% of year over year earnings momentum have gained a geometric average of 2.95% per month in an equally weighted portfolio while those in the bottom 10% have gained a geometric average of 3.00%. A portfolio during this period would have yielded the following returns:

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THREE YEAR PRICE MOMENTUM:

Results indicate that there is a slight negative correlation to 3 year movements in the price of a stock and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the greatest percentage gains over a 3 year history and short positions in the 10% of stocks with the worst 3 year percent gains in price would have given the returns depicted in the graph below.

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2003-2004 results

The negative correlations persisted from January 2003 through March of 2004. Over the 15 months stocks in the top 10% of percentage gainers in terms of price have gained a geometric average of 3.17% per month in an equally weighted portfolio while those in the bottom 10% have gained a geometric average of 5.27%. A similar portfolio during this period would have yielded the following monthly returns:

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ONE YEAR PRICE MOMENTUM:

Results indicate that there is a slight positive correlation to the one year price movement in a stock and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the greatest percentage gains over the past year and short positions in the 10% of stocks with the worst one year percent increases (or greatest decreases) in price would have given the returns depicted in the graph below.

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2003-2004 results

The slight positive correlation reversed itself in 2003 and through March of 2004. Over the 15 months stocks in the top 10% of percentage gainers in terms of price have gained a geometric average of 3.41% per month in an equally weighted portfolio while those in the bottom 10% have gained a geometric average of 4.80%. A similar portfolio during this period would have yielded the following returns:

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ONE MONTH PRICE MOMENTUM:

Results indicate that there is very little correlation to 1 month movement in the price of a stock and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the greatest month over month percent increases in price and short positions in the 10% of stocks with the worst month over month percent increases in price would have given the returns depicted in the graph below.

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2003-2004 results

The correlations have been slightly negative from January 2003 through March of 2004. Over the 15 months stocks in the top 10% of percentage gainers in terms of price have gained a geometric average of 3.47% in an equally weighted portfolio per month while those in the bottom 10% have gained a geometric average of 4.17%. A similar portfolio during this period would have yielded the following returns:

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ONE YEAR MINUS ONE MONTH PRICE MOMENTUM:

Results indicate that there is an extremely high correlation to the difference between a stock’s previous year’s gain and its previous month’s gain and positive stock returns. A portfolio consisting of long positions in the 10% of stocks with the greatest positive differences between the previous year and the previous month and short positions in the 10% of stocks with the lowest year minus month percent differences would have given the returns depicted in the graph below.

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2003-2004 results

The positive returns have not held constant from January 2003 through March of 2004. An equally weighted portfolio would have returned a geometric average of 3.38% in the top tier and 4.54% in the bottom tier over the last 15 months.

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MARKET CAPITALIZATION

Results indicate that there is a positive correlation to smaller companies and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the smallest 10% of stocks and short positions in the largest 10% of stocks would have given the returns depicted in the graph below.

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2003-2004 results

These results have been especially strong from January 2003 through March of 2004. An equally weighted portfolio would have yielded an average of 14.79% per month in the top tier and 2.63% per month in the bottom tier over the last 15 months.

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DEBT TO EQUITY

Results indicate that there is a positive correlation to the debt to equity ratio and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the greatest debt to equity ratios and short positions in the 10% of stocks with lowest debt to equity ratios would have given the returns depicted in the graph below.

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2003-2004 results

The positive correlations have not been significant from January 2003 through March of 2004. Over the 15 months stocks in the top 10% of debt to equity values have gained a geometric average of 3.22% per month and 2.63% in the bottom tier while those in the bottom 10% have gained a geometric average of 3.14%. A similar portfolio during this period would have yielded the following returns:

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BOOK TO PRICE RATIO

Results indicate that there is a slight positive correlation with the book to price ratio and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the highest book to price ratios (“value stocks”) and short positions in the 10% of stocks with the lowest book to price ratios would have given the returns depicted in the graph below.

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2003-2004 results

The extra positive return on value stocks has been extremely significant from January 2003 through March of 2004. Over the 15 months stocks in the top 10% of book to equity values have gained a geometric average of 5.25% per month in an equally weighted portfolio while those in the bottom 10% have gained a geometric average of 2.53% per month. A similar portfolio during this period would have yielded the following returns:

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CASH FLOW YIELD

Results indicate that there is a positive correlation with cash flow yield and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the highest cash flow yield and short positions in the 10% of stocks with the lowest cash flow yield would have given the returns depicted in the graph below.

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2003-2004 results

The extra positive return on stocks yielding higher cash flows continued from January 2003 through March of 2004. Over the 15 months the 10% of stocks yielding the highest cash flow gained a geometric average of 4.15% per month while those in the bottom 10% gained a geometric average of 2.74% per month. A similar portfolio during this period would have yielded the following returns:

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DIVIDEND YIELD

Results indicate that historically there has been a slight negative correlation with dividend yield and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the highest dividend yield and short positions in the 10% of stocks with the lowest dividend yield would have given the returns depicted in the graph below:

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2003-2004 results

The negative correlation appears to have reversed itself in the time period from January 2003 through March of 2004. Over the 15 months the 10% of stocks yielding the highest dividend gained a geometric average of 3.61% per month in an equally weighted portfolio while those in the bottom 10% gained a geometric average of 3.08% per month. A similar portfolio during this period would have yielded the following returns:

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REINVESTMENT RATE

Results indicate that there is a positive correlation with reinvestment rates and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the highest reinvestment rate and short positions in the 10% of stocks with the lowest reinvestment rate would have given the returns depicted in the graph below:

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2003-2004 results

The positive correlation appears to have reversed itself in the time period from January 2003 through March of 2004. Over the 15 months the 10% of stocks with the highest reinvestment rate gained a geometric average of 3.27% per month in an equally weighted portfolio while those with reinvestment rates in the bottom 10% gained a geometric average of 4.05% per month. A similar portfolio during this period would have yielded the following returns:

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MULTI-FACTOR MODEL

The Multi-Factor Model Results indicate that there is a very strong correlation between the factors chosen and positive stock returns. An equally weighted market neutral portfolio consisting of long positions in the 10% of stocks with the highest decile rankings rate and short positions in the 10% of stocks with the lowest decile rankings would have given the returns depicted in the graph below:

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The results have not held so strong over the past 15 months. An equally weighted portfolio would have yield a geometric average of 3.81% in the top decile and a strong 4.00% return in the bottom decile. A graph of the month to month returns of a long short portfolio from January 2003 through March 2004 is below.

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Calculations:

Following are the explanations for the calculations behind the data in the fractile summary report calculated in FACTSET for the period-specific fractile report. The summary statistics displayed throughout these reports are the same as the fractile statistics; however, they are calculated for the model's entire universe of companies.

Equal Wgt. Return

In the fractile summary report for all periods, this calculation returns the geometric average of all periods for each fractile. This value is equal to 100 * (the geometric average of (1 + each period’s average return ÷ 100) - 1). In the period-specific fractile report, this value is the arithmetic average return of fractile constituents.

Universe Median Return

This calculation returns the geometric average of each period's median return.

StdDev Return (Standard Deviation Return)

This value is the standard deviation of the fractile return through time.

Residual Risk

This value is equal to the variance of returns for the fractile throughout time less the square of the beta value times the variance of the S&P500 return

Sharpe Ratio

This calculation is equal to (average return - risk free rate) ÷ standard deviation of returns. The Sharpe ratio is a risk-adjusted financial measure, used to determine the reward per unit of risk. The higher the Sharpe ratio, the better the “risk-adjusted” performance.

% > Bench

This calculation is the percentage of periods that outperformed the S&P500.

% > Up Bench

This calculation is the percentage of periods in an up market (S&P500 return greater than zero) that the fractile outperforms the S&P500. This calculation only appears in the fractile summary report.

% > Down Bench

This calculation is the percentage of periods in a down market (S&P500 return less than zero) that the fractile outperforms the S&P500. This calculation only appears in the fractile summary report.

% New Cos

This calculation is the percentage of new companies in the fractile. It is equal to 100 * (the number of companies that are in the current period but not in the immediately previous period)/(total number of companies in period). This calculation only appears in the fractile summary report.

% Old Cos

This calculation is the percentage of old companies not re-appearing in the fractile. It is equal to 100 * (the number of companies that are in the immediately previous period but not the current one)/(total number of companies in the immediately previous period). This calculation only appears in the fractile summary report.

% Total Turnover

This calculation is equal to ((# of companies that exited the old universe) + (# of new companies that entered)) ÷ (total # of companies in the old universe). The blue values display fractile-specific turnover and the red value displays the average turnover for the entire duration of the study.

% Weighted Turnover

This calculation takes the average of all the period-specific % weighted turnover calculations for a specific fractile. To view period-specific % weighted turnover, you need to go to the periods report. The underlining calculation for % weighted turnover is:

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Avg Mcap (Average Market Capitalization)

In the fractile summary report for all periods, this calculation is the arithmetic average of each period's average market value. In the period-specific fractile report, this is the arithmetic average of the constituent market values.

Xs vs. Univ

When using the weighted return, this calculation is each fractile’s return minus the universe’s return. For all other returns (i.e., equal-weighted): this is the geometric average of the differences in period returns for a given fractile.

Std Xs vs. Univ

This calculation is the standard deviation of the excess return vs. the universe return.

Xs vs. Bench

In the fractile summary report, this calculation is the geometric average of each period return minus the S&P500 period return. In the fractile period report, this is the period return minus the S&P500 period return.

Std Xs vs. Bench

This calculation is the standard deviation of the excess return vs. the S&P500 return.

Total Alpha

This calculation returns the alpha value of each fractile’s constituents. The alpha value is the intercept of the regression line drawn for the S&P500’s returns versus those of the fractile.

T-Stat (Alpha)

This calculation is the alpha value ÷ by the standard error of alpha, where n is the number of periods in the model.

(alpha * square root of (n - 2)) ÷ (the standard deviation of (return - (S&P500 * beta)))

Total Beta

This calculation is the beta value for each fractile’s constituents. Beta is the slope of the regression line of the S&P500 returns versus those of the model.

T-Stat (Beta)

This calculation hypothesizes that the population beta = 0.

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The R2 value is the R squared for the regression line (beta). The result will take the same sign as beta.

R Squared for Regression Line (Beta)

This calculation regresses the R2 for the 1st fractile. We regress the return value for the 1st fractile against the return of the S&P500 for the duration of the model.

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rb is the return for the S&P500

rp is the return for the portfolio

IC (F1) Calc (Information Coefficient)

The Information Coefficient (IC) is a Spearman ranked correlation. The IC for any given fractile is computed by taking the mean of that fractile's IC value over each period in the test. The IC value is computed by assigning a rank to all the formula values and a rank to all the returns, and then calculating the correlation coefficient between these two series. As with any correlation coefficient, this value will lie between -1 and +1, where a high positive value indicates that companies with high factor values tend to yield high returns. Negative IC values indicate that high factor values tend to yield low returns. A company must have both a ranking factor value and a subsequent return available to be included in the IC universe for a particular period.

This number is an average of each period's value from the fractile period report.

T-Stat (F1) Corrl. - IC

This value indicates if the found IC (Information Coefficient) is significant based on the number of companies that went into the computation (significant t-scores must be looked up in a t-table). This value is equal to the square root of [(the number of companies in the universe - 2) ÷ (1 - IC × IC)] × IC, where the number of companies in the universe excludes companies that do not have either a factor or subsequent return value. This number is an average of each period's value from the fractile period report.

Factor 1 Average

This calculation is the arithmetic average of constituent company values for the first ranking formula.

Factor 1 Low

This calculation returns the lowest value in the fractile for the first ranking formula.

Factor 1 High

This calculation returns the highest value in the fractile for the first ranking formula.

Factor 1 Median

This calculation returns the median fractile value in the fractile for the first ranking formula.

Factor 1 Std Dev

This calculation returns the standard deviation of the arithmetic average for each fractile for the first ranking formula.

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