(9/29/2013 Update: The American Association of Individual Investors created test portfolios of the Cornerstone Growth and Value strategy described in this book and of several best strategies from O’Shaughnessy’s newest book on formula investing (entitled Predicting the Markets of Tomorrow: A Contrarian Investment Strategy for the Next Twenty Years). The test-portfolio returns are published free of charge in the AAII.com stock screens web site.)

## Introduction

Author James O’Shaughnessy tested a variety of strategies for investing in stocks with the use of numerical models. His winning strategies outperformed both the broad U.S. stock market and Standard & Poor’s 500 Stock Index by wide margins.

## Approach

Mr. O’Shaughnessy cited publications from the scientific and financial literature to support the policy of investment-by-formulation rather than investment-by-intuition. Formulation involves the application of stock data to a quantitative model and intuition depends on human judgment. He formulated numerous single-factor and multifactor models of investment, then back-tested the models by analyzing historical returns over 40- or 52-year time periods. The benchmark of performance was one of several stock universes that the author obtained from Compustat’s large database. The universes were categorized according to levels of market capitalization among stocks. The risks and returns of his test portfolios were compared to the appropriate universe.

## Winning strategies

**PERFORMANCE TABLE**

The **PERFORMANCE TABLE **presents a selection of the author’s investment strategies that yielded exceptional returns. Column headings are the labels of 7 investment strategies that were tested over 40 years (white columns) and 52 years (blue columns), both periods ending on 12/31/2003. Notice that the *cornerstone *and *S&P500 *strategies were tested in both periods. Row headings are the labels of 4 statistics commonly used to describe the risk-return performance of investment portfolios. Cells contain numerical *spreads*. Each *spread* is the difference in statistical results between an investment strategy and the *All Stocks* universe (described in the Appendix). For example, a *spread* of 0 would mean that the outcomes of the strategy and universe are identical.

The spreads in the **PERFORMANCE TABLE** provide a comparison of exceptional strategies to the *All Stocks Universe*. **CAGR spread: **Compound annual growth rate (CAGR or geometric mean) is a statistic for the annualized growth rate of the portfolio’s market value. Positive spreads show the desired result, namely that the strategy outperformed the universe. All strategies outperformed the universe except the *S&P500*, which performed worse than the universe. **Std Deviation spread**: The standard (Std) deviation is used to evaluate an investment’s risk, which is the chance that an investment unexpectedly increases or decreases in value. A larger standard deviation implies a greater scatter of portfolio values over the time period of analysis. In the performance table, a positive std deviation spread infers that investing according to strategy is riskier than investing in a representative sample of the universe. All strategies except the *S&P500* were riskier than the universe. **Downside risk spread**: Downside risk is the chance that the investment’s market value will decline. In the performance table, the desired result is a negative downside risk spread. The *S&P500* and *mending values(tri-ratio)* had lower downside risks than the universe. Investors who are risk averse might consider using these strategies. **Sharpe Ratio spread**: Sharpe ratio is a statistic that relates investment return (numerator) to investment risk (denominator). In the performance table, the desired result is a positive Sharpe ratio spread. All strategies except the *S&P500* outperformed the universe.

Here’s a description of exceptional strategies listed in the performance table:

*Cornerstone improved*(book table 20-7), a strategy tested over 40 years while the portfolio is rebalanced at monthly intervals to account for stocks with a monthly depreciation of price. The strategy selected 50 stocks from the*All Stocks Universe*(described in the Appendix of this article) with the best 1-year price appreciation among stocks with market capitalizations exceeding the deflated $200 million value, having a Price-to-Sales ratio (P/S) below 1.5, showing 3- and 6-month price appreciations above average, and showing a 12-month increase in earnings-per-share (EPS). The selected stocks were equally weighted. [notes: Multifactor strategies might reduce risk and increase return. Betting on price momentum supports the theory that stock prices have “memory” and opposes the claim that past price performance cannot predict future price performance.]*Mending small value*(book table 18-3), a strategy tested over 40 years while the portfolio was rebalanced at monthly intervals. The strategy selected 50 stocks from the*All Stocks Universe*with the best 3-, 6-, & 12-month price appreciations coupled with a low P/S from the sub-universe of small stocks. The small stocks had market capitalizations above the inflation-adjusted value of $185 million USD and below the database average. The selected stocks were equally weighted.*Cornerstone*, a strategy tested over 52 years (book table 20-1) and 40 years (book table 20-7) while the portfolio was rebalanced at yearly or monthly intervals. The strategy selected 50 stocks from the*All Stocks Universe*with the best 1-year price appreciation among stocks with market-capitalizations above $200 million USD, P/S ratios below 1, and 12-month increase in EPS. The selected stocks were equally weighted. [note: A side-benefit of annual rebalancing is the lower tax rate on annual capital gains compared to monthly capital gains.]*S&P500*(book tables 4-1, 17-2), an index of 500 U.S. stocks with the largest market capitalizations exclusive of foreign stocks traded in U.S. stock exchanges. The test portfolio was weighted according to the market capitalization of the stocks.*Mending value(tri-ratio)*(book table 16-4), a strategy tested over 52 years while the portfolio was rebalanced at yearly intervals. The strategy selected 50 stocks from the*All Stocks Universe*with the best 1-year price appreciation among stocks pre-screened for desired ranges of low price-to-earnings ratio (P/E), low price-to-book ratio (P/B), and low P/S. The selected stocks were equally weighted. [notes: The author found that investing in bargain, single-value factors (i.e., low P/E, low P/B, low P/S, or low P/C) provided superior returns among several universes (i.e., all stocks, large stocks, small stocks, market leaders) whether using monthly or annually rebalanced test portfolios. The disadvantage of using single-value factors was volatility, which makes it difficult for “jittery investors” to sustain the strategy in real time with real money. “Jittery investors” tend to prefer index funds.]*Mending value(P/B)*(book table 16-1), a strategy tested over 52 years while the portfolio was rebalanced at yearly intervals. The strategy selected 50 stocks from the*All Stocks Universe*with the best 1-year price appreciation among stocks screened for P/B below 1. The selected stocks were equally weighted.*Mending value(P/S)*(book table 16-2), a strategy tested over 52 years while the portfolio was rebalanced at yearly intervals. The strategy selected 50 stocks from the*All Stocks Universe*with the best 1-year price appreciation among stocks screened for P/S below 1. The selected stocks were equally weighted.

## Summary of the author’s strategies

The data published by author James O’Shaughnessy are re-plotted in the following chart to show that the Sharpe ratio is a predictor of long-term return. The Sharpe ratio is the difference between a portfolio’s rate of return and that of a risk-free investment, such as the 10-year U.S. Treasury bond, divided by the standard deviation of the portfolio’s return. The result is an expression of the portfolio’s risk-adjusted return, in which a high ratio is the desired value.

**Chart. Outcomes of the back-tests.**

The chart’s X axis, labeled *relative Sharpe Ratio*, displays values for the quotient of a test portfolio’s Sharpe ratio divided by the Sharpe ratio of the benchmark universe. X >1 is the domain for portfolios with Sharpe ratios exceeding (better than) the universe. The Y axis, labeled *relative Return*, displays values for the quotient of the final market value of the test portfolio divided by the final market value of the universe. Y >1 is the range for test portfolios with higher (better) investment outcomes than the universe. The dashed line in the chart represents the best fit of all data to the exponential equation Y = ae^{bX}. A regression analysis provided the values of a = 0.0144 and b = 4.309 for the equation, and R^{2} = 80.2% for the ‘predictability’ of the equation. The data-point markers are black triangles for all back-tested portfolios except blue dots for the winning portfolios and yellow squares for the S&P500 Index. The winning portfolios and S&P500 Index were discussed in the preceding table of this article

## Conclusions

This is a book about picking stocks that yield high returns. It was written to provide useful information for household and institutional investors. Due to the book’s vast number of statistics, the more appropriate audience is the institutional investor who manages stock portfolios for clients. The author’s winning strategies are based on historical data reviewed over 40-52 year time periods. Readers should be cautioned that applying the winning strategies to 5-10 year time periods might not achieve the same fantastic results.

### What Works on Wall Street, A Guide to the Best Performing Investment Strategies of All Time. Third Edition. James P. O’Shaughnessy. McGraw-Hill, New York, 2005.

## Appendix

**All Stocks Universe table**

Legend: The* All Stocks Universe* (book tables 16-2, 17-2) was comprised of stocks in the Standard & Poor’s *Computstat* database with market capitalizations above $185 million USD. Smaller market-capitalized stocks were excluded due to the high risk of illiquidity. *Compustat* is the largest database for the U.S. Stock market