In comparison with the USA there have been relatively few studies conducted on what works in investing in the European stock markets. With this paper we would like to make a contribution and examine what factors led to excess returns in the European markets over the 12-year period from 13 June 1999 to 13 June 2011. The factors we tested were:

- Earnings yield
- Free cash flow yield
- Price-to-book
- Price-to-sales
- Piotroski F-score
- Return on invested capital (ROIC)
- Return on assets (ROA)
- Net debt on Market Cap
- Relative strength / price index

We didn't only test the historical value of the factors, but where it made sense, we also tested the 5-year average to see if it is a better indicator to use to generate market outperformance. When we found a factor that showed strong out-performance we tested it together with other factors to see if two factors generate even more market outperformance. In addition, we also tested two investment strategies, the Magic Formula and the ERP5 strategy, for their ability to outperform the market. What we found mostly confirmed what other research studies found, but a few results were really astounding.

If we averaged the return over large, medium and small companies, the best factor was the price-to-book ratio, generating an average compound annual return of 10.92% compared with 2.25% for the market over the period. The second best average factor was the 12 month free cash flow yield that generated a compound annual return of 10,87%.

For small companies the best single factor was the 6-month price index which generated a compound annual return of 11.91%. The second best factor was the 12-month price index, generating a return of 10.32%.

For medium sized companies the best factor was price-to-book value, which generated an astounding compound return of 14.36% over the period. Second was the five year average free cash flow, generating a compound 12,83%.

For large companies the best factor was free cash flow yield, leading to compound growth of 10.81%, with earnings yield a close second with a compound return of 10.64%.

Interesting to note is that with small companies, unlike with medium and large companies, valuation factors did not lead to the best returns.

Of the two investment strategies we tested, the ERP5 strategy beat the Magic Formula for small (compound 12.95% compared with 7.33%), medium (compound 11.76% compared with 9.05%) and large companies (compound 8.60% compared with 8.39%).

What if we told you we found a simple two factor method you can use to select investments that led to a 23.5% per year compound return (market was 2.25%) over the 12 years we tested? That is a total return of 1157.5% compared with the 30.54% the market returned! That is what a combination of the 6-month price index with the lowest price-to-book value companies returned. Very interesting was that the 10 best performing two-factor strategies all had one momentum factor as one of the factors.

This was hard for us to fully grasp as classical value investors. We always thought buying a cheap, good company would give you market beating results. And the cheaper the company gets, the higher your returns would be. This strategy will give you market beating results, but not nearly as good as buying companies where the share prices are already increasing.

For example, the 11th best performing two-factor strategy, 12 month free cash flow yield combined with price-to-book ratio, led to a total return of 713.7%. Not bad. But if you used the best performing strategy, your return would have been 11.57 times your initial capital compared with only 7.13 times if you used the 11th best strategy!

This paper examines which historical value factors or financial ratios have the highest probability of consistently outperforming the market.

Considerable research has documented the use of individual ratios or combinations to create portfolios that outperform the market. One factor that received a lot of attention in the past is the book-to-market investment strategy. Studies by Lakonishok, Shleifer and Vishny (1994) and Fama and French (1992) have demonstrated that buying a portfolio of high book-to-market (low price-to-book ratio) companies results in market outperformance. Joseph Piotroski (2000) extended this research by creating his own Piotroski F-score; an accounting based 9-point scoring system that when used in combination with high book-to-market (low price to book) companies shows a consistent upward shift in distribution of returns.

Other authors focused on different ratios. Joel Greenblatt focused on earnings yield and ROIC, and found that ranking US companies based on these measures and investing on a consistent basis in the top companies resulted in an outperformance of 23% compared with the benchmark. In our previous papers, we concluded that these results can be reproduced when we tested it on European companies. James O’Shaughnessy focused on different factors, such as price-to-sales, and proved in his tests that these value factors help create portfolios that outperform the US market on a consistent basis.

The studies above were performed using different datasets and periods, so it’s not trivial to understand which factors or combination of factors leads to the most market outperformance. The goal of this paper is to provide more clarity in this area and to help investors understand which ratios lead to the biggest market outperformance and which have no effect. Finally, we combine the single factors generating the highest market outperformance with a second factor to determine if this increases market outperformance even more.

In his book, 'The Big Secret for the Small Investor’, Joel Greenblatt wrote that the best performing stock mutual fund of the last decade earned more than 18% annually. This is impressive since the market, as measured by the S&P 500, was actually down close to 1% per year between 2000 and 2009. Yet the average investor, in the same fund, managed to lose 11% per year over those 10 years. How is that possible?

After every period in which the fund did poorly, investors ran for the exits, and after every period in which the fund did well, investors piled in. The average investor managed to lose money in the best performing fund by buying and selling the fund at just the wrong times. Investors seem to forget that even the best-performing fund managers go through long periods of significant underperformance.

Our emotions and our behaviour are under the continuous influences of the media, and of course of other people. Emotions are simply a wrong guide to base investment decisions on. Where money is concerned, emotions regularly overcome rationality. This can also be seen in the market as stocks go up and down for no reason other than fear, greed, hope or despair.

In order to avoid your emotions influencing your investment decisions, you should invest using a strict standardized process; a proven system which you can rely on that removes emotions from the decision making process. Think of this system as the process or procedure that a doctor needs to follow when performing an operation. It does not guarantee success, but the procedure has proven its reliability over time and has a high probability of success.

The need to focus on the investment process with the highest probability of success, rather than the outcome, is critical when investing. This is because investment outcomes are probability based, and even if they have a high probability of success there is still a chance that they will be negative. However, only if you invest using a system with a high probability of market beating returns over the long term do you have a high probability of being a successful investor.

And this is exactly what we would like to do with this paper. Determine exactly what factors you should use when selecting your investments to give you the highest probability of substantially outperforming the market. In order to do this we looked at factors based on historical financial data to see how effective each factor is in generating market outperformance. We did this using a computer database that can quickly and accurately process or screen a large number of companies, but more importantly, a computer has no emotions. Once you have identified what factors have a probability of outperforming the market, you can add them to the computerised stock screener to generate the names of companies that meet these factors. This list is an excellent starting point for selecting market beating investment ideas.

In the paper we only use historical accounting data and no forecasts. The reason being is that there is ample evidence that forecasts cannot be relied on. For example, in his excellent book, ‘The New Contrarian Investment Strategy’, David Dreman mentioned a study that used a sample of 67.375 analysts' quarterly estimates for companies listed on US stock exchanges.

The study found that the average analysts’ error was 40%, and that the estimates were misleading two-third of the time! A less important but not insignificant factor is that historical accounting data is also cheaper.

Our backtest universe is a subset of companies in the Datastream database containing an average of about 1500 companies in the 17 country Eurozone market during our 12-year test period (13 June 1999 to 13 June 2011). We excluded banks, insurance companies, investment funds, certain holdings companies, and REITS. We included bankrupt companies to avoid any survivorship bias, and excluded companies with an average 30-day trading volume of less than €10 000. For bankrupt companies, or companies that were taken over, returns were calculated using the last stock market price available before the company was delisted.

In order to create a market portfolio to compare our results against - remember we excluded certain types of companies - we constructed a market portfolio based on the 250 most traded companies in our test universe, over the previous 30 days, weighted by trading volume in Euros. Each year on 13 June the market portfolio was reconstructed with the then 250 most liquid companies, weighted by trading volume (average over the previous 30 days before 13 June).

As you can see below, our constructed market portfolio is closely correlated with the EURO STOXX index, a broad but liquid subset of the STOXX Europe 600 Index. Over the 12-year period of the study, the market portfolio generated a return of 30.54 % or 2.25% pa, dividends included.

The test period was most certainly not a good time to be invested in stocks.

The 12-year period we tested included a stock market bubble (1999), two recessions (2001, 2008-2009) and two bear markets (2001-2003, 2007-2009). In spite of all the substantial movements, over the whole period it was essentially a sideways market, as Vitaliy Katsenelson defined in his book, ‘The Little Book of Sideways Markets’. The tables below show the movement of the market portfolio over the 12-year time period we tested:

Each year, as with the market portfolio, all the portfolios we tested were formed on 16 June. We chose 16 June as most European companies have a December year-end and by this date all their previous year-end results would be available in the database. The annual returns for our back test portfolios were calculated as the 12-month price change plus dividends received over the period. Returns were compounded on an annual basis. This means each year the return of the portfolio (dividends included) would be reinvested (equally weighted) in the strategy the following year. The portfolios were all constructed on an equal-weighted basis.

In order to test the effectiveness of a strategy, we divided our back test universe into five equal groups (quintiles), according to the factor we were testing. For example, when testing a low price-to-book (PB) value strategy, we ranked our back test universe from the cheapest (lowest PB) to the most expensive (highest PB) stocks.

The cheapest 20% of companies were put in the first quintile (Q1), the next in the second, and so on, with the 20 % of companies with the highest price-to-book value in the fifth quintile (Q5).

We defined a good factor or strategy as one where:

- The top quintile (Q1) outperforms the bottom quintile (Q5) over the 12 years we back tested and
- There must be a linearity of returns among the quintiles (quintile one must outperform quintile 2 which must outperform quintile 3, up to quintile 5) over the 12 years we tested, and
- The strategy must also consistently outperform the market over time. We defined consistent outperformance when the first quintile (Q1) outperformed the market portfolio 60% or more of the time.

So, in summary, we are looking for factors that increase the probability of positive returns, beat the market, and how strong or weak this probability is.

In order to determine if the size of the company has any effect on the effectiveness of a one factor test, we divided the back test universe into three groups based on of market capitalization:

- SMALL CAP - companies with a market capitalization between 15 million Euro and 100 million Euro.
- MID CAP - companies with a market cap between 100 million and 1 billion Euro.
- LARGE CAP - companies with a market capitalization greater than 1 billion Euro.

Compared with US studies, our Small Cap group can also be classified as Nano capitalization companies, and our Mid Cap group equivalent to US small capitalization companies.

Using only one factor we tested the following:

- Value factors (earnings yield, free cash flow yield, price-to-book ratio and price-to-sales),
- Quality factors (Piotroski F-score, ROIC, ROA, net debt ratio), and
- Momentum factors (price Index/relative strength).

We also tested two investment strategies; the MF strategy developed by Joel Greenblatt and explained in his book, ‘The Little Book that Still Beats the Market’ and the ERP5 strategy developed by MFIE Capital.

Our goal was to look at each factor and determine if it is a strong or a weak contributor for generating market beating returns.

When we tested single factors the portfolios sizes were quite large. As our back test universe was quite large, with an average of 1500 companies, the average portfolio’s size per quintile was around 300 companies. It is of course not practical to have a portfolio with such a large number of companies. Thus in the two-factor strategies we tested, we formed portfolios with 30 to a maximum of 60 companies for each quintile. We did this by taking the first quintile of the first factor we tested (about 300 companies), sorted it by the second factor, and divided it into five quintile portfolios (300/5=60). By testing the two-factors this way you have the added advantage of accurately identifying the stronger and weaker factor, as the first factor is emphasized due to the inclusion of only its first quintile companies.

For the two-factor tests, we did not split the universe into different market capitalization as in doing so we would not have been able to form portfolios with at least 30 to 60 companies.

We defined the earnings yield ratio (EY) as operating income / enterprise value. We also tested the ratio in two ways: trailing 12-month operating income divided by enterprise value, and 5-year average operating income divided by enterprise value. Thus the lower the EY, the more investors are paying for operating income and the larger their expectations of future growth of the company.

**Earnings Yield 12 months**

**Earnings Yield 5 year average**

As you can see, trailing 12-months EY is a strong factor (as we defined it) over the test period. The returns in Q1 were higher than Q5 for all company sizes. It is interesting to note that the factor led to substantially better performance with mid and large companies. Also, for large companies, Q1 outperformed the market more than 80%, but only 67% of the time with small companies.

Market outperformance was substantial, with Q1 for the mid and large companies outperforming the market by more than 8% per year (pa). Small companies did not perform as well, but still outperformed the market portfolio by more than 4,6% pa.

Market outperformance was substantial, with Q1 for the mid and large companies outperforming the market by more than 8% per year (pa). Small companies did not perform as well, but still outperformed the market portfolio by more than 4,6% pa.

The 12-months EY was the second most successful single factor strategy to select large cap companies. The 5-year average EY is not as strong a factor as the one year. For all company sizes Q1 performed better than Q5, but the results were not linear with Q5 performing better than Q4 for all company sizes.

A stock with a low price-to-book (PB) ratio is cheap, based on the price of acquiring its book equity. This factor does not take the earnings power of the company into consideration and relies on the assets and liabilities of the company being fairly valued. The price-to-book value was a favorite tool of Benjamin Graham and other earlier value investors. In spite of its shortcomings, PB is a strong factor in generating market outperformance, and also works well with other factors as you will see later.

Investors who believe PB is an important factor when looking for bargains would be correct. It certainly is for the mid cap companies, with Q1 generating market outperformance of 12,1% pa, and Q5 underperforming the market by 8,5 % pa. For the other company sizes, the factor is less strong. However, for all three company sizes it led to market outperformance between 66% and 75% of the time over the 12-year test period.

Of all the single factors we tested, a low PB strategy applied to mid cap companies led to the highest return of 400,3% over 12 years. That was nearly 370% better than the market portfolio. It did not work as well for large cap companies, returning only 203,6%, and was even less successful when applied to small companies, leading to a 172,5% return. So over the 12 years tested you would have been well rewarded if you used only a low price-to-book strategy.

The price-to-sales measures the market value of the company against its annual sales. Investors buy low PSR stocks because they believe companies are undervalued when they are not paying much for the sales the company generates. Also, PSR is a more stable ratio than EY, for example as sales fluctuate less than earnings, and it can be used to value companies that temporarily have no earnings.

James O'Shaughnessy in his book, ‘What works on Wall Street’, called the PSR the ‘king of the valuation factors’ as it beat the returns of all the valuation ratios he tested.

James Montier, in his 2008 paper, ‘Joining the dark side: Pirates, Spies and Short Sellers’, on the other hand, used the price-to-sales ratio to find overpriced companies that may be good candidates to sell short. A high PSR allows you to hone in on companies whose valuation has lost all touch with reality.

As you can see, this is a strong factor with linear returns for all three company sizes. However, it is not as effective with small companies as it only beat the market 58% of the time. Returns of Q1 were also not as high as some of the other single factors we tested. This may be because sales do not automatically lead to profits, and thus this ratio may work better in combination with another factor; something we tested in the two-factor strategies.

Free cash flow (FCF) can best be defined as the cash available from operations minus capital expenditure, and is the cash available to the company to pay dividends, make investments and buy back shares. We defined the free cash flow yield as cash from operations minus capital expenditure, divided by enterprise value. And we analysed the trailing 12-month FCF yield and the 5-year average FCF yield.

If you think about it, a high FCF yield should have strong predictive power over future returns. This may be because the market is less efficient when it comes to pricing free cash flow and its growth in the stock price. Another reason may be because FCF is more difficult to manipulate compared with earnings.

**12 Month FCF Yield**

As you can see, the 12-month trailing FCF yield is a strong factor and it is very consistent. High FCF companies (Q1) outperform low FCF yield companies (Q5) consistently for all three market size companies, with the outperformance also completely linear over the five quintiles. Thus FCF valuation really matters in separating the winners from the losers. This valuation factor has a strong predictive power for the mid cap stocks, but less so for small companies.

**5 Year Average FCF Yield**

Even though using the 5-year average FCF yield on mid cap companies (third best single factor we tested) over the test period would have given you a higher return than the 12-month FCF yield, the results for the other market size companies would have been a lot lower. As a factor it is also not strong, with the results not being linear over the five quintiles. Q1 did, however, outperform Q5 by a substantial margin.

As a value investor we are sure you also believe that buying bad companies at very low prices is a perfectly viable strategy, provided of course, that the companies don’t go bankrupt. But what about buying good companies that generate a high return on invested capital without looking to see if the companies are over- or undervalued? A lot of investors believe that this is a way to identify market beating investments as it measures how effectively a company invests shareholder's money.

Previous research shows this is not the case. In his book, ‘What works on Wall Street’, in chapter 14, James O'Shaughnessy tested return on equity using a decile analysis and found that stocks in the top decile (highest return on equity) were on average only mediocre investments underperforming the market. Surprisingly, decile two and three did considerably better than their market.

We defined ROIC as the past 12-months operating income divided by the sum of net working capital (current assets minus excess cash minus current liabilities) and net fixed assets (total assets minus current assets minus intangible assets). We tested ROIC over one year, as well as the 5-year average, and this is what we found.

**12 Month ROIC**

**5 Year Average ROIC**

Similar to the above mentioned study, we also found ROIC to have a mixed influence on the returns during the test period. Companies with the highest ROIC (Q1) did not always perform the best, and there was no linearity in returns from Q1 to Q5. Thus you can safely say that a great company does not automatically make for a great investment.

We not only wanted to test return on equity but also return on assets as a factor that can generate market outperformance. We defined return on assets (ROA) as net profit after tax divided by total assets. But I'm sure you can immediately see the shortcomings of using return on assets when selecting investments. Some companies, like auto manufacturers, need a lot of assets whereas others like software companies have hardly any assets that all. In the first example, return on assets is likely to be low, whereas is the second example it is likely to be extremely high.

However, it does not say how cheap or expensive the shares of the companies are priced, and that, as you saw with the valuation factors we tested, is more important.

As you can see, ROA is not a very effective factor to use when selecting companies to invest in. Even though Q1 had higher returns than Q5, the results are not linear and the number of years this factor outperformed the market was only 58% for all three market size companies. Of all the single factors we tested, buying companies with the highest ROA was the second worst performing strategy you could have followed.

Joseph Piotroski is an associate professor of accounting at the Stanford University Graduate School of Business. He developed the F-score in 2000 while at the University of Chicago. Piotroski recognized that, although it has long been shown that value stocks (or high book-to-market firms as he calls them) have strong returns as a group, there is nevertheless a very wide variability in terms of the returns of these stocks, with most of them performing worse than the market.

In his research paper called ‘Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers’, he noted:

Embedded in that mix of companies, you have some that are just stellar. Their performance turns around. People become optimistic about the stock and it really takes off [but] half of the firms languish; they continue to perform poorly and eventually delist or enter bankruptcy.

The F-score he developed essentially looks for companies that are profit-making, have improving margins, don't employ any (obvious) accounting tricks, and are strengthening their balance sheets. The score consists of nine variables are split into three groups:

- Profitability
- Balance sheet health, and
- Operating efficiency.

More information on exactly how the Piotroski F-Score is calculated can be found in Appendix 2. In our back tests we ordered our universe according to their F-score without taking into account the valuations of the stocks. We first wanted to determine if the F-score on its own is a strong predictor of market outperformance, because if so, it may be an even better predictor in combination with other parameters valuation factors, for example.

In the above table you can see that the F-score is a strong factor as we defined it. It led to market outperformance for all three company sizes and worked particularly well for mid cap companies. Also, the strategy outperformed the market 75% of the time for small and mid-sized companies, and 83% for large companies. The results were also completely linear.

With this factor we wanted to test if the amount of debt a company had on its balance sheet had any impact on its stock price over the following 12-months. To do this we used the net debt (long term debt minus excess cash) to market value ratio.

The results above show that the market rewards companies that take risks and punishes those that are too conservative. Companies with high cash balances and thus low debt to market value ratios (Q1) underperform those with less cash and a high amount of debt (on average).

This was most extreme with mid-sized companies where returns are linear, and highly leveraged companies outperformed companies with low amounts of leverage by over 140%. But overall the results were mixed, showing the net debt-to-market value ratio as a weak factor for achieving market outperformance.

The idea behind relative strength is to find companies with the best performing stock prices; the ones that have gone up in price the most over a specific period of time.

In his book, ‘What works on Wall Street’, James O'Shaughnessy calculated relative strength by looking at the price increase of a stock over the past year. Looking at the change in stock prices over a year, he found that winners seem to continue to win and the losers kept on loosing.

In this study we first set out to also see if relative strength can separate winners from losers. Then with the multiple factor portfolios, we will see if the combination of reasonable priced stocks with momentum can give you even higher excess returns. We have analysed two periods of short term price momentum:

- Companies with the best 6-month price appreciation (stock price on the day the portfolio was compiled minus the stock price six months ago which we called the 6-month Price Index, and
- Companies with the best 12-month price appreciation (stock price on the day the portfolio was compiled minus the stock price 12-months ago, which we called the 12-month Price Index.

**6 Month Price Index**

**12 Month Price Index**

As you can see the short term price index (6-months) is a strong factor as we defined it. Results are linear with Q1 beating Q5 for all size companies and the factor outperformed the market just over 83% of the time for all three market sized companies.

The 12-months price index is not strong as it is not linear for large cap companies. It also outperformed the market only 58% of the time for mid cap companies.

What is very clear is that companies with a low price index (Q5) for both the 6- and 12-month price index are to be avoided at all costs as for small companies as the 6-months was the worst, and 12-months price index the second worst single factor strategy we tested.

The results also show good or bad news about a company may be quickly incorporated in the stock price, but clearly with some delay, otherwise the top quintiles would not outperform the bottom quintiles as well as the market. The factor is particularly strong for small and mid-cap companies. This may be, for example, if a company's order book is decreasing the company’s employees, or suppliers may notice this and start selling the shares who then tell others who then sell shares before the news is really public.

The increased numbers of sellers that are selling leads to supply exceeding demand, causing the stock price to decline. But there may also be other reasons, such as company insiders that may be buying.

Another reason why short term momentum works is the so called ‘inertia effect’. In his book, ‘The New Finance’, Robert Haugen said stock prices exhibit inertia in the short-term and often have reversals in the long-term. This is driven by the tendency of companies in competitive industries to revert to the mean. Yesterday's winners become losers or average performers, while yesterday's losers improve. The market is slow to recognise these reversals and thus share price trends continue.

The following two factors are not really single factors, but really a combination of several parameters. However, we wanted to include them under the single factor tests as we also wanted to combine them with other factors to see if their market outperformance could be improved even further.

The Magic Formula was developed by Joel Greenblatt in his book, ‘The Little Book That Still Beats the Market’. The basic idea behind the rank is to identify good businesses that are selling at attractive prices. This is done through the use of two ratios:

- Return on Invested Capital (ROIC) - which is calculated as EBIT / (Net Working Capital + Net Fixed Assets)
- Earning Yield - which is calculated as EBIT / Enterprise Value.

The rank then combines these two ratios to give you a list of companies with good businesses that are trading at an attractive price.

Kindly note that we tested the Magic Formula based on our interpretation of it after reading Joel Greenblatt’s book mentioned above. Neither Mr Greenblatt nor the website (magicformulainvesting.com) have endorsed this study or have had anything to do with it, or recommended any of the companies included in our back tests. We also made use of our own database and did not have access to Mr Greenblatt's

As you can see, the Magic Formula is a strong factor that leads to substantial market outperformance. Q1 performs better than Q5, and the results are completely linear. It is, however, not that consistent - outperforming the market 50% of the time for small companies and 58% of the time for mid and large companies.

The ERP5 rank is a screen designed by MFIE Capital that uses the following ratios to identify good companies that are trading at undervalued prices:

- Return on Invested Capital (ROIC) - EBIT / (Net Working Capital + Net Fixed Assets).
- Earning Yield - EBIT / Enterprise Value.
- Price-to-Book Value - Market Capitalization / Book Value.
- 5Y Trailing ROIC - five year average EBIT / (Net Working Capital + Net Fixed Assets).

The results show that the ERP5 rank is a factor that works very well when applied to small cap companies, with the second best results of all single factors we tested. Q1 results are substantially better than Q5. However, the results for small cap companies are not completely linear.

What is worth noting is that the Q1 results for the ERP5 for all size companies are higher than that of the MF rank. The ERP5 screen is particularly effective in identifying market beating small companies. It is also a very consistent factor, beating the market 83% of the time for small and medium-size companies, and 67% of the time for large companies.

Here are the main points for the one factor tests:

- Valuation factors have a strong predictive power to achieve market outperformance.
- The mid cap companies seem to outperform the small cap and large cap companies except for the results of the ERP5 rank.
- The fact that a company generates a high return on invested capital does not make it a market beating investment; valuation is more important.
- Investing in companies with a good F-score, which suggests improving fundamentals, results in market beating returns.
- Winners continue to win and losers continue to lose, as shown in our test using 6- and 12-months price index factors.

In the following table we show how all the single factors we tested met our criteria of being classified as a strong factor.

As a reminder, this is how we defined a strong factor:

- The top quintile (Q1) outperforms the bottom quintile (Q5), and
- There must be a linearity of returns among the quintiles (quintile one must outperform quintile 2 which must outperform quintile 3, up to quintile 5), and
- The strategy must also consistently outperform the market over time. We defined consistent outperformance when the first quintile (Q1) outperformed the market portfolio 60% or more of the time.

If you only looked at the first quintile of each single factor we tested, this detailed the two best and worse strategies for each market size group of companies:

**LARGE COMPANIES:**

**MEDIUM-SIZED COMPANIES:**

**SMALL COMPANIES:**

In this second part of the paper we build portfolios by combining two of the factors we have already tested. Through the combination of the second factor we want to find out, using the strong factors we have already identified, if it leads to higher market outperformance more consistently.

To do this we first sorted all the companies in our investment universe by the first factor. We then selected only the companies in the first quintile, and then used only this group of companies and sorted them into five quintiles using the second factor. So the two-factors were not weighed equally. The first factor in each case had more weight as we only selected the best quintile from this factor to use with the second factor.

We also tested the same factor twice; for example, using price-to-book as the first and second factor. We did this to determine if this combination leads to higher market outperformance compared with the original one-factor tests. As explained, for the two-factor tests we did not split the universe into different market capitalization as in doing so we would not have been able to form second factor quintiles with at least 30 to 40 companies in each quintile.

Overall, what we found was that all the two-factors we tested, even the worst performing quintiles, substantially outperformed the market portfolio.

For this backtest we first sorted our universe of stocks by earnings yield (EY) which we defined as operating income divided by enterprise value. We then took the 300 or so companies with the highest earnings yield and sorted them by the 14 second factors we tested.

For each of the second factors, we divided the 300 companies into five quintiles and calculated the performance of each quintile.

As you can see, using EY (valuation factor) is very effective to identify market beating stocks. On average, across all second factors tested, the strategy led to an average performance of just under 405% (median was 368%); substantially higher than the market portfolio return of 30.54%.

The best return of 814% was achieved by combining the earnings yield with the 6-month price index. This means a combination of price momentum, as well as undervaluation based on earnings yield. Interesting was that the second best combination was earnings yield combined with a 12-month price index, also a momentum factor.

The worst performing strategy was earnings yield combined with return on invested capital, which returned 143% over 12 years. Even though this strategy also beat the market portfolio, it was not nearly as effective as using price momentum as a second factor. Even though the results of this two-factor strategy were good, based on the average Q1 returns, this was the sixth best two factor strategy we tested.

With this two-factor back test we took the cheapest 20% of companies in our universe with the lowest price-to-book value and then sorted these companies into five quintiles based on the second factor we tested.

Of the nine two-factor strategies we tested, using the price-to-book as the first factor led to by far the highest average return of 620% (median 617.5%). The best two-factor strategy was combining cheap price-to-book companies with the companies that had the highest 6-month price index value. This led to a total return of nearly 1030% over the 12 year period we tested. The second best combination was also momentum, and was the combination of price-to-book value with the highest 12-months price index companies. This led to a total return of 987%.

The worst strategy was the combination of low price-to-book companies with companies that had the highest 5-year average earnings yield. This would have led to a total return of 354.3%. Not bad at all, but not close to the 1030% of the best performing two-factors.

It is of course very hard to make predictions about what investment strategy will work best in future, but looking at the dreadful market over the last 12 years the returns of buying low price-to-book companies with a high 6-months price index is truly astounding.

With this two-factor backtest we combined the cheapest 20% of companies based on price-to-free cash flow (over the past 12-months) in our investment universe with all the second factors we tested for.

As you can see the results were also very good, with an average return of just under 470% (median was 488.8%). On average this was the third best two factor strategy we tested.

The best performing strategy was combining a high price-to-free cash flow ratio with the 12-months price index. This led to a total return of 755%. With this strategy the second best performance was not the 6-month price index but buying the lowest price-to-book ratio companies. If you did this, your return over the 12 years would have been just under 714%.

The two-factor strategy with the lowest return was the combination of high free cash flow companies with companies that generated high returns on invested capital. In this case the 12 year return was 199.1%

With this combination we took the lowest 20% of price-to-sales ratio companies and combined them with the second factors we tested for.

Even though price-to-sales is also a valuation factor, on average, using this combination gave the lowest returns of all the two-factor strategies we tested, generating an average return of 345.3% (median 333.4%). The best performing strategy was selecting companies with a cheap price-to-sales ratio as well as companies with the highest 6-months price index values. This would have given you returns of 563% over 12 years.

The worst combination would have been combining the low price-to-sales ratio companies with those that generated the highest ROIC over the past five years. Using this strategy your return would have been 184.8%.

With this combination we first selected the 20% of companies with the highest Piotroski F-score and then divided these companies into quintiles based on the second factors we tested. It's worth mentioning that even though you may think that combining the F-score with low price-to-book companies would be what Joseph Piotroski did in the paper mentioned previously, but that would not be correct.

In his paper Mr Piotroski first selected low price-to-book companies and then sorted these by the F-score. So for you to see the results that the strategy based on Mr. Piotroski’s paper, you would have to look under price-to-book as the first factor and the F-score as the second factor.

Based on average returns of the best quintile of all the second factors, this strategy returned 422% (median was 421%). Out of the nine two-factor strategies we tested this one on average was the fifth best strategy. The best combination that would have given you a 680.4% return over 12 years would have been to combine a high F-score with companies that had the highest 12-month free cash flow yield.

Here we first took the 20% of companies in our investment universe with the highest 12-month price index and then combined these companies with the 14 second factors we tested.

On average, across all the second factors we tested, this strategy would have given you a return of 404.9% (median was 420.7%). This was the seventh best (out of nine) two-factor strategy we tested. The best combination was combining the 12-month price index with the companies with the highest earnings yield, using the past 12 months earnings. The strategy would have given you a return of 802.4%.

The worst strategy would have been to combine the highest 12-months price index with the same factor again. This means from the 20% of companies with the highest share price increase over the past 12 months, you would have chosen the 20% that went up the most price over the past 12 months. In this case your return would have been 114.9%.

In some of the previous combination strategies the 6-months price index was one of the best second factors to use. In this combination would like to determine if it is also a good first factor to use. We thus selected the 20% of companies with a higher 6-months price index and used only these companies when we made up the portfolios for the second factor tests.

And it turns out that using the 6-months price index as a first factor gives you a very satisfactory return. On average, across all 14 second factors we tested, the best quintile would have given you an average return of 566% (median was 610%). The best performing strategy was combining the 6-months price index with the lowest price-to-book companies. If you did this to select investments, your return over the past 12 years would have been 1157.5%.

The worst performing strategy combination would have been combining the best 6-months price index companies by the same factor again. This would have given you a return of only 122.1%.

With this combination we wanted to determine if the results of the Magic Formula could be improved by adding an additional factor to select companies to invest in. Out of our universe of companies we thus took the 20% of companies with the best MF-ranking and combined them with the second factors we tested.

Across all the second factors we tested the average return was 401.8% (median was 359.3%) over 12 years. On average, this was the eighth best (out of nine) two-factor strategy we tested. The best performing combination would have been to combine the best Magic Formula companies with the companies that had the highest 6-months price index. This would have given you a return of 783.3% over 12 years.

The worst performing strategy would have been to combine the MF-rank with return on invested capital. In this case your returns would have been 121.6%.

With this combination we combined the 20% of companies with the highest ERP5-rank with all the second factors we tested.

Your average return of combining the ERP5 score with all the second factors would have been 458.5% (median was 479.9%) over 12 years. The average this was the fourth best two-factor strategies we tested.

Similar to what we found with the MF-rank, the best performing strategy was combining the ERP5 score with companies that had the highest 6-month price index. If you did this your returns would have been 732.1%.

The worst return was generated by combining the ERP5 score with companies that had the highest return on investment capital on average over the past five years. This would have only given you a return of 114.4%.

Here are the main points of the two-factors tests:

- All two-factor strategies we tested substantially outperformed the market with even the worst performing strategy returning 114.4% over 12 years compared with the 30.54% of the market portfolio.
- Price momentum, both 6- and 12-months played a substantial part in all 10 of the best performing two-factor strategies.
- The three best performing strategies that all generated returns of more than 1000%, all either as first or second factors, contained the highest 6-month price index as a factor.
- A low price-to-book value was also a very important factor as it formed part, either as first or second factor, in three out of four of the best performing two-factor strategies.

If you only looked at the first quintile of all two-factor strategies we tested, these were the five best and worse strategies:

**Best Strategies:**

Even though we tested some single factors that did lead to strong market outperformance, the two-factor strategies we tested were substantially better. For example, if we combine the first quintile performance of all the one and two-factor strategies we tested, and sort them from best to worst, the best single factor performance (achieved by applying a low price-to-book ratio to mid-cap companies) was at position 69 (the next was at position 91). All the strategies that performed better were two-factor strategies.

The most surprising result we found, especially for value investors, is that price movements over previous 6- and 12-months (6- and 12-months price index) were factors in each of the 10 best performing two factor strategies we tested. This is not what we learned as classical value investors. We learned that the more a company share price declined, as long as it became cheaper in terms of valuation, the more attractive it was as an investment.

With our back testing we found that valuation still matters, but it has to be applied in a different way. You first have to look for the 20% of companies that increased the most in price over the previous 6-months and then sort these companies by price-to-book value and buy the 30 companies with the lowest price-to-book value.

At this point you may be asking yourself the same question we have - the results we have shown are all based on historical financial information, but what does this mean for my future investment returns? The simple answer is we cannot say for certain, but we have a good idea. We now know what strategies were very successful in arguably one of the worst 12 years in terms of stock market performance in at least half a century.

For the next 10 years the top performing strategy we tested of buying the lowest 20% of companies by book value of the 20% of companies that have increased the most in price over the past six months will most likely not be the best strategy. But it will still give you outstanding market beating returns. In the past 12 years the strategy returned just under 1160%, compared with the market portfolio 30.54%. Does it really matter if the strategy falls to position 20 of the strategies we tested and generated a total return of 670%? Most likely not, because you would probably have outperformed 99% of all investment funds worldwide. This means that the strategies that performed the best over the past 12 years may not do so over the next 10 years, but they will still be amongst the top strategies in terms of overall returns.

But what will happen if everybody starts using the best performing strategies; surely they will stop working, you may be thinking. If everybody does they will definitely stop working as investors pile in and push up prices to where these companies would not be undervalued anymore. But as Joel Greenblatt in his book, ‘The Little Book That Still Beats The Market’ mentioned, the reason everybody will not follow strategy is because it doesn't work all the time. And as soon as it stops working investors will abandon it like they abandoned the top performing investment fund we mentioned above. Most likely at exactly the wrong time; just before the strategy would substantially start outperforming the market once again. Remember the best performing strategy we mentioned outperformed the market only 83% of the time and had negative returns in three of the 12 years. In one of the last years, or one of the other years that the strategy didn't outperform the market, it would most likely have been exactly the time when investors abandoned the strategy.

One last point we would like to mention. Do not for a minute think that it is easy to follow these strategies. If you see what companies they come up with you will immediately start analysing them and for example say, ‘There's no way I am investing in that industry at the current time’, or ‘Look at this company's financial statements, it’s completely hopeless’. That may be so with one or two of the companies that the strategy comes up with. That is the reason why we suggest that whatever strategy you follow you invest in a minimum of 30 companies. This means that even if one of two companies go bankrupt, the others will do extremely well and your overall performance will still be outstanding.

We sincerely hope that you found the study of value and it substantially improves your investment returns. If it has, or if you have any comments or suggestions please let us know.

- What works on Wall Street – James O’Shaughnessy
- Contrarian Investment Strategies : The next generation – David Dreman
- The little Book of Sideways Markets – Vitaliy Katsenelson
- The Big Secret for the Small Investor – Joel Greenblatt
- Quantitative Strategies for achieving Alpha – Richard Tortoriello
- Value Investing – Tools and Techniques for Intelligent Investment – James Montier
- Predicting the Markets of Tomorrow – James O’Shaughnessy
- Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers - Joseph D. Piotroski
- The Little Book That Still Beats the Market – Joel Greenblatt
- Contrarian Investment, Extrapolation, and Risk, Journal of Finance 49, 1541-1578 - Lakonishok, Josef, Andrei Shleifer, and Robert W. Vishny
- The Cross-Section of Expected Stock Returns, Journal of Finance 47, 427-465 - Fama, Eugene F., Kenneth R. French

Copyright © 2012 MFIE Capital. All rights reserved.

This research was possible using the database and models created by the MFIE Capital team.

Unless otherwise indicated, all materials on these pages are copyrighted by MFIE Capital. All rights reserved. No part of these pages, either text or image may be used for any purpose other than personal use. Therefore, reproduction, modification, storage in a retrieval system or retransmission, in any form or by any means, electronic, mechanical or otherwise, for reasons other than personal use, is strictly prohibited without prior written permission.

**Research, Modelling & Development**

- Philip Vanstraceele
- Olivier Dambrine
- Luc Allaeys

**Editing**

- Philip Vanstraceele
- Olivier Dambrine
- Tim du Toit