Research over the last 4 decades has revealed a robust and persistent value premium -- value stocks have outperformed growth stocks over many time periods and markets worldwide^{1}. In its simplest form, value stocks can be defined as having discounted prices based on some financial fundamental such as sales, net income, dividends or book value. While some investors mistakenly believe they are receiving some sort of "deal" in terms of buying companies at discounted prices, what they fail to understand is that the market is discounting these stock prices based on the uncertainty (i.e. risk) involved in the future sales, net income, dividends or book value of the company. Remember, there is no "free lunch" to investing.

A simple way to understand the risk inherent in value stocks is to compare their performance versus their growth counterpart during extreme market contractions like the downturn from 1929-1932 or 2007-2009. The table below displays the ** total** return of IFA U.S. Large Value Index, IFA U.S Large Growth Index, IFA U.S. Small Value Index, and IFA U.S. Small Growth Index for the 34-month period ending 06/30/1932 and the 21-month period ending 02/28/2009.

IFA Index | 09/01/1929 - 06/30/1932 | 06/01/2007-02/28/2009 |

IFA U.S. Large Growth Index | -84.20% | -43.64% |

IFA U.S. Large Value Index | -90.29% | -60.60% |

Difference | -6.09% | -16.96% |

IFA U.S. Small Growth Index | -85.35% | -51.95% |

IFA U.S. Small Value Index | -88.27% | -58.19% |

Difference | -2.92% | -6.24% |

_{Sources and backtested information:} _{ifaindexes.com} _{and} _{ifabt.com}

As we would expect, the riskier value stocks had significantly more losses than their growth counterparts across both the large- and small-cap segments of the market. You would anticipate that any economic uncertainty would affect these companies more than those with more reliable or predictable sales, net income dividends or book value. But although we have to be able to stomach the tough times, we are expected to be rewarded for our discipline. The table below shows the ** annualized** return of the same IFA Indexes from 1928 to 2015.

IFA Index | 01/01/1928-12/31/2015 |

IFA U.S. Large Growth Index | 8.18% |

IFA U.S. Large Value Index | 10.50% |

Difference | 2.32% |

IFA U.S. Small Growth Index | 9.03% |

IFA U.S. Small Value Index | 12.53% |

Difference | 3.50% |

_{Sources and backtested information:} _{ifaindexes.com} _{and} _{ifabt.com}

The premium for having exposure to value stocks versus growth stocks has been roughly 2.32% to 3.50% over almost nine decades, but capturing the value premium is not easy or universal. As we mentioned before, there are multiple ways of defining a "value" stock depending on the fundamental variable we use to compare to the company's stock price. A short list includes Sales-to-Price (S/P), Earning-to-Price (E/P), Cash Flow-to-Price (C/P), or Book Value-to-Market (B/M). Theoretically, we could use one or all of these variables to define our "value universe," but this overlooks some very important practicalities in terms of portfolio implementation.

Dimensional Fund Advisors explains this concept in detail:

"We believe that using as few variables as possible is also crucial for portfolio implementation. A streamlined framework allows us to build portfolios that seek higher expected returns in a more transparent and efficient way. It also allows for more robust portfolio risk controls. Greater transparency can reduce monitoring costs. Efficient implementation helps reduce implementation costs."

^{2}

In other words, while we could look to gain exposure to value companies through a process that includes "everything but the kitchen sink," it can be inefficient in terms of potentially generating costs that pass through to the investor that are unnecessary and therefore not beneficial or optimal. These costs can be detrimental to investor returns over long time horizons and could possibly destroy the benefit we are trying to seek (i.e. capture the value premium).

Of the possible choices in terms of defining value, one in particular stands out, which happens to be Book Value-to-Market (B/M). Why is this the case? This is where the story gets a bit technical, but stay with us here.

The table exhibit below shows an output for a few cross-sectional US equity return regressions from January 1964 to December 2015. Remember, we know that there are certain dimensions of expected return (or Betas) that exist in the stock market like size, value, profitability, and investment^{3}.

First, we have Panel A, which is controlling for Size and one valuation ratio (Book-to-Market B/M, Earnings-to-Price E/P, Cash Flow-to-Price C/P, or Sales-to-Price S/P). As you can see, every single valuation ratio produces a positive result that is highly statistically significant (t-statistics are in parentheses under the regression estimates). For example, the Book-to-Market Ratio indicated a monthly premium of 0.292% with a 4.52 t-statistic (99th percentile). You may also notice that each valuation ratio, controlling for size, also explains roughly the same variation in the overall performance of US equities, which is measured by R-squared (0.019 for the B/M factor, for example). This is good news for the portfolio manager. There are a few different ways for us to gain exposure to the value premium that are highly reliable, which gives the portfolio manager some flexibility.

Panel B includes the same regressions, but now controls for both Size, Book-to-Market and an additional valuation ratio. What we are trying to accomplish is to see if there is any additional value beyond what is captured in the Book-to-Market ratio. As you can see, the t-statistics for the Book-to-Market ratio are about the same in magnitude as Panel A. What is different is that the t-statistics for the other valuation ratios have all decreased (some dramatically). What this tells us is that a lot of the benefit that we originally found in using the Earnings-to-Price ratio, Cash Flow-to-Price ratio, or Sales-to-Price ratio, is already found in the Book-to-Market Ratio. Further, the R-squared, or the percentage of variation explained by controlling both size and book-to-market, hasn't dramatically changed, so we haven't lost in any explanation of the variation in returns of US equities.

This is also great news for the portfolio manager. Instead of wasting resources by continually estimating four different variables, they can just focus on Book-to-Market and still reliably capture the value premium. This leads to more efficient implementation and lower costs for investors. As we mentioned before, this benefit can have a dramatic impact on overall performance over long time horizons.

Most recently, researchers have discovered the Profitability Factor, which states that companies with robust profits outperform companies with weak profits after controlling for both Size and Relative Price (i.e., Value). Panel C introduces the profitability factor (OTCPK:PROF) into the regression to see how it influences results. As you can see, the t-statistics for Earnings-to-Price, Cash Flow-to-Price and Sales-to-Price are now zero and even negative, but the t-statistic for Book-to-Market remains highly reliable. Once again, the R-squared remains almost identical. Therefore, the combination of the Book-to-Market Ratio and the Profitability factor not only completely subsumes the other factors but also increases the reliability of the Book-to-Market factor, which allows us to more reliably capture the value premium.

Research has indicated a premium for exposure to value stocks. In theory, index fund managers can define value by controlling for a few different variables. In practice, this can lead to inefficiencies in terms of portfolio implementation that end up costing the investor. Multiple regressions are helpful in terms of isolating or even removing certain variables that are of no additional value. By combining the Book-to-Market Ratio with the Profitability Factor, index fund managers can reliably define and capture the value premium in a cost-efficient way that leads to better results for investors.

_{1. Fama, Eugene & Ken French. "The Cross-Section of Expected Stock Returns." The Journal of Finance, Vol. XLVII. June 1992.} _{https://faculty.fuqua.duke.edu/~charvey/Teaching/IntesaBci_2001/FF_The_crosssection.pdf}

_{2. Marlena Lee, PhD, Savina Rizova, PhD, & Antonio Picca, PhD, "Capturing Value: Why Less Can Be More", DFA Research, August 2016}

_{3. Fama, Eugene & Ken French. "A Five Factor Asset Pricing Model." University of Chicago & Amos Tuck School of Business, Dartmouth College. March 2014.} _{http://www8.gsb.columbia.edu/programs/sites/programs/files/finance/Finance%20Seminar/spring%202014/ken%20french.pdf}

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **We utilize mutual funds offered by Dimensional Fund Advisors, LP in our 100 Index Portfolios that we recommend to our clients.