#### The Five-Factor Fama-French Model: International Evidence by SSRN

Fordham University

May 2, 2015

**Abstract: **

In this paper, I examine the five-factor Fama-French model in 23 developed stock markets. Using the firm level data from July 1992 to December 2014, I form the 25 size-book to market, the 25 size-GP, and the 25 size-Inv. Portfolios. I use three factor, four factor and five factor models to explain the returns on these portfolios using regional as well as global factors. I find strong evidence for the five-factor model in North America, Europe, and Global markets similar to the results for the U.S. stock market. But the results for Gross Profitability (GP) and Investment (Inv.) suggest that these two new factors either do not exist or are much weaker in Japan and Asia Pacific portfolios. The results suggest that regional models perform much better than global models. This may imply that markets are still not fully integrated. With inclusion of the two new factors, the value factor becomes redundant in North America, Europe, and Global portfolios, similar to the US market results. However, in Asia Pacific and Japan, the value factor’s importance is not lessened by inclusion of the GP and Inv.

### The Five-Factor Fama-French Model: International Evidence – Introduction

There is a large body of research that shows that average stock returns are related to the book-to-market ratio (B/M) of equity in almost all markets of the world (Asness et. al 2013). This is called the value effect. The value effect is the fact that stocks with high to book-to-market ratio tend to have higher average returns than stocks with lower book-to-market ratios (DeBondt and Thaler (1985), Fama and French (1992), Lakonishok, Shleifer, and Vishny (1994)). There is also some evidence that profitability and investment are also related to the average stock returns. Fama and French (FF 2015) use the dividend discount model to explain why these variables under certain assumptions are related to average returns.

The dividend discount model says that the price of a stock is the present value of expected dividends,

In equation (1) is the share price at time t, is the expected dividend per share for period and r is the the long-term average expected stock return on expected dividends.

FF (2015) show that total market value of the firm’s stock implied by equation (1) is,

In equation (2), is the total equity earnings for period and is the change in total book equity. Dividing by time t book equity gives,

(3) implies the following: (1) Given everything else is fixed, then a high book-to-market ratio implies higher expected return; (2) Given everything else is fixed, then a higher expected earnings (profitability) imply a higher expected return; (3) Assuming everything else is fixed, then higher expected growth in book equity (Investment) implies a lower expected return. The difficulty in empirically testing these implications arises from the fact that it is not easy to identify expected earnings and investment.

Fama and French (1992, 1993) presented empirical evidence that the CAPM of Sharpe (1964) cannot explain the cross-sectional variation in expected returns related to size and book-to-market.

Then they presented an empirical three-factor model which includes size and book-to-market factors in addition to the market factor. Empirical test of the three factor model is based on the time series regressions.

In this equation is the return on security or portfolio i for period is the risk-free rate of return, is the return on the value-weighted market portfolio. is the difference between returns on diversified portfolio of small stocks and big stocks; is the difference between the returns on diversified portfolios of high B/M and low B/M stocks. If the model captures all variation in expected stock returns, then the intercept is zero for all securities and portfolios i.

Over the past 20 years it became clear however, that the three-factor model has difficulty to explain the cross-sectional variation in expected returns especially related to profitability and investment among other anomalies. These anomalies include accruals (Sloan 1996), net share issues (Ikenberry, Lakonishok, and Vermaelen 1995, Loughran and Ritter 1995), momentum (Jegadeesh and Titman 1993), and idiosyncratic volatility (Ang, Hodrick, Xing, and Zhang 2006), maximum daily returns (Bali, Cakici and Whitelaw 2011), liquidity risk (Pastor and Stambaugh (2003), and many others.

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