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The Sources of Return


For investors, the important point is that certain factors seem to have predictive powers for returns. This pattern in the behavior of stock returns is consistent with the three-factor pricing model introduced by Eugene F. Fama and Kenneth R. French in 1993. Today this model remains the most widely used benchmark for academic studies of investment returns.


The Three-Factor Model


According to Fama and French the expected return of a broadly diversified stock portfolio is a function of that portfolio’s exposure to three common risk factors:


  • Market factor, calculated by the difference in returns between the overall stock and a risk free rate

  • Size factor, calculated by the difference in returns between small stocks and large stocks

  • Relative price factor, calculated by the difference in returns between value stocks and growth stocks

The practical application of the Three Factor Model is this: investors comfortable with higher proportions of equity risk can increase the long-term expected return of their portfolio without raising their stock-bond ratio. They can achieve this by tilting their stock allocation to a larger portion of small cap and value stocks, two asset classes that have a history of offering average returns above the market.


About Table 1: US Value & Size Effects


CRSP data shows that US small cap (CRSP 6-10) and value stocks have historically had higher average returns than domestic large cap and growth stocks. This pattern in the behavior of stock returns is consistent with research published by Eugene Fama and Kenneth French (1992). Long-term returns in this table are based on monthly data courtesy of DFA.


Table 1

US Equities: Value and Size Effects, 1927 – 2010

 

Large

Value

S&P

500

Large

Growth

Small

Value

CRSP

6–10

Small

Growth

Annualized Returns

10.5

9.8

9.0

13.8

11.7

9.0

Standard Deviation

27.0

20.5

21.9

35.1

30.9

34.0

Average Annual  Returns

14.0

11.9

11.3

19.2

16.0

14.0

 

About Table 2: Non-US Value & Size Effects


Table 2 shows the same pattern with foreign small capitalization stocks and stocks with a high ratio of book–to–market equity (value stocks). Historically these stocks have had higher average returns than large capitalization stocks and stocks with a low ratio of book-to-market equity (growth stocks).


Table 2

Non-US Equities: Value and Size Effects, 1975-2010

 

MSCI World

ex USA

Int’l

Small

Int’l

Value

Int’l

Growth

Annualized Returns

10.57

15.72

15.72

9.04

Standard Deviation

21.47

28.13

24.46

22.14

Average Annual  Returns

12.74

19.17

18.39

11.28



About Table 3: Global Value and Size Premiums


Table 3 shows estimates of the size and value premiums for the US and international developed markets over several time periods.


  • From 1927 to 2010, the average US size premium, defined as the returns on a portfolio of small capitalization stocks (CRSP 6-10) minus the returns on the S&P 500, was 4.1% per year.

 

  • From 1970 to 2010, the longest common period for US and developed ex-US small cap stock returns, the average US size premium was 3.1% per year.

 

  • Over the same span of time, the average international size premium, defined as the returns on a portfolio of international small stocks minus the returns on the MSCI World ex USA index, was 7.2% per year.

 

  • From 1970 to 2010, the worldwide average for the size premium was 5.2% per year.

Table 3

Global Market Value and Size Premiums

 

 Difference of Avg Pct. Returns

US 

Value

Size

1927-2010

 Large Value minus Large Growth

2.7

1927-2010

 Small Value minus Small Growth

5.2

1927-2010

 CRSP 6-10 minus S&P 500

4.1

1975-2010

 Large Value minus Large Growth

1.9

1975-2010

 Small Value minus Small Growth

6.4

1970-2010

 CRSP 6-10 (Small) minus S&P 500

3.1

 

Developed ex US  

1970-2010

 Int’l Small minus World ex US

7.2

1975-2010

 Int’l Large Value minus Int’l Large Growth 

7.1

 

Worldwide  Average  “50 US, 50 Devlp World ex US”

1970-2010

 Worldwide Small Cap Premium

5.2

1975-2010

 Worldwide Value Premium

4.5


  • The US value premium of large cap stocks defined as the returns on a portfolio of large cap value stocks minus the returns on a portfolio of large cap growth stocks was 2.7% per year on average from 1927 to 2010.

 

  • The US Value premium for small cap stocks, defined as the returns on a portfolio of small cap value stocks minus the returns on a portfolio of small growth stocks was 5.2% per year on average from 1927 to 2010.

 

  • The average value premium for all US stocks from 1927 to 2010, as calculated by Fama and French was 4.0% per year.

 

  • From 1975 to 2010, the longest common period for US and Int'l Large Cap growth returns, the average value premium for US large cap stocks was 1.9% per year, while the average value premium for international large cap stocks was 7.1% per year.

 

  • From 1975 to 2010, the worldwide average for the large cap value premium was 4.5% per year.

Conclusion


For investors, there are two crucial points to remember. First, the small cap and value premiums are well established over various time horizons in US market history. Second, ample academic evidence proves that value and size premiums are positive in the developed and emerging markets, with the value premium observed in nearly every country that it has been studied.