In the old days of investing, there was basically one variable that people looked at. That was the percent of stocks a person had in their portfolio. This can also be called the market factor or beta of the portfolio, which is a measure of the risk of the portfolio relative to the risk of the overall market. The June 1992 Journal of Finance article “The Cross-Section of Expected Stock Returns” by Eugene F. Fama and Kenneth R. French added two more variables: size and value.
Market factor: Stocks have higher expected returns than bonds. It is the annual return of the total stock market minus the return of one-month treasury bills.
Size factor: Small company stocks have higher expected returns than large company stocks. It is the annual return of small stocks minus the return of large stocks.
Value factor: Lower-priced value stocks have higher expected returns than higher-priced growth stocks. It is measured as the annual return of high book/market stocks (value stocks) minus the return of low book/market stocks (growth stocks).
Using average annual returns from 1/1/1928 to 12/31/2012, the factors have been calculated to be
- market factor = 7.63%
- size factor = 3.14%
- value factor = 4.82%
Now the question is, what can we do with this? The answer is that we can use it to help diversify risk.
Let’s say the expectation for future annual stock returns is 7%. And the annual return for intermediate bonds is 3%. If we have a 50/50 portfolio, we would expect the combined return to be 5%. Say you are after a higher return. To get that, you have to invest more heavily in stocks. Let’s say you want to target 6% total return for your portfolio. Using the single market factor, we would need to target 75% in stocks and 25% in bonds.
(75% x 7%) + (25% x 3%) = 6%
To add in size and price factors, we can look at small cap stocks and value stocks. Historically, small cap stocks have outperformed large cap stocks, and value stocks have outperformed growth stocks. This is shown graphically in Figure 1.
Using monthly data from 1926 to 2009, small-cap growth stocks had higher returns than the total market by only 1.70%. Small-cap value stocks, on the other hand, outperformed the total market by 6.56%. Historically, small-cap value stocks have given the highest returns. Let’s add small-cap value stocks to our example portfolio. Further, let’s split our equity holdings equally between the total stock market and small-cap value. This will give us an expected return of
(25% x 7%) + (25% x (7% + 6.56%)) + (50% x 3%) = 6.64%
But of course we have added more risk to get the higher expected return. What if we would be happy with the 6% return but we want to lower our risk.
We can do that by lowering the overall equity allocation from 50% to 42% of our portfolio.
(21% x 7%) + (21% x (7% + 6.56%)) + (58% x 3%) = 6.06%
We now have the same expected return of 6% as the initial case where we held 75% stocks, but now with only 42% of our portfolio in stocks. This is known as diversified risk. We still have risk that will give an expected return of 6%, but we have diversified that risk by using the total stock market risk combined with small-cap value stock risk.
No one can accurately predict the future, but the Fama-French 3-factor model shows us other opportunities for either increasing our return, or diversifying our risk.
Figure 1: Relationship between risk factors and expected return