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Fama-French Three Factor Model

Fama-French defined the size premium as the difference in returns between the largest stocks and the smallest stocks in the CRSP database. They defined the value premium as the difference in returns between the stocks with the 30% highest Book to Market Ratios (BTM) and the 30% lowest BTM.

So, the formula becomes the sum of:

The zero risk returnThe market premium (Beta)Size PremiumValue PremiumThe impact of management (Alpha)Random Error

In a particular time frame, none of these market factors is necessarily positive. However, over longer periods the premiums are persistent and generous. Value is more persistent than size but both are worthy of the investor's attention.

It's important to note that size and value risks are different than the market risk, but do not necessarily add total risk to the portfolio (at least as measured by standard deviation). So, a portfolio tilted away from the center of the market will act differently from the market, but will not necessarily have more risk.

The further you tilt the portfolio, the less it will look like the more commonly reported indexes. So, an investor that can't stand having different performance than his neighbor's ought not to tilt his portfolio very far, even if doing so might increase his total performance over the long haul. His mental "tracking error" against the nightly news might make the portfolio unsuitable for him.

Investment advisors understand that they can get fired for looking too different from everybody else. So, they tend to gravitate toward the center of the market. The Wall Street default strategy is "Don't stand out, don't get fired." Unfortunately, that strategy stands little chance of systematically achieving returns above market.

In general, small stocks do add volatility to a portfolio, but value stocks do not. Under Modern Portfolio Theory these risks may be partially offset by mixing asset classes with low correlations to existing assets. For instance, foreign small stocks have a very low correlation to US stocks, adding a diversification benefit that actually reduces risk at the portfolio level.

Going back to our theoretical portfolio, suppose that it was tilted strongly toward both small and value. The calculation for expected return might look like this:
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