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One time-honored rule in the field of finance is that risk and return are related. Often called the "no free lunch" principle, it asserts that over the long run it is not possible to achieve exceptional returns without accepting substantial risk. Any standard equilibrium model of asset pricing justifies this relationship. Data from Ibbotson Associates confirm that since 1926, U.S. common stocks have provided a total return of 10.7% per year, about seven percentage points greater than the return from riskless Treasury bills.
RISK AND RETURN ACCORDING TO THE CAPITAL ASSET PRICING MODEL
For decades, the standard way to model the risk/return relationship and to measure risk has been to use the capital asset pricing model (CAPM), the product of William Sharpe [1964] and others. The CAPM insight is that volatility arising from specific events (called specific, or idiosyncratic, risk) can be eliminated in a diversified portfolio, and that investors will not be paid for bearing these risks with extra returns.
But volatility resulting from general movements in stock prices and the tendency of all stocks to fluctuate to some extent in sympathy cannot be diversified away. According to the CAPM, the risk variable that will be (linearly) related to return is beta, the measure of relative volatility, or systematic risk. The higher the beta of an individual stock or portfolio, the higher the returns an investor should expect.
Unfortunately, theory and practice do not always accord. In a remarkable article, Eugene Fama and Kenneth French [1992] find that over a twentyseven-year period, from 1963 through 1990, returns and the beta measure of risk appeared to be completely unrelated.
Fama and French divide all stocks in their sample into ten subsamples according to their market capitalization (a measure of size). Within each subsample, they construct ten portfolios according to their beta levels, for a total of a hundred portfolios each year. They could then test whether size or beta is more effective in explaining the cross-section of returns, and whether beta could explain the pattern of stock returns within size deciles.
We have constructed the same hundred portfolios using a somewhat larger sample through 1994. For illustrative purposes, we group our sample of stocks into ten portfolios according to beta. In other words, decile 1...