The mathematical underpinnings of beta coefficients are considered so elegant, they could be works of art. They were also considered groundbreaking enough to help a couple of economists win the Nobel Prize. But for investors, you can just consider them bunk. Investment analysts rely on beta coefficients to help determine the risk of one stock against the risk of the broader market. Most fund companies list the betas with their funds to help you measure your risk. For example, a fund with a beta of 0.80 is expected to advance about 80% of whatever the market -- or S&P 500 -- has gained. The complete mathematical basis is more complex, with a risk-free rate of return, such as that from short-term Treasury bills, factored in. But if the last three years are any indication, beta coefficients simply don't work. TheStreet.com Ratings tested to see whether beta coefficients for the three-year period ended April 30, 2004, helped determine relative returns for the subsequent three years ending April 30, 2007. The test was limited to diversified, domestic open-end growth funds. Further, it was limited only to those most closely correlated with the S&P 500 for the three years ended in April 2004. The correlations were gauged by the funds' respective R-squared values, which are measures of how closely the movements of the funds correspond to those of the S&P 500. Funds with R-squared values of 95.00 or greater, expressed in percentage term, were included, producing a sample of 99 open-end mutual funds. The graph below is a "scatter diagram" showing the relationship of the funds' beta coefficients compared with their rates of return, and they weren't much help in predicting how the funds would perform for the subsequent three years.