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.

 "BETAS" & FUND RETURNS: A CORRELATION? Click here for larger image. Source: TheStreet.com Ratings

As you can see, the majority of the plots, which represent certain mutual funds, fall well below or above the "expectations line." Had the beta coefficients more accurately predicted the relative performance, the majority of the dots on the graph would cluster along that line.

We computed an "expected" return for each of the funds on the basis of its April 2004 beta coefficient and then calculated the difference -- as measured in percentage points of three-year total returns -- between the beta coefficient and the funds' subsequent returns. We identified the funds that most exceeded their expected returns and those that lagged by the most percentage points.

The beta coefficient is considered a measure of "market risk" by many analysts. Therefore, a tendency to exceed the return indicated by a fund's beta coefficient can be described as a "risk-adjusted" return.

For example, the beta coefficient of 0.80 for the Fidelity ( FDEQX) Disciplined Equity Fund (FDEQX) indicated that it should have advanced less than the S&P's 12.24% annual rate over the past three years. But it surpassed its "expected" return of 10.49% by a whopping 4.87 percentage points per year.

Similarly the Fidelity ( FTXMX) Tax Managed Stock Fund FTXMX), with a beta of 1.04, would have been expected to perform slightly better than the S&P -- at an annual rate of 12.59%. Instead, it roared ahead at an annual pace of 16.71%.

On the other hand, the T. Rowe Price ( PTEGX) Tax Efficient Growth Fund (PTEGX), with a beta of 1.06, was expected to outpace the annual growth of the S&P and return 12.77% annually. Its actual annual total return of 6.73% was barely half the growth rate predicted by its beta coefficient.

An even greater shortfall, vis-a-vis its beta-generated expectations, was suffered by the American Century ( TWCIX) Select Investment Fund (TWCIX). The fund's expected return, according to its April 2004 beta of 0.86, was 11.02% annually. The actual annual rate of gain for the three years was a sluggish 4.38%.

Richard Widows is a financial analyst for TheStreet.com Ratings. Prior to joining TheStreet.com, Widows was senior product manager for quantitative analytics at Thomson Financial. After receiving an M.B.A. from Santa Clara University in California, his career included development of investment information systems at data firms, including the Lipper division of Reuters. His international experience includes assignments in the U.K. and East Asia.