What is the relationship between alpha, beta, and r-squared when analyzing a fund?

I'm curious about alpha, beta, and r-squared. I have researched funds where the fund outperforms the index, but the alpha is negative with a high r-squared. Does r-squared need to be close to 100 to use alpha and beta?

Mutual Funds
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May 2016

Alpha is how much more or less return the fund has relative to a benchmark. For example, if the benchmark is the S&P 500 (the 500 largest US companies), it has an average annual return in a year of 8%. If the alpha of that fund is 1.2%, then it performed 1.2% better than the benchmark.  

Beta describes risk. The benchmark beta is always 1.0. If the fund has a beta of 1.3, then it has more risk than the benchmark with potentially more volatility but it may have more potential for higher returns or lose more than the benchmark. If the fund has a benchmark of 0.7, then it has less risk than the benchmark. It is common to have growth equity funds with a beta higher than the benchmark and value equity funds with a beta lower than the benchmark.

R Squared describes how much the fund is like the benchmark in terms of its holdings. If the R Squared is 0.92, the holdings are very similar to the benchmark. The lower the number, the less likely the fund is relative to the benchmark.  

June 2016