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?
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.
“Alpha” refers to the excess performance of a fund after it has been adjusted for risk or “Beta.” Beta is typically characterized as “market risk.” We would measure the correlation between a particular manager’s fund and the overall stock market. For example, if the fund goes up by 20% when the market goes up by 15%, then we would say that the fund has a Beta of 1.33. Because the fund is more volatile than the overall market, we would expect the fund to outperform the overall market overtime. This might have nothing to do with skill by the fund manager, rather just the particular set of stocks the fund has exposure to. Once we control for Beta, then we can see how much “Alpha” the manager is able to generate above what we would expect to be compensated for in terms of market risk.
It is important to note, there have been advancements in the field of financial economics in terms of Beta. Multiple Betas have been discovered such as market capitalization (size), relative price (value), profitability, and momentum. We must control for all of these factors before we can attribute “alpha” to a particular fund manager.
R-squared measures how much the variability in returns for a particular fund is explained by the benchmark. In other words, it measures how well the benchmark tracks the overall performance of the fund. We would typically want to see something above 0.95, which means that the benchmark tracks the fund over 95% of the time. This is important because we want to make sure we are properly benchmarking a particular fund. If there is a substantial mismatch between the benchmark and the fund, then we may be making false conclusions about metrics such as “alpha.” A practical example would be to compare a manager who focuses on International Growth Stocks to the S&P 500. Two completely different samples and therefore it is not a proper benchmark.