First, a bit of background. Alpha, Beta, Sharpe, and R2 are metrics that were proposed over 50 years ago by academics (like Eugene Fama and William Sharpe) that sought to understand financial markets. It was part of a model known as CAPM (Capital Asset Pricing Model) which is one of the only unified frameworks unique to the discipline of finance. Since then, the market has changed significantly, and so has the state-of-the-art in mathematical/statistical technology. These changes brought about huge criticism of the aforementioned metrics (see, for instance, limitations of the sharpe ratio or the shortcomings of CAPM) and propositions for newer metrics.
For example, the Sharpe ratio is returns adjusted by both downside and upside volatility, or in other words, a portfolio is considered risky if it has above-average performance on certain days—this doesn’t make much sense. As an alternative, more robust measures such as the Sortino Ratio have come about, where the returns are only adjusted to downside risk.
Assuming we’re going to use these metrics anyway, here is a brief tutorial:
Alpha is the return over the benchmark (positive means you’re beating the benchmark). Beta is a measure of how closely your portfolio moves with the market (+1 means it moves closely with the market, >1 means it tends to move with the market but with larger swings, and 0 means it moves on its own and has little or no relationship with the market, <0 means it moves in the opposite direction). Sharpe is mentioned above and R2 is a measure of how closely your portfolio tracks the market (an R2 of 100 means perfect tracking while 0 means no tracking at all).
Portfolio managers, or people from more traditional financial backgrounds tend to prefer Beta = 0 and Alpha > 0 (known as a market-neutral active strategy), but this is exactly the reason why most of them fail: this is not something that can be achieved consistently. You may have seen this in your own research and there is data to support these findings.
The ideal passive strategy for the SP500, on the other hand, would have an Alpha of 0, Beta of 1, Sharpe of 0.5 (since this is roughly the Sharpe of the SP500 historically) and R2 of 100. If your portfolio has an Alpha of 12% (0.12), Beta of 1.08, and Sharpe Ratio of 1, this means you outperform the benchmark by about 12% every year (alpha), you tend to move closely with the market (beta), and your risk-adjusted returns are twice that of the SP500 (Sharpe Ratio). R2 may not be important to you in this case since you are not attempting to perfectly track the index, you want to beat it.