R-Squared (R2): How Closely Can Performance Be Explained by a Benchmark?

R-squared (R2) is a statistical measure that represents the proportion of the variance of a dependent variable that is explained by one or more independent variables in a regression model.

In finance, R2 is typically calculated for a security vs a benchmark and can be thought of as the percentage of a security's movements that can be explained by movements in the benchmark.

R2 Formula

There is a complex formula for calculating R2, but we will refrain from going into that in this post. The simplest way to calculate R2 is to use the RSQ function in Excel. If you know programming languages, such as Python or R, there are built-in functions for R2 you can use.

R2 can be calculated for an individual security, a fund (e.g. ETF or mutual fund), or an entire portfolio.

Understanding R2

R2 values range from 0 to 1. An R2 value of 1 means that all of the movements of a security are completely explained by movements in the benchmark. The opposite is true for a security with an R2 of 0.

In finance, an R2 greater than 0.85 is generally considered to be high. A security with a high R2 will generally move in line with the benchmark. On the other hand, an R2 below 0.7 is considered to be moderate to low. A security with a low R2 does not generally follow the movements of the benchmark.

R2 vs Correlation

Although in finance, R2 is often thought of as a measure of correlation, it is not technically correlation. In statistics, the correlation coefficient is known as R. R2 is simply the square of R. Since most of us aren't statisticians, it can be helpful to think of R2 as related to correlation instead of using the technical definition, which many find harder to understand.

So What?

R2 is an important metric for portfolio management. In particular, it can tell you how diversified your portfolio is. Diversification helps to mitigate systematic risk.

If you find your portfolio's R2 to be too high, you can take steps to reduce it. For example, large-cap stocks tend to have a high correlation with common benchmarks, such as the S&P 500. If you wanted to reduce your portfolio's R2, you could increase your exposure to mid and small-cap stocks. You could also increase your exposure to sectors and markets that have a lower correlation with the S&P 500 (e.g. emerging markets).

On the other hand, perhaps your goal is to track a benchmark as closely as possible. In this case, you would want to make sure your R2 is as high as possible. The easiest thing to do here would be to simply buy an ETF that tracks the index in question.

R2 is also useful for evaluating a fund's returns. If a fund performs well but has a high R2, then that fund is said to have highly correlated returns. That is, most of the fund's returns can be explained by the benchmark. Therefore, the fund will likely have a low level of alpha, and you would be better off buying an ETF that tracks the benchmark in question instead of investing in the fund itself. On the other hand, if a fund performs well and has a low R2, it is said to have uncorrelated returns. This means that the fund is providing real alpha that cannot be easily replicated by others. In this case, the fund would be a good investment.

Limitations

Although R2 will give you an estimate of the correlation between your portfolio and a benchmark, it doesn't tell you whether your portfolio construction and/or strategy is good or bad. You would also want to evaluate other key metrics, such as alpha, beta, and volatility, to better understand your portfolio's performance.

How alphaAI Can Help

At alphaAI, our goal is to minimize our strategies’ R2 values. Doing so enables us to deliver returns that are uncorrelated with the market, and, in turn, reduces risk and maximizes alpha. Learn more about our low R2 strategies here.