R-Squared vs. Beta: An Overview
Most stock investors are familiar with the use of beta and alpha coefficients to understand how particular securities performed against a market index, but R-squared is also a useful tool for the investor.
- Beta is an estimate of the marginal effect of a unit change in the return on a market index on the return of the chose security.
- R-squared (R2) is an estimate of how much beta and alpha together help to explain the return on a security, versus how much is random variation.
These statistics can both indicate how closely the movement of one investment parallels the movement of an index over time. Beta can be used to estimate the size of the direct relationship between the market and the security. R-squared is used to determine the reliability of the relationship between the index on one hand and alpha and beta on the other.
- A stock's beta indicates how closely its price follows the same pattern as a relevant index over time.
- R-squared indicates how closely alpha and beta reflect a stock's return as opposed to how much is random or due to other unobserved factors.
- Both statistics are useful for understanding the relative risk and return on a security.
Beta is a numerical representation of how much the return of an overall market index impacts the return on a chosen security. A beta of 1 indicates that an increase (or decrease) in the market index return is associated with an equal increase (or decrease) in the return on the selected security. Beta greater than 1 means that the chosen security is more sensitive to the return on its general market index, and beta less than one is relatively insensitive to overall market returns. Negative values on beta mean that the selected security tend to have an inverse relationship to its overall market rate of return.
Finding two perfectly related (beta equal to 1) securities is highly unusual. Readings below 1 indicate the security is less volatile than the benchmark, while readings of exactly 1 indicate its price should move with the benchmark. Readings greater than 1 indicate the asset is more volatile than the benchmark.
On the other hand, the alpha coefficient is often viewed as a key performance indicator for stock funds. Alpha is a measure of the risk-adjusted performance of a fund or asset compared to a benchmark index. An alpha of 1.0 indicates that the investment outperformed the index by 1%. An alpha of less than 0 indicates that the investment returned less than the benchmark, adjusted for their respective volatility.
R-squared (R2) is a method an investor or analyst can use to see how well alpha and beta capture the relationship between the return on a security and the return on the overall market. R2 is also called the coefficient of determination, or the proportion of the variation in the security's return that is determined by the market return given the estimated values of alpha and beta.
As an investor, you want to know how your holding is doing over time against the benchmark index (shown by the size of alpha and beta), but you also want to know how reliable the relationship (expressed by alpha and beta) is between that security and the overall market.
R2 defines the practical value of alpha and beta on a scale from 0 to 1. A high R-squared number (from .85 to 1) indicates that alpha and beta together explain much of the variation in the returns on a security. A low R2 (anything below .7, though this is arbitrary) indicates that there is little relationship between the performance pattern of the security as estimated by alpha and beta and that of the index. Instead the returns on the security may be more random, or may be explained by unobserved factors other than the market index return.
You can determine R2 by using a standard formula. Some mutual fund companies report the R2 of their funds in their advertising literature, but others do not. Yahoo Finance and Morningstar calculate and publish R2 data as well as beta figures daily.
In general, investments with a high beta reading are seen as relatively risky. Stocks with a high beta will tend to rise more quickly than their benchmarks in bull markets and fall more quickly in bear markets. However, one should also consider R2, because it indicates the reliability of alpha and beta, because high (or low) beta with a low R2 may not be all that meaningful, or may even be deceptive to the unwary. On the other hand a high R2 suggests that the given estimates of alpha and beta should be taken more seriously.