Beta and R-squared are two related, but different, measures. A mutual fund with a high R-squared correlates highly with a benchmark. If the beta is also high, it may produce higher returns than the benchmark, particularly in bull markets.
R-squared measures how closely each change in the price of an asset is correlated to a benchmark. Beta measures how large those price changes arein relation to a benchmark. Used together, R-squared and beta give investors a thorough picture of the performance of asset managers.
Key Takeaways
- R-squared measures how closely the performance of an asset can be attributed to the performance of a selected benchmark index.
- R-squared is measured on a scale between 0 and 100; the higher the R-squared number, the more correlated the asset is to its benchmark.
- Beta measures the volatility of an asset compared to its benchmark.
- A mutual fund with a beta of 1.0 is exactly as sensitive, or volatile, as its benchmark, whereas a fund with a beta of 1.20 is 20% more sensitive or volatile.
- Used in conjunction with alpha, R-squared and beta are valuable measures investors can review to determine how effective a fund manager is at capturing profit when a benchmark is also profiting.
R-Squared Measures Benchmark Correlation
R-squared is a measure of the percentage of an asset or mutual fund's performance as a result of a benchmark. Fund managers use a benchmark to evaluate the performance of a mutual fund. For example, a mutual fund might use the S&P 500 as its benchmark index. The goal of the fund would be to closely track or mirror the performance of the S&P 500 index.
Price charts that plot R-squared values are useful to help investors see the relationship between the movement of the mutual fund's price compared to its benchmark.
R-squared measures the degree to which the fund's performance can be attributed to the performance of the selected benchmark index. R-squaredis reported as a number between 0 and 100. A hypothetical mutual fund with an R-squared of 0 has no correlation to its benchmark at all. A mutual fund with an R-squared of 100 matches the performance of its benchmark precisely.
Beta Measures Volatility
Beta is a measure of a fund or asset's sensitivity to the correlated moves of a benchmark. Beta measures the systematic risk or volatility of an asset, security, or fund compared to its benchmark. Volatility is often associated with the wide swings in prices seen with securities in the stock market.
Understanding volatility is important because high volatility indicates the price of a stock can change dramatically in either direction over a short time period.
A mutual fund with a beta of 1.0 is exactly as sensitive, or volatile, as its benchmark. A fund with a beta of 0.80 is 20% less sensitive or volatile, and a fund with a beta of 1.20 is 20% more sensitive or volatile.
Alpha Measures an Asset Manager's Performance
Alpha is a third measure, which measures asset managers' ability to capture profitwhen a benchmark is also profiting. Alpha is reported as a number less than, equal to, or greater than 1.0.
The higher a manager's alpha, the greater the manager's ability to profit from moves in the underlying benchmark. Some top-performing hedge fund managers have achieved short-term alphas as high as 5or more using the Standard & Poor's 500 Index as a benchmark.
When using alpha to measure a manager's performance, it's important for investors to compare funds that are in the same asset class. Funds in different asset classes can have different levels of risk.
For example, if an investor is interested in investing in a mutual fund that focuses on small-cap companies, then a comparison of similar mutual funds would generate a more meaningful alpha. Comparing small-cap companies to large-cap companies would be less meaningful because the risks associated with each type of company differ.
What Does R-Squared Tell You in Investing?
In the investment world, the statistical figure of R-squared indicates how close the performance of a specific asset correlates to the performance of a specific benchmark. The R-squared scale ranges from 0 to 100 and the higher it is, the more correlated the performance of the asset is to the performance of the benchmark.
What Is a Good R-Squared for a Mutual Fund?
A fund that tracks an index should have performance results that are similar to that of an index. This is particularly important in investing as an investor should know what their expected returns will be. The R-squared scale ranges from 0 to 100, with 100 indicating that a fund's performance is highly correlated with the index it tracks. A fund that has an R-squared between 85 to 100 is considered one with a good R-squared. A fund with an R-squared of 70 or less is considered a poor R-squared.
Are High R-Squared and Betas Good?
Yes, the higher the R-squared and the higher the beta, the better the performance will be of an asset or fund. A higher R-squared indicates a strong correlation to a benchmark. Coupled with a high beta, the asset will most likely perform better than the benchmark.
The Bottom Line
The alpha and beta of assets with R-squared figures below 50 are thought to be unreliable because the assets are not correlated enough to make a worthwhile comparison. A low R-squared or beta does not necessarily make an investment a poor choice, it merely means its performance is statistically unrelated to its benchmark.
FAQs
Beta and R-squared are two related, but different, measures. A mutual fund with a high R-squared correlates highly with a benchmark. If the beta is also high, it may produce higher returns than the benchmark, particularly in bull markets.
What is the relationship between R-squared and beta? ›
A fund with a high r-squared closely tracks the benchmark's return. If it also has a high beta, above 1, that could mean outperforming the benchmark in a rising stock market—or doing worse than the benchmark when markets are declining.
What is the relationship between R and beta in a simple regression? ›
Beta coefficient (i.e., standardized regression slope) and r would be equal only when X and Y have equal SDs, because Beta = Cor (Y, X) * SD (Y)/ SD (X) in a regression equation with only one predictor (i.e, Yi = a + BXi + ei). In this way, Beta cannot be the same as r, except for when the SDs are equal.
What is the relationship between beta and correlation? ›
Beta gives the magnitude of the move, while correlation tells about the directional relationship. Beta is mainly relevant in the investment world. Tells us about how much risk an investment adds to the underlying portfolio. Correlation has wider applications outside of finance as well.
What does alpha beta and R-squared mean? ›
Beta is the slope of this line. Alpha, the vertical intercept, tells you how much better the fund did than CAPM predicted (or maybe more typically, a negative alpha tells you how much worse it did, probably due to high management fees). The quality of the fit is given by the statistical number r-squared.
What does R-squared tell you about correlation? ›
The R-squared value, denoted by R 2, is the square of the correlation. It measures the proportion of variation in the dependent variable that can be attributed to the independent variable. The R-squared value R 2 is always between 0 and 1 inclusive.
What does R2 tell us about the relationship between variables? ›
R-squared is a statistical measure that indicates how much of the variation of a dependent variable is explained by an independent variable in a regression model.
What is a good R-squared value? ›
A R-squared between 0.50 to 0.99 is acceptable in social science research especially when most of the explanatory variables are statistically significant.
How to interpret beta coefficient in R? ›
The interpretation of beta coefficients in a linear regression model is dependent on the units of the predictor variables. For example, if the predictor variable is age and the beta coefficient is 2, this means that for a one-year increase in age, the dependent variable is expected to change by 2 units, on average.
What does a β indicate regression? ›
The parameter β (the regression coefficient) signifies the amount by which change in x must be multiplied to give the corresponding average change in y, or the amount y changes for a unit increase in x.
B is an unstandardized coefficient which means original units besides the slope and tell if the independent variable is a significant predictor of the dependent variable. Beta is a standardised coefficient between -1 to +1 in range and show the strength of the prediction.
What is a good beta for a correlation? ›
Most investors understand beta more easily by example. A stock that tracks the market perfectly has a beta of 1, in that its returns always match the overall market. A stock with a beta of 2 that's perfectly correlated with the market has returns that are twice as extreme as the market's returns.
What does an R-squared value of 0.3 mean? ›
We often denote this as R2 or r2, more commonly known as R Squared, indicating the extent of influence a specific independent variable exerts on the dependent variable. Typically ranging between 0 and 1, values below 0.3 suggest weak influence, while those between 0.3 and 0.5 indicate moderate influence.
What does R-squared and p-value mean? ›
The greater R-square the better the model. Whereas p-value tells you about the F statistic hypothesis testing of the “fit of the intercept-only model and your model are equal”. So if the p-value is less than the significance level (usually 0.05) then your model fits the data well.
Is R-squared a measure of risk? ›
R-Squared (R²) is one of the statistical tools to measure the risk of a mutual fund. R-squared compares the performance of a mutual fund scheme to a given benchmark index. There are tools like alpha, beta as well, which measure the risk of a mutual fund in other ways.
What is beta in regression in R? ›
Beta regression. The class of beta regression models, as introduced by Ferrari and Cribari-Neto (2004), is useful for modeling continuous variables y that assume values in the open standard unit interval (0,1). Note that if the variable takes on values in (a, b) (with a < b known) one can model (y − a)/(b − a).
What is the difference between R value and beta value? ›
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.
What is the beta coefficient in regression in R? ›
Beta coefficients are regression coefficients (analogous to the slope in a simple regression/correlation) that are standardized against one another. This standardization means that they are “on the same scale”, or have the same units, which allows you to compare the magnitude of their effects directly.
What is the relationship between the linear coefficient R and the slope b1 of a regression line? ›
Answer and Explanation:
r is the correlation coefficient; is the slope of the regression equation. As the relation shared by r value and slope coefficient b1 is directly proportional . So, both values must contain the same sign.
