Investing in the stock market requires an investor to study multiple elements to decide whether to invest in a stock. One such method that analysts commonly use is regression analysis. Regression analysis helps to find alpha, beta, and R-squared provide insights into stock movement.
In this blog, let's break down R-squared in depth to understand- what it means and how you can use it for your stock analysis.
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What is R-squared?
R-Squared (R²), also known as the coefficient of determination, is a metric used in regression analysis to quantify the degree to which the variability of a dependent variable can be accounted for by one or more independent variables.
A higher R-squared value shows a strong correlation between the stock/ mutual fund and its benchmark. This means the stock's performance is largely correlated to the benchmark's movement.
Index funds aim to replicate their benchmark accurately and will have high R-squared values. Active equity funds outperform the benchmark and may have lower R-squared values since their portfolios don’t match the index.
There is also something known as the adjusted R-squared. It is a refined version of R-squared that accounts for independent variables in the model. It shows whether adding more variables will enhance the model's performance.
Unlike R-squared, which can increase with the addition of any predictor, adjusted R-squared only improves if the new predictors contribute meaningfully.
How does an R-Squared Works?
R-Squared values range from 0 to 100 and show the extent to which a fund's movements are influenced by its benchmark index. R-squared cannot be negative. A value of 0 means that the independent variables do not explain any of the variation in the dependent variable and a value of 1 shows that the model perfectly fits the data.
- 100% R-Squared: It means that the fund's movements are entirely explained by the benchmark. Index funds or Nifty50 mutual funds that track the Nifty 50 have R-squared values near 100.
- Low R-Squared: This means that the benchmark has low influence on the fund's performance. For example, an R-Squared of 18 means only 18% of the fund's movements are explained by the benchmark.
R-Squared Formula
R-Squared is expressed as a percentage between 0 and 100 and can be categorised into three tiers based on its value.
R-Squared Formula =(Correlation)^2
Correlation=Cov(Benchmark,Portfolio)/(SD of Portfolio×SD of Benchmark)
- Covariance shows how two variables move together.
- Standard Deviation (SD) shows the amount of variation or dispersion of a set of values.
By understanding and calculating R-Squared, investors can better assess how closely a mutual fund follows its benchmark, aiding in more informed investment decisions.
Relationship Between R-Squared and Beta
Beta is a statistical measure that assesses the risk of a mutual fund by showing its volatility compared to a benchmark. It shows how much a fund’s price fluctuates compared to the benchmark’s movements.
In mutual fund analysis, a beta of 1 means that the fund's volatility mirrors that of the benchmark index. This means the fund’s price changes are in line with the index. A beta greater than 1 shows higher volatility than the benchmark, while a beta below 1 suggests lower volatility.
R-squared and beta provides a complete view of a fund’s performance. For example, a high beta with a low R-squared implies that, despite the fund being volatile, its movements aren’t closely aligned with the benchmark. Therefore, relying solely on beta could be misleading if the R-squared is low.
When used in tandem, R-squared and beta offer investors a detailed understanding of how an asset manager is performing in relation to the benchmark.
Using R-Squared for Investment Decisions
In conclusion, R-squared alone provides very limited insights into a portfolio’s performance. Calculating R-squared requires statistical expertise and is most effective when used across all funds in a portfolio.
For meaningful comparisons, R-squared should be evaluated alongside beta or alpha. R-squared is a valuable tool that helps in investment research but it should not be the sole factor in decision-making.
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