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Paathshaala : R Squared

r2 (Correlation Coefficient)

r2 is a measure of the association between a fund and its benchmark. Values are between 0 and 1. 1 indicates a perfect correlation and 0 indicates no correlation. This measure is useful in determining if the fund manager is adding value in their investment choices or acting as a closet tracker mirroring the market and making little difference. For example, an index fund will have an R-squared with its benchmark index very close to 1, indicating close to perfect correlation (the index fund's fees and tracking error prevent the correlation from ever equalling 1).

In statistics, the coefficient of determination r2 is the proportion of variability in a data set that is accounted for by a statistical model. In this definition, the term "variability" stands for variance or, equivalently, sum of squares. There are equivalent expressions for r2. The version most common in statistics texts is based on an analysis of variance decomposition as follows:

r2 = RSS/TSS = 1-(ESS/TSS)

In the above definition,

RSS : Residual Sum of Squares
TSS : Total Sum of Squares
ESS : Explained Sum of Squares

r2 is the statistic that will give information about the goodness of fit of the model. It has a drawback: r2 increases as we increase the number of variables in the model (r2 will not decrease), so the alternative technique is to look for adjusted r2 .

In finance, r2 measures how well the Capital Asset Pricing Model (CAPM) predicts the actual performance of an investment or portfolio

The r2 of a fund advises investors, if the beta of a mutual fund is measured against an appropriate benchmark. Measuring the correlation of a fund’s movements to that of an index, R- squared describes the level of association between the fund’s volatility and market risk, or more specifically, the degree to which a fund’s volatility is a result of the day to day fluctuations experienced by the overall market.

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