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
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.