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## R2

Barron’s defines R2 as a mutual fund term indicating “on a scale of 0 to 100, the percentage of a fund’s performance…explained by movements of its benchmark index.” For example, if the benchmark was the S&P 500, the typical large cap blend fund would likely have an R2 of > 90%. R2 can be used to gauge relevancy of a fund’s beta; the higher the R2, the greater the importance of beta.

A correlation measures the relationship between two securities or benchmarks, usually a return correlation, often abbreviated as correlation (a scale ranging from -1.0 to +1.0). R2 is similar except it is limited to the return correlation of a benchmark or index; the two most commonly used benchmarks for U.S. investors are the S&P 500 and the Barclays Aggregate Bond Index. The website statisticshowto.com points out R2 is the “square of the correlation coefficient (hence the term R2). For example, when a person gets pregnant has a direct relation to when they give birth.” Any statistical inference from R2, sometimes referred to as Pearson’s correlation coefficient, is sensitive to the sample distribution. The closer return distribution resembles a bell-shaped curve, the greater the R2 predictibility.

An excellent stock portfolio can have a very low R2 since R2 is simply a measure of portfolio return correlation to the benchmark. In the case of U.S. stocks, the most commonly used benchmark is the S&P 500. For example, if the XYZ Large Cap Growth Fund had an R2 of 60, 60% of its movements are expected to be explained by S&P 500 movements. According to Morningstar, the general range for R2 is: 70-100% = good return correlation between the portfolio and benchmark; 40-70% = average correlation; and 1-40% = low correlation. According to Mathbits.com, “a correlation > 0.8 is generally described as strong, whereas a correlation of < 0.5 is generally described as weak.

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