R-Squared

Reflects the percentage of a portfolio's movements that can be explained by movements in its benchmark.

4Overview of R-Squared

70-100% = good correlation between the portfolio's returns and the benchmark's returns  

40-70% = average correlation between the portfolio�s returns and the benchmark's returns

1-40% = low correlation between the portfolio�s returns and the benchmark's returns

4Use of R-squared

An R-squared of 100 indicates that all movements of a portfolio can be explained by movements in the benchmark. Thus, index funds that invest only in S&P 500 stocks will have an R-squared very close to 100. Conversely, a low R-squared indicates that very few of the portfolio's movements can be explained by movements in its benchmark index. An R-squared measure of 35, for example, means that only 35% of the portfolio�s movements can be explained by movements in the benchmark index.

4Calculation

CVxy = covariance between portfolio and benchmark

Vx = variance of benchmark

Vy = variance of portfolio

R2 = CVxy2 /(Vx *Vy)

4Example

For this example, the plots are near the best-fit line so the fund would have a high R2 in relation to this index:

 

This fund's points are not very close to the line, and don't describe a line well. Therefore, it would have a low R2:

 

4References

  Modern Portfolio Statistics Research Paper