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The value of R square would not decrease when more variables are added to the model. As a result, there is always a temptation to add more variables in the model, because of which problem can arise therefore in that case Adjusted R2 is used as a measure.
R-squared does not, however, measure the performance of a portfolio, but it does measure the correlation of the portfolio's returns to the benchmark's returns. If an investor is seeking a portfolio or a fund that moves like the benchmark it would be wise to invest in a product or strategy with a high R-squared number.