Adjusted R-squared is nothing but the change of R-square that adjusts the number of terms in a model. Adjusted R square calculates the proportion of the variation in the dependent variable accounted by the explanatory variables.
A fund has a sample R-squared value close to 0.5 and it is most likely offering higher risk-adjusted returns with the sample size of 50 for 5 predictors.
Sample size = 50 Number of predictors = 5 Sample R -square = 0.5
Adjusted R square value
Substitute the values in the formula,
| R2adjusted | = 1 - ( 1 - 0.52)(50 - 1) / (50 - 5 -1) |
| = 1 - (0.75) x (49 / 44) | |
| = 1 - 0.8352 | |
| = 0.1648 |
