What is R-Squared?

B is correct. Fund A's R-squared of 0.95 (95%) means that 95% of its movement is explained by S&P 500 movements, indicating it closely tracks the benchmark with minimal deviation. Fund B's R-squared of 0.65 (65%) means only 65% of its movement is explained by the S&P 500, with 35% coming from other factors like manager stock selection, sector tilts, or company-specific events. Both have the same beta (1.15), but Fund B's beta is less reliable as a predictor because of the significant non-market influences.

A is incorrect because R-squared does not measure volatility; both funds have identical beta (1.15), which indicates similar systematic volatility. Higher R-squared indicates correlation strength, not volatility level. C is incorrect because lower R-squared does not necessarily mean better diversification; it means the portfolio behaves differently from the benchmark, which could be due to concentration risk, active management, or different market segment exposure. D is incorrect because lower R-squared actually makes beta LESS reliable, not more reliable. When R-squared is low (below 0.70-0.85), beta becomes a poor predictor of portfolio behavior because much of the portfolio's movement is not explained by market movements.

D is correct. R-squared can be expressed either as a decimal from 0 to 1.0 or as a percentage from 0% to 100%; both representations are mathematically equivalent and commonly used. An R-squared of 0.85 is the same as 85%. The value represents the proportion (or percentage) of a portfolio's variance that is explained by the benchmark's variance.

A is incorrect because R-squared cannot be negative. While the correlation coefficient ranges from -1.0 to +1.0, R-squared is the square of correlation, which eliminates negative values. An R-squared of 0 means no linear relationship with the benchmark, and 1.0 (or 100%) means perfect positive correlation. B alone is incomplete because while technically correct for the decimal representation, R-squared is also commonly expressed as a percentage (0% to 100%). C alone is incomplete for the same reason; the percentage scale (0% to 100%) is correct but doesn't acknowledge the decimal representation.

C is correct. An R-squared of 0.42 (42%) means that only 42% of the fund's price movements can be explained by movements in the S&P 500, with the remaining 58% due to other factors (sector-specific trends, individual stock selection, etc.). This low R-squared indicates that beta relative to the S&P 500 would not be a reliable predictor of the fund's behavior, since most of its movement is driven by non-market factors. This is expected for a sector fund compared to a broad market index.

A is incorrect because R-squared of 0.42 indicates that the correlation coefficient is approximately 0.65 (the square root of 0.42), not 42%. R-squared is the square of the correlation coefficient. B is incorrect because R-squared does not predict the magnitude of declines; that is determined by beta. R-squared only tells you how much of the fund's variance is explained by the benchmark's variance. D is incorrect because R-squared measures statistical relationship (explained variance), not portfolio composition. A fund could have high R-squared with a benchmark without holding any of the same stocks, or vice versa.

C is correct (the EXCEPT answer). R-squared does NOT range from -1.0 to +1.0; it always ranges from 0 to 1.0 (or 0% to 100%). R-squared is the square of the correlation coefficient, and squaring any number always produces a non-negative result. Even if correlation is negative (inverse relationship), R-squared is still positive because squaring eliminates the sign. For example, a correlation of -0.8 produces R-squared of 0.64 (64%), not negative.

A is accurate: R-squared specifically measures the proportion (percentage) of a portfolio's variance that can be explained by variance in the benchmark index. An R-squared of 0.80 means 80% of the portfolio's movement is explained by the benchmark. B is accurate: when R-squared is high (typically above 0.85 or 85%), the portfolio moves closely with the benchmark, making beta a reliable predictor of how the portfolio will respond to market movements. D is accurate: low R-squared (typically below 0.70) indicates that much of the portfolio's movement cannot be explained by the benchmark, suggesting significant unsystematic (non-market) risk from factors like sector concentration, individual stock selection, or style tilts.

B is correct. Statements 1, 2, and 3 are accurate, but statement 4 is not necessarily true.

Statement 1 is TRUE: Beta of 1.20 means the fund is 20% more volatile than the Russell Midcap Growth Index. When the index moves 10%, the fund would be expected to move approximately 12%. Higher beta indicates greater systematic volatility relative to the benchmark.

Statement 2 is TRUE: R-squared of 0.88 (88%) means that 88% of the fund's price variance can be explained by variance in the Russell Midcap Growth Index. The remaining 12% is explained by other factors like individual stock selection, sector tilts, or timing differences.

Statement 3 is TRUE: R-squared of 0.88 is above the 0.85 threshold generally considered to indicate high correlation. This high R-squared means the fund tracks the benchmark closely, making the beta of 1.20 a reliable predictor of how the fund will behave when the benchmark moves.

Statement 4 is FALSE: While the high R-squared indicates the fund moves closely with its benchmark, this does not necessarily mean unsystematic risk has been eliminated. The fund could still have significant concentration in individual stocks or sectors within the mid-cap growth universe. R-squared measures explained variance relative to the benchmark, not diversification quality. A concentrated portfolio of 15 mid-cap growth stocks could have high R-squared to the index but still carry substantial unsystematic (company-specific) risk.