R² · coefficient of determination
R-squared
The percentage of a fund's return variability explained by its benchmark. R² of 0.95 on a NZ-equity benchmark means 95% of the fund's movement tracked that benchmark.
R-squared (R², the coefficient of determination) is the share of variance in a fund's returns that is explained by movements in its benchmark. R² of 1.0 means the fund moves entirely with the benchmark; R² of 0.0 means there is no statistical relationship.
R² is used as a sanity check on beta and tracking error. A high R² (above 0.90) makes beta meaningful — the relationship to the benchmark is strong enough that beta describes most of the fund's movement. A low R² (below 0.50) suggests the benchmark is a poor reference: the fund's return is being driven by exposures the benchmark doesn't capture.
For NZ index funds tracking a published benchmark, R² is typically 0.97 or higher. For diversified-multi-asset funds, R² against any single benchmark is usually lower because the fund's asset mix moves with several benchmarks at once.
Related terms
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beta
Beta
A measure of how much a fund moves in response to its benchmark. Beta of 1 means the fund moves one-for-one with the benchmark; beta of 0.7 means it moves 30% less.
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tracking-error
Tracking error
The standard deviation of a fund's return differences against its benchmark. For an index fund, low tracking error means tight replication; for an active fund, high tracking error means more active risk relative to benchmark.
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index-vs-active
Index fund vs active fund
An index fund mechanically tracks a published market index. An active fund's manager makes discretionary buy/sell decisions trying to beat or differ from a benchmark.