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Constant asset returns and undefined R-squared

With no asset-return variation, slope can be zero while correlation and R² are undefined.

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Use an original constant asset record

Suppose benchmark returns are −1%, 0% and 1%, while the asset return is always 2%. The fitted line has slope zero and intercept 2%, with every residual zero. Benchmark variation still identifies the slope.

Inspect the total centered sum

Asset total centered sum Syy is zero. The R² expression 1−SSE/Syy then divides zero by zero. Correlation also divides by asset dispersion, so it is not defined by its usual formula.

Read the different outputs

Constant asset case
QuantityStatus
Slope0, identified
Intercept2% per period
Residual error0
Correlation/R²Undefined ratios

Avoid a fabricated fit score

The tool omits correlation and R² instead of inventing a 100% explained-variation value. A constant observed record also does not establish that the asset has no future risk.

Further references