R-Squared

R-squared (R²) is a coefficient of determination that expresses how much of the variation in one variable is explained by another. In trading and portfolio analysis, R-squared measures how much of a portfolio's or strategy's returns are explained by its benchmark — typically the S&P 500 (SPY). A value of 0.95 means 95% of the portfolio's price movements track the benchmark, leaving only 5% attributable to the manager's specific choices or alpha-generating skill. A value of 0.20 means the portfolio moves largely independently of the market. R-squared ranges from 0 to 1 (or 0% to 100%). It is not directional — a high R-squared only means strong explanatory power, not positive correlation. Understanding R-squared is prerequisite to correctly interpreting alpha, beta, and active return.

R-squared values create a practical spectrum for evaluating strategy independence from the broad market. An R-squared above 0.85 suggests the strategy behaves very similarly to a passive index fund. For active strategies charging management fees or requiring significant effort to run, this raises the question of whether the manager is adding value beyond simple market exposure. R-squared between 0.50 and 0.85 is common for diversified active strategies that maintain some market sensitivity while generating uncorrelated returns on a meaningful portion of the portfolio. R-squared below 0.30 indicates a highly independent strategy — pure alpha generators, market-neutral strategies, and alternative risk premia tend to fall here. For day traders and systematic traders, a moderate R-squared is often desirable: enough market correlation to benefit from broad bull markets, but enough independence to generate returns when the broader market is flat or declining.

Beyond portfolio benchmarking, R-squared appears in regression analysis embedded in technical indicators. The Linear Regression indicator plots a best-fit line through recent prices, and its R-squared value tells you how well prices are adhering to a linear trend. A high R-squared (above 0.8) on a price regression confirms a strong, consistent trend; prices have been moving in a disciplined linear fashion. A low R-squared (below 0.3) indicates noisy, trendless price action where linear regression is a poor model. Some traders use R-squared as a regime filter — applying trend-following strategies only when R-squared confirms a clean trend, and switching to range-trading strategies when R-squared is low. This adaptive use of R-squared as a regime indicator is more sophisticated than using price alone to identify trend vs. chop.

R-squared and correlation are mathematically related — R-squared equals the square of the Pearson correlation coefficient for simple two-variable regressions. But they convey different information. Correlation (ranging from -1 to +1) describes the direction and strength of a linear relationship between two variables. R-squared (ranging from 0 to 1) describes only the strength of that relationship, not its direction. A correlation of -0.90 and a correlation of +0.90 both produce an R-squared of 0.81. For portfolio analysis, this distinction matters: a strategy with -0.90 correlation to SPY (strongly inverse, like a short-biased fund) has the same R-squared as a strategy with +0.90 correlation (strongly positive). Both have 81% of their variance explained by the benchmark, but their behavior in bull markets is opposite.

In multi-factor models (Fama-French three-factor, Carhart four-factor, or custom factor models), R-squared indicates how well the chosen set of risk factors explains a strategy's returns. A high R-squared from a multi-factor regression means most of the strategy's returns can be attributed to known systematic risk factors — size, value, momentum, profitability. What remains unexplained is the true idiosyncratic alpha. A strategy showing a compelling positive alpha in a single-factor model (CAPM) but near-zero alpha in a five-factor model likely has returns explained by factor exposures rather than genuine skill. This is why sophisticated performance analysis always reports R-squared alongside alpha: alpha is only as meaningful as the R-squared of the model used to calculate it. Tradewink reports R-squared alongside alpha in its strategy analytics so traders can contextualize whether their edge is factor-driven or genuinely uncorrelated.