Residual Momentum OLS Regression (Model 02) | KoshX Learning
Isolating true idiosyncratic stock alpha from market beta using 126-day rolling ordinary least squares regression on Nifty 50 constituents.
Empirical Quantitative Methodology
Residual momentum decomposes individual stock returns into market-driven beta and idiosyncratic company alpha via a 126-day rolling Ordinary Least Squares (OLS) regression against Nifty 50. Stocks with the highest positive standardized residuals represent true institutional accumulation independent of macro market beta.
R_{i,t} - R_{f,t} = \alpha_i + \beta_i (R_{m,t} - R_{f,t}) + \epsilon_{i,t}, \quad \text{Score}_i = \frac{\bar{\epsilon}_i}{\sigma_{\epsilon_i}}
Frequently Asked Questions
What is the difference between total price momentum and residual momentum?
Total price momentum measures a stock’s absolute percentage return, which is heavily contaminated by broad market beta (when Nifty rises 5%, almost every stock rises). Residual momentum strips away the market tide using linear regression: R_i(t) = alpha_i + beta_i * R_m(t) + epsilon_i(t). It identifies stocks with genuine institutional accumulation independent of macro index rallies.
Why regress against Nifty 50 rather than sector indices?
Regressing against the broad market benchmark (Nifty 50) isolates macro risk factor exposure. If an individual sector surges, stocks in that sector with positive residual alpha are outperforming both the broad market and their peers.
How does residual momentum prevent buying bull-market traps?
During speculative market rallies, high-beta cyclical stocks surge simply because beta is high (e.g. beta = 2.2). When the market corrects, these high-beta stocks crash hardest. Residual momentum filters these out, favoring stocks with high positive residuals (true alpha) rather than high beta.