We develop a new test for threshold-type regime changes in the risk exposures in portfolios with a large number of financial assets whose returns exhibit an approximate factor structure. Unlike existing procedures to detect discrete shifts in factor models, our test is robust to regime-specific second moment of the common factors. We rely on an auxiliary threshold regression: we take a weighted cross-sectional average of the cross-sectional units; we estimate the factors from the original model under the null hypothesis of no regime changes; we construct a Lagrange multiplier statistic to test for threshold effect in the auxiliary regression. Numerical results show the good finite sample properties of our procedure. The empirical analysis uncovers the dynamics of portfolio weights and diversification benefits in factor mimicking portfolios across different regimes.