We study how three large emerging equity markets, Brazil, China, and India, move together. The window runs from January 2017 to June 2026 and covers 2,151 matched daily observations of each market's headline index in local currency, measured in natural logarithms. We use a transparent time-series toolkit. Augmented Dickey-Fuller tests, complemented by Phillips-Perron and KPSS tests, place all three series in the same class: each index has a unit root in levels and becomes stationary after one difference. Johansen trace and maximum-eigenvalue tests then search for a shared long-run path and find none, and a break-robust test that allows for the pandemic and the 2022 rate shock confirms this absence of a common trend. The short run tells a different story. Estimated on stationary daily returns within a multivariate framework that controls for global-market movements, and using the Toda-Yamamoto procedure with a correction for multiple testing, the results reveal a set of short-run lead-lag linkages in which Brazil tends to lead both China and India while receiving little in return; India mostly follows and China sits between the two. These are predictive return linkages rather than evidence of structural causation or volatility spillovers. For portfolio design the reading is indicative: because the markets share no long-run tie, the long-run diversification case for holding all three appears intact, though, since returns are measured in local currency and no dollar-denominated or back tested portfolio is estimated, a formal claim for a U.S. investor would require dollar returns and an explicit portfolio exercise. The same investor should still anticipate quick short-run co-movement, typically led by Brazil.