The random walk hypothesis is an important area of research in finance and many tools have been proposed to investigate the behaviour of the fluctuations in stock prices. However, a detail study on emerging Asian stock markets which employ the various unit root tests has not been done. In this paper, we employ six different unit root tests such as the Augmented Dickey and Fuller test (1979), Phillips and Perron test (1988), Kwiatkowski-Phillips-Schmidt-Shin test(1992), Dickey-Fuller GLS (ERS) test (1996), Elliot-Rothenberg-Stock Point-Optimal test (1996) and Ng and Perron (2001) unit root tests on 10 emerging Asian stock markets to detect for the presence of a random walk in stock prices. We have conducted the unit root tests during different sub-sample time periods of global financial crisis to check for robustness. To be specific, we have found that during the overall sample period (2001-2015) 8 out of 10 Asian stock markets and during the pre-crisis period (2001-2007) all the 10 Asian stock market prices do follow random walk according to the unit root tests under consideration. However, during the crisis & post-crisis period (2008-2015) we have found only 5 out of 10 Asian markets follow the random walk movement based on unit root tests.