We document a directional asymmetry in the small stock concurrent and lagged response to large stock movements. When returns on large stocks are negative, the concurrent beta for small stocks is high, but the lagged beta is insignificant. When returns on large stocks are positive, small stocks...

This paper uses a Markov chain model to test the random walk hypothesis of stock prices. Given a time series of returns, a Markov chain is defined by letting one state represent high returns and the other represent low returns. The random walk hypothesis restricts the transition probabilities of...