The optimal time to buy and hold stock in a reversal

Investors cannot anticipate a return reversal in the stock market. Therefore, choosing the optimal time to buy and hold a stock is vital. This paper formulates a disorder problem using the optimal stopping theory to study the optimal time to buy and hold a stock when a downward trend is about to reverse. The results show that investors should buy a stock when the conditional probability of a return reversal hits an optimal boundary for the first time. The optimal boundary is uniquely determined by the stock return, volatility, and the intensity of return reversal. Moreover, the optimal boundary decreases as the stock volatility and the intensity of return reversal increase. We use the China Securities Index 300 (CSI 300), Standard & Poor's 500 (S&P 500), Dow Jones Industrial Average (DJIA), and Russell 2000 indexes to estimate the parameters and the related optimal boundary. We find that the estimated optimal boundary can be used to time stock buying.