We study a stochastic programming approach to multicriteria multi-period portfolio optimization problem. We use a Single Index Model to estimate the returns of stocks from a market-representative index and a random walk model to generate scenarios on the possible values of the index return. We consider expected return, Conditional Value at Risk and liquidity as our criteria. With stocks from Istanbul Stock Exchange, we make computational studies for the two and three-criteria cases. We demonstrate the tradeoffs between criteria and show that treating these criteria simultaneously yields meaningful efficient solutions. We provide insights based on our experiments.