This paper explores the role of portfolio constraints in generating multiplicity of equilibrium.  We present a simple asset market economy with two goods and two households, households who face constraints on their ability to take unbounded positions in risky stocks. Absent such constraints, equilibrium allocation is unique and is Pareto efficient. With a single portfolio constraint in place, the efficient equilibrium is still possible; however, additional inefficient equilibria in which the constraint is binding may emerge. We show further that with sunspots, there may be a continuum of equilibria; sunspots may lead to real indeterminacy. Extending our analysis of sunspot phenomena to three periods, we show that our model is also capable of generating moves in stock prices unrelated to so-called fundamentals; such movements are triggered purely by sunspots which only affect investors' (rational) expectations about future market behavior. This provides a simple, coherent explanation for the apparent inability of empirical studies to link many sharp price movements in stock markets to news about economic fundamentals.