An Introduction to Financial Markets

Part Three Equity portfolios

Chapter Seven Decision-Making under Uncertainty: The Static Case

Uncertainty is the rule in most financial decision-making problems. The prototypical case is the allocation of wealth to a set of assets with uncertain returns. If we make a here-and-now decision and observe the return of the portfolio after a given holding period, we are considering a static decision problem, since we disregard the possibility of adjusting our decisions along the way, when we observe the actual unfolding of uncertain risk factors. This is not to say that, in reality, the portfolio will not be adjusted after a while, possibly by solving the same model again; the point is that this is not explicitly considered in the decision model itself. On the contrary, multistage decision models take into account the possibility of updating decisions, depending on the incoming information flow over time. It is important to avoid a potential confusion between multistage and multiperiod models. A multiperiod problem requires the planning of decisions to be executed over a sequence of time instants. However, if the plan is specified here and now, once for all, the problem is actually static, as there is no dynamic adaptation. The solution of a multiperiod problem is a sequence of numbers, representing the decisions that are supposed to be implemented, no matter what. On the contrary, the solution of a multistage problem consists of a set of random variables, since decisions will ...