Investigating the Investment Opportunities, Uncertain Implicit Transaction Costs and Maximum Downside Risk in Dynamic Stochastic Financial Optimization

Individual investors, investment managers and fund managers are all concerned with achieving
optimal portfolios of a set of investment assets. Regardless of whether portfolios are selected for a
bank’s derivative mix, an investor’s equity holdings or a firm’s asset and liability management, the
common objective in all models is the minimization of some measure of risk while maximizing some
reward measure. A dynamic stochastic methodology in optimal portfolio selection that maximizes
investment opportunities and minimizes maximum downside risk while taking into account implicit
transaction costs incurred in initial trading and in subsequent rebalancing of the portfolio is proposed.
The famous mean-variance (MV) model [1] and the mean absolute deviation (MAD) model [2] both
penalize gains (upside deviations) and losses (downside deviations) in the same way. However,
investors are concerned about downside deviations and are happy of upside deviations. Hence the
proposed model penalizes only downside deviations and, instead, maximizes upside deviations. The
methodology maintains transaction cost at the investor’s prescribed level. Dynamic stochastic
programming is employed with stochastic data given in the form of a scenario tree. Consideration a
set of discrete scenarios of asset returns and implicit transaction costs is given, taking deviation
around each return scenario. Model validation is done by comparing its performance with those of the
MV, MAD and minimax models. The results show that the proposed model generates optimal
portfolios with least risk, highest portfolio wealth and minimum implicit transaction costs.