Reliability assessment of scenarios generated for stock index returns incorporating momentum

Stochastic programming models for portfolio optimization rely on scenario paths for returns derived from stochastic process models. This paper investigates a variant of the geometric Brownian motion process for stock index returns that incorporates index momentum. Based on this model, three different processes for generating scenarios on a rolling basis are devised, which differ according to how frequently the momentum parameter is updated and whether it is estimated according to a simple moving average or an exponentially weighted moving average of returns. The reliability of scenario sets generated for multiple instances is assessed by applying a recently developed statistical tool. Backtesting is conducted in case studies of the Standard & Poor's 500 Index and the Financial Times Stock Exchange 100 Index for two different historical periods. The numerical results show that the frequency with which the expected return is updated does not significantly influence the performance of the scenario generation procedure, whereas how the expected return is calculated affects the autocorrelation and dispersion of generated scenarios drastically. All scenario generation schemes are highly sensitive to the estimated volatility of the index returns. Among the three processes tested, the algorithms that incorporate momentum estimates according to an exponentially weighted moving average can generate reliable scenarios when the volatility estimation error is small.