Convex combinations of long memory estimates from different sampling rates

Convex combinations of long memory estimates using the same data observed at different sampling rates can decrease the standard deviation of the estimates, at the cost of inducing a slight bias. The convex combination of such estimates requires a preliminary correction for the bias observed at lower sampling rates, reported by Souza and Smith (2002). Through Monte Carlo simulations, we investigate the bias and the standard deviation of the combined estimates, as well as the root mean squared error (RMSE), which takes both into account. While comparing the results of standard methods and their combined versions, the latter achieve lower RMSE, for the two semi-parametric estimators under study (by about 30% on average for ARFIMA(0,d,0) series).

The growing importance of the ETF industry - the pros and cons of passive management

O objectivo deste projecto é a comparação entre os prós e contras de gestão passiva e ativa através da realização de um estudo estatístico de várias estratégias através dos Exchange-Traded Funds. Em particular, a análise vai passar pela estratégia mais passiva, ou seja, buy and hold, para um grau diferente de active indexing management, tais como rotações do sector e / ou classe de ativos com base no bottom-up, top-down e indicadores técnicos. A análise mostra que as estratégias ativas, se forem devidamente aplicadas, conseguem obter retornos ajustados ao risco substancialmente superiores quando comparados com uma abordagem passiva, superando as questões de custos de transação e diversificação que normalmente são reivindicadas por uma gestão passiva.

Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.