@MASTERSTHESIS\{IMM2012-06369,
    author       = "M. S. Helledie",
    title        = "Statistical analysis of Exchange Traded Funds for investment purposes",
    year         = "2012",
    school       = "Technical University of Denmark, {DTU} Informatics, {E-}mail: reception@imm.dtu.dk",
    address      = "Asmussens Alle, Building 305, {DK-}2800 Kgs. Lyngby, Denmark",
    type         = "",
    note         = "Supervised by Associate Professor Lasse Engbo Christiansen, lec@imm.dtu.dk, {DTU} Informatics, and Kourosh Marjani Rasmussen, {DTU} Management",
    url          = "http://www.imm.dtu.dk/English.aspx",
    abstract     = "The aim of the thesis is twofold. First the thesis sets out to examine the replicative capacity of 20 widely diversified exchange traded index funds. The means is an analysis and subsequent modelling of the deviance of returns, over the life time of the funds. The life time of the considered funds span from 5 to 12 years. It is shown that the deviance processes, with one exception, can be modelled in an {ARMA-GARCH} framework with mean deviances in the range of [-4.57e-{3,} 3.81e-3] on weekly returns and [-1.13e-{3,} 8.54e-4] on daily returns. Considering correlation between returns, one out of 20 funds is only vaguely correlated in weekly returns, while this is true for four out of 20 funds considering daily returns. the remaining pairs of fund and index returns are highly correlated. It is thus concluded that on the bottom line the funds do in fact replicate the indices.
Given the replicative capacity of the funds, deduced from the close correlation and low mean deviance, a selection of the underlying indices are applied as proxies for the funds in a scenario generation intended to form the basis of a portfolio optimisation. The indices are considered due to lack of historic information on the funds. Four methods are applied and evaluated for four point predictions, namely bootstrapping, an {ARMAGARCH} model, a Markov Switching Autoregressive model and lastly a dependent mixture model. While the first two models consider the index returns in their entirety, the latter two part data into regimes and estimate separate models in each regime. The models are further distinguished as the dependent mixture model considers the market, as represented by the selected indices, in its whole, while the three models consider each asset individually.
It is found that bootstrapping returns in an attempt to predict new ones falls short in capturing the economic changes, relative to the remaining models. {ARMA-GARCH} and the Markov Switching autoregressive model perform roughly equal in generating out of sample predictions, altough with a favour towards {ARMA-GARCH} which is generally more accurate. The dependent mixture model is the preferred model amongst the considered, for portfolio optimisation purposes, due to its superior ability to adequately reflect the financial situation."
}