| Summary: | 碩士 === 國立清華大學 === 統計學研究所 === 103 === Markowitz's celebrated Mean-Variance model is the most popular method used in asset allocation for searching an optimal portfolio. Such an optimization relies on the independent and identically distributed (i.i.d.) assumption for the underlying multiple return series, as well as the known parameter values for the mean and covariance matrix. But, in practice, the mean and covariance matrix are unknown and have to be estimated from historical data. Many studies have found that the optimal portfolio based on the estimated parameters performance not well. The reason is mainly due to the estimation errors. Therefore, using more robust estimations would generally enhance the empirical performance of Markowitz's optimal portfolio. To justify the advantage of using more robust methods in determining the portfolio, this thesis compares different estimation methods in terms of several performance measures, including the efficiency frontier, Sharpe ratio, estimation error for the portfolio weights and Frobenius norm for the covariance matrix. The methods considered include the shrinkage estimates, the estimates using factor models, and the NPEB methods. Besides the i.i.d. modeling, the vector AR modeling is also considered for examining its advantage in asset allocation. Based on the simulation results, we found that shrinkage and factor model methods perform better when short position is allowed but the advantage is insignificant when short position is not allowed.
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