Sophisticated vs Naive Diversification: The Optimal Trade-off

This thesis operates in a Modern Portfolio Theory framework, but in a critical way. The objective is to understand if it is possible to improve optimal strategies by combining them with the naive diversification rule.
By definition, all the optimal (or sophisticated) strategies require for their implementation the estimation of some statistics relative to the return distributions of the assets considered, namely the expected value and/or the variance-covariance matrix. These estimates rely on unbiased estimators, which, however, could suffer from a considerable variance, stemming from the relatively short time series of returns used to conduct the estimations. It follows that the estimation errors could make the mathematical methods underlying the optimal strategies output weights, which are far from the true optimal ones. Instead, the weights of a naive diversification strategy, which equally allocates the capital across the assets considered, do not rely on any type of estimate. Consequently, they are not subject to variance, but are clearly biased with respect to the optimal weights computed by an optimization strategy.
Therefore, in line with Tu and Zhou (2011), we combine equally weighted and optimally weighted portfolios in order to find out the best trade-off between bias and variance of the weight estimators. This way, we can achieve a better capital allocation and make the out-of-sample optimal portfolios perform closer to their in-sample counterparts.
Furthermore, we discuss separately the impact of estimation errors and the impact of transaction costs on performances, in order to achieve a better understanding of the single components which affect the risk-adjusted returns of the uncombined and combined strategies.