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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.

Mostra/Nascondi contenuto.
9 2. Literature review In his seminal paper on portfolio selection, the father of the Modern Portfolio Theory (MPT), Harry Markowitz, suggests an interpretation of risk in terms of variance (Markowitz, 1952). To understand why, assume that individuals are risk-averse, so that we can describe their preferences with a concave utility function. This way, starting from an initial wealth w0, the disutility of losing an amount x of money will be always higher, in absolute terms, than the utility of gaining the same amount. Moreover, given the decreasing marginal utility of wealth, this gap will become bigger and bigger as we increase the x. It follows that such an investor would rather invest in assets with more stable and less volatile returns. More specifically, the mean-variance framework, built by Markowitz, allows constructing a portfolio efficient frontier using the assets traded in a particular market. In other words, we can estimate standard deviations and expected returns of the assets considered and, solving a relatively simple minimization problem with respect to the standard deviation of the portfolio made of these assets, find the less volatile portfolio for each level of expected return. A rational mean-variance investor will consider only efficient portfolios to allocate her wealth, her exact choice depending on the particular shape of her utility function. Although this framework is more than sixty years old, it is still widely used by investment professionals and performance measures based on a concept of risk in terms of standard deviation, like the Sharpe ratio (Sharpe, 1966) and the certainty equivalent (based on the utility function of a mean-variance investor),

Laurea liv.II (specialistica)

Facoltà: Economia

Autore: Marco Foggia Contatta »

Composta da 61 pagine.


Questa tesi ha raggiunto 168 click dal 20/09/2016.

Disponibile in PDF, la consultazione è esclusivamente in formato digitale.