Estimation methodology for portfolio construction under uncertainty
Portfolio selection is a financial decision problem faced by all investors. Private investors, companies or financial institutions need to decide on how to invest in assets by selecting a portfolio according to some optimality criterion and under possible constraints. Expressed in mathematical terms, the portfolio optimization problem involves quantities which are usually estimated from historical data. Such estimates are accompanied by uncertainty which, via the optimization process, is transferred to the investment decisions, thus rendering many portfolio estimators unstable or unreliable. This thesis approaches the problem from two angles. On the one hand, we propose an improvement of the sample moments plug-in estimator through its bootstrap distribution. A robust measure of location of this distribution results, on average, in better out-of-sample performance, especially when the original estimator exhibits high instability, as illustrated by simulations. On the other hand we propose an alternative way of choosing the optimal intensity of two shrinkage estimators. These estimators stabilize the portfolio by applying shrinkage towards desirable targets. In the first case, these targets are the conventional ones for the mean and the covariance matrix, whereas in the second case we allow for additional market information to be included. Our method again uses bootstrap resamples to account for each estimator's possible out-of-sample performance. Finally, we consider the problem from a practitioner's perspective by including transaction costs. We exploit a striking similarity between the new optimization problem and the lasso estimator, a variation of the ordinary least squares estimator. We modify accordingly and extend further an existing algorithm for the solution of this problem and present the results. The new algorithm allows for additional constraints on the model coefficients and could be useful in a regression framework when assumptions on the coefficients' sign or magnitude are made.