Calibration of shrinkage estimators for portfolio optimization

Shrinkage estimators is an area widely studied in statistics. In this paper, we contemplate the role of shrinkage estimators on the construction of the investor's portfolio. We study the performance of shrinking the sample moments to estimate portfolio weights as well as the performance of shrinking the naive sample portfolio weights themselves. We provide a theoretical and empirical analysis of different new methods to calibrate shrinkage estimators within portfolio optimizationPortfolio choice, Estimation error, Shrinkage estimators, Smoothed bootstrap

Parameter uncertainty in multiperiod portfolio optimization with transaction costs

We study the impact of parameter uncertainty in the expected utility of a multiperiod investor subject to quadratic transaction costs. We characterize the utility loss associated with ignoring parameter uncertainty, and show that it is equal to the product between the single-period utility loss and another term that captures the effects of the multiperiod mean-variance utility and transaction cost losses. To mitigate the impact of parameter uncertainty, we propose two multiperiod shrinkage portfolios and demonstrate with simulated and empirical datasets that they substantially outperform portfolios that ignore parameter uncertainty, transaction costs, or both

What multistage stochastic programming can do for network revenue management

Airlines must dynamically choose how to allocate their flight capacity to incoming travel demand. Because some passengers take connecting flights, the decisions for all network flights must be made simultaneously. To simplify the decision making process, most practitioners assume demand is deterministic and equal to average demand. We propose a multistage stochastic programming approach that models demand via a scenario tree and can accommodate any discrete demand distribution. This approach reflects the dynamic nature of the problem and does not assume the decision maker has perfect information on future demand. We consider four different methodologies for multistage scenario tree generation (MonteCarlo sampling, principalcomponent sampling, moment matching, and bootstrapping) and conclude that the sampling methods are best. Finally, our numerical results show that the multistage approach performs significantly better than the deterministic approach and that revenue managers who ignore demand uncertainty may be losing between 1% and 2% in average revenue. Moreover, the multistage approach is also significantly better than the randomized linear programming approach of Talluri and Van Ryzin [22] provided the multistage scenario tree has a sufficiently large number of branches

Portfolio Investment with the Exact Tax Basis via Nonlinear Programming

Computing the optimal portfolio policy of an investor facing capital gains tax is a challenging problem: because the tax to be paid depends on the price at which the security was purchased (the tax basis), the optimal policy is path dependent and the size of the problem grows exponentially with the number of time periods. Dammon et al. (2001, 2002, 2004), Garlappi et al. (2001), and Gallmeyer et al. (2001) address this problem by approximating the exact tax basis by the weighted average purchase price. Our contribution is threefold. First, we show that the structure of the problem has several attractive features that can be exploited to determine the optimal portfolio policy using the exact tax basis via nonlinear programming. Second, we characterize the optimal portfolio policy in the presence of capital gains tax when using the exact tax basis. Third, we show that the certainty equivalent loss from using the average tax basis instead of the exact basis is very small: it is typically less than 1% for problems with up to 10 periods, and this result is robust to the choice of parameter values and to the presence of transaction costs, dividends, intermediate consumption, labor income, tax reset provision at death, and wash-sale constraints.portfolio choice, capital gains tax, optimization, nonlinear programming