Parameter Uncertainty in Multiperiod Portfolio Optimization with Transaction Costs

Abstract

We study the impact of parameter uncertainty on 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 data sets that they substantially outperform portfolios that ignore parameter uncertainty, transaction costs, or both.

How much should portfolios shrink?

“…The above finding conveys an important message as the deviation penalty models with resemble the models that take transaction costs into account (e.g., Gârleanu & Pedersen, ; DeMiguel et al., ; Olivares‐Nadal & DeMiguel, ). Shrinking toward the current portfolio does improve portfolio performance but is less effective than shrinking toward the equal‐weight portfolio regardless of transaction costs.…”

Untitled

“…The variant of the equation (1) with  equal to 1, which means that market impact is linear in the traded volume, is used, for example, in [DeMiguel et al 2014]. The linear dependence of market impact on the transaction volume can be partly justified in financial market microstructure theory by the Kyle model [Bouchaud 2009].…”

Portfolio Selection Based on Bayesian Theory

“…One of the implications is that the Bayesian theory can be mainly used to estimate the uncertain returns or other factors (such as a shrinkage estimator and so on) in portfolio [15,[25][26][27][28][29]. In addition, for the parameter uncertainty of portfolio selection, in other words, for the estimation risk evaluation or the estimation error correction, researchers also tend to choose Bayesian methods [4,[30][31][32][33][34]. Besides, the Bayesian theory is also used in model analysis [35], risk measurement or return-risk trade off [36], portfolio optimization [37,38], and so on.…”