Portfolio Optimization Under Tracking Error and Weights Constraints

Abstract

The performance of active portfolio managers who must comply with a weights constraint is often assessed against a benchmark. The weights constraint is common as the funds are committed by their own prospectus to a minimum (or maximum) portfolio concentration. We characterize the optimal asset allocation and analyze the implications of the weights constraint on the manager's performance and on the relevance of the information ratio. We obtain that because of the weights constraint, at the optimum, the information ratio often decreases when the manager is free to deviate more from the benchmark.

A Martingale Approach to Optimal Portfolios with Jump-diffusions

“…as µ π (t) = r(t) + π(t) ⊺ α(t) − π(t) ⊺ σ(t)π(t) and was dened in (3.18). If one chooses π such that the growth rate µ π is maximized, then one obtains, by setting the rst derivative of µ π with respect to π equal to zero, the growth optimal portfolio by 4) where λ are the market prices of risk given by λ(t) := ξ(t) −1 α(t). The portfolio π * as dened in (5.4) is called the growth optimal portfolio process and maximizes the long term performance of a wealth process (cf.…”

A Numerical Study for Robust Active Portfolio Management with Worst-Case Downside Risk Measure

“…The notation "= (≤ )" means the equality only (or inequality only) weights constraint. Under the estimation of and Σ is exactly obtained and selling short is allowed, Bajeux-Besnainou et al [36] considered the following active portfolio optimization problem with single weight constraint:…”

“…Our model can be extended to the case of parameters uncertainty, for which parameters are not estimated exactly. Similar to Erdog an et al [33] and Bajeux-Besnainou et al [36], we normalize the benchmark portfolio w ;that is, e w = 1 and introduce a new variable y = w − w . Notice the w = y + w ; then optimization problem (7) with multiple equality weights constraints can be written into the following form: We call y a self-financing portfolio and w a fully investing portfolio.…”

“…If = 0, that is, there is not weights constraint, then problem (25) is nothing but Roll's VTE problem. If = 1, that is, = e 1 , then problem (25) becomes the case of single weight constraint problem which has been considered by Bajeux-Besnainou et al [36].…”

“…However, it is to be regretted that weights constraint is rarely used in the current tracking error (robust) portfolio literature. Recently, Bajeux-Besnainou et al (2011) [36] first introduce this kind of constraint into a mean-variance index tracking portfolio model. In their paper, Bajeux-Besnainou et al described a comparison with and without weights constraint and showed that the influence of weights constraint is very remarkable and cannot be ignored for the returns of portfolio.…”