In this paper, the authors describe a simple procedure for blending statistical estimates with expert opinions to produce a forward-looking view of the performance of assets. They discuss the impact of behavioural biases on the views and propose general modelling principles to biases. Standard...

We derive and interpret the mathematical principles for portfolio selection. We show these principles not only guarantee efficiency and value-adding, but also ideally address Treynor and Black (1973)’s long-standing normative call for reconciling subjective analyst views with objective...

Despite foreign reserves' strategic asset allocation relies mainly on Modern Portfolio Theory (MPT), the unique characteristics of central banks obliges them to articulate and reconcile typical optimization procedures with reserves' management objectives such as providing confidence regarding...

Unknown model parameters, like expected returns, cannot be accurately estimated from short samples. Respective estimation error most likely leads to the portfolio, inconsistent with its target risk/return profile. We investigate the ways of reducing the impact of estimation error on portfolio...

We consider the problem of maximizing expected utility for a power investor who can allocate his wealth in a stock, a defaultable security, and a money market account. The dynamics of these security prices are governed by geometric Brownian motions modulated by a hidden continuous time finite...

All the financial practitioners are working in incomplete markets full of unhedgeable risk-factors. Making the situation worse, they are only equipped with the imperfect information on the relevant processes. In addition to the market risk, fund and insurance managers have to be prepared for...

We demystify why, after 70 years of the Markowitz Modern Portfolio Theory (MPT) publication, the investment-management industry still persistently favours some seemingly disconnected rules-of-thumb or behaviours (e.g., equal-weighting, risk-parity, factor-ranking etc.), and validate the...

The Black-Litterman model is one of the most popular models in quantitative finance, with numerous theoretical and practical achievements. From the standpoint of investment theory, the Black-Litterman model allows a seamless incorporation of Bayesian statistics into the portfolio optimization...

The authors propose a general framework referred to as Black-Litterman-Bayes (BLB) for constructing optimal portfolios for factor-based investing. In the spirit of the classical Black-Litterman model, the framework allows for the incorporation of investor views and different priors on factor...