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Abstract:
Active portfolio management is about leveraging forecasts. The Black and Litterman Global Portfolio Optimisation Model (BL) (Black and Litterman, 1992) sets forecast in a Bayesian analytic framework. In this framework, portfolio manager (PM) needs only produce views and the model translates the views into security return forecasts. As a portfolio construction tool, the BL model is appealing both in theory and in practice.

Although there has been no shortage of literature explaining it, the model still appears somehow mysterious and suffers from practical issues. This paper is dedicated to enabling better understanding of the model itself through:
- An economic interpretation
- A clarification of the model assumptions and formulation
- An implementation guidance
- A full proof of the main result in the appendix

To make the model practical, we also discuss a dimension-reduction technique to enable large portfolio applications; and form a checklist of other practical issues that we aim to address in our forthcoming papers.

asset allocation, portfolio construction, Bayes' Rule, view blending and shrinkage, CAPM, semi-strong market efficiency, mean-variance optimisation

Abstract:
The Fama and French (1992 and 1993 etc.) factor ranking approach is very popular among quantitative fund managers. However, this approach suffers from hidden factor view, loss of information, etc. issues. Based on the Black-Litterman model (Black and Litterman, 1992; as explained in Cheung, 2009A), we design a technique that endogenises the ranking process and elegantly resolves these issues. This model explicitly seeks forward-looking factor views and smoothly blends them to deliver robust allocation to securities. Our numerical experiments show this is an intuitive and practical framework for factor-based portfolio construction, and beyond. The paper is featured by:

- A new and unified framework for strategy combination, factor mimicking and security-specific bets
- An elegant and ranking-free approach to factor style construction
- Worked examples based on the FTSE EUROTOP 100 universe
- Insight into the classic issue of confidence parameter setting
- An implementation guidance in the appendix

asset allocation, portfolio construction, Bayes' Rule, Black-Litterman, view blending and shrinkage, CAPM, semi-strong market efficiency, Fama-French, factor ranking, factor risk model, mean-variance optimisation, robustness

Abstract:
You have some factor, strategy, and/or stock-specific alpha ideas. Without an optimiser, some straightforward linear algebra gives you the diversified and efficient Bayesian allocation that allows greater performance accountability. All you need is just a factor risk model. How does this sound‘ This paper derives a transparent version of the ABL model (Cheung, 2009B) with an explicit allocation expression, including components for all the needed functionalities. In addition to further insights, it allows more tangible implementation of strategy combination, factor mimicking, hedging, and stock-specific bets in a unified framework. More specifically, it enables the following:

- A unified, open, and optimiser-free allocation framework with parsimonious use of risk model
- Modularised alpha generation: 'portable alphas' with Bayesian assembly
- Implied new efficient techniques respectively for strategy combination, composite factor mimicking, hedging, and stock-specific betting
- Deeper insight into the ultimate Bayesian allocation mechanism
- Complete guidance on Black-Litterman practical issues, making the technique genuinely practical
- An interface between the art and science of portfolio construction

portfolio construction, Bayes' Rule, Augmented Black-Litterman (ABL), view blending and shrinkage, semi-strong market efficiency, Fama-French, factor ranking, factor risk model, optimisation, robustness, portable alpha, strategy combination, factor mimicking, hedging, stock-specific betting

Abstract:
Traditional equity risk models focus on estimating stock return variance-covariance matrix. Ignoring high-order moments, they implicitly assumes normal return distributions. The recent credit crisis has reminded us again that the normality assumption is insufficient in risk management. Moving away from normality requires a tractable technique to allow investigation of alternative distributions. Copula is a good choice since it helps modulise our job and enriches our distribution selection menu.

This paper aims to demystify copulas for equity portfolio managers by addressing the following questions:1) What is copula and what does it represent 2) With correlation as a commonly used dependence measure, why is copula worth the extra complexity 3) What is 'tail dependence' 4) What are Gaussian, t-, Clayton, Gumbel and Frank copulas; how do they look and behave; and how to simulate 5) How to model equity markets with copulas where the dimensions are high 6) How can copula-based market model be applied to equity PM process.

copula, dependence, correlation, financial contagion, tail risk, non-normal portfolio management

Abstract:
The augmented Black-Litterman (ABL) model is an elegant view processor, as well as a natural, robust and unified allocation framework suitable for multiple investment styles (Cheung, 2009B&C). In this paper, we extend the model into a generalised factor view blending (GFVB) framework, suitable for tail risk-aware allocation in non-normal markets with non-linear instruments, factor structures and views. We highlight the following features: 1) Freedom in considering any market factor structure with any security and factor distributions 2) Generic prior distribution without normality restrictions 3) Freedom in forming non-linear, non-normal views 4) View blending strictly based on the Bayes' Rule 5) A structural approach to constructing portfolio of exotic products.

Augmented Black-Litterman (ABL), view blending and shrinkage, Bayes' Rule, CAPM, semi-strong market efficiency, non-normality, non-linear factor model, Monte Carlo, Bayesian posterior sampling, portfolio construction, optimisation, robustness, CVaR minimisation

Abstract:
When investment or hedging views are generated on a factor which is not directly investible, creating a quality factor proxy or mimicking portfolio becomes a basic implementation requirement. For fundamental factors, traditional factor-mimicking techniques include the Fama-French (FF) factor-ranking approach (Fama-French, 1993), and constrained optimisation that controls portfolio exposure to factors. In a seemingly different connection, Cheung (2009B) shows how to construct factor portfolios in the Augmented Black-Litterman (ABL) framework, which makes its intrinsic choice of factor-mimicking technique. In this paper, we test the performance of this technique, along with traditional techniques. Our results show that the ABL factor-mimicking technique is more efficient.

This article features: -
- A brief review of two families of traditional and the new ABL FM techniques;
- A simulation-based testing methodology that isolates the FM quality issue from peripheral risk model and view quality issues, thereby avoiding unnecessary joint tests; and
- Numerical comparison between these techniques, leading to concrete evidence that the ABL technique is more efficient.

factor mimicking, portfolio construction, Augmented Black-Litterman (ABL), factor tilt, Fama-French, factor ranking, factor risk model, optimisation, OLS, GLS