Black-Litterman Asset Allocation under Hidden Truncation Distribution

ArXiv ID: 2310.12333 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we study the Black-Litterman (BL) asset allocation model (Black and Litterman, 1990) under the hidden truncation skew-normal distribution (Arnold and Beaver, 2000). In particular, when returns are assumed to follow this skew normal distribution, we show that the posterior returns, after incorporating views, are also skew normal. By using Simaan three moments risk model (Simaan, 1993), we could then obtain the optimal portfolio. Empirical data show that the optimal portfolio obtained this way has less risk compared to an optimal portfolio of the classical BL model and that they become more negatively skewed as the expected returns of portfolios increase, which suggests that the investors trade a negative skewness for a higher expected return. We also observe a negative relation between portfolio volatility and portfolio skewness. This observation suggests that investors may be making a trade-off, opting for lower volatility in exchange for higher skewness, or vice versa. This trade-off indicates that stocks with significant price declines tend to exhibit increased volatility.

Keywords: Black-Litterman model, skew-normal distribution, Simann three moments, asset allocation, portfolio optimization

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper involves advanced mathematics including hidden truncation skew-normal distributions, Bayesian posterior derivations, and Simaan’s three-moment optimization framework, but the empirical evidence is limited to described observations without backtesting code, specific datasets, or implementation details.

  flowchart TD
    A["Research Goal: Study BL Model under<br>Hidden Truncation Skew-Normal Distribution"] --> B["Data: Historical Asset Returns"]
    B --> C["Methodology: Parametric Assumptions<br>Skew-Normal Distribution for Returns"]
    C --> D["Process: Derive Posterior Returns<br>Skew-Normal Distribution"]
    D --> E["Process: Optimize Portfolio using<br>Simaan Three-Moments Risk Model"]
    E --> F{"Key Findings & Outcomes"}
    F --> G["Optimal Portfolio: Lower Risk<br>vs. Classical BL Model"]
    F --> H["Trade-off: Higher Expected Return<br>leads to More Negative Skewness"]
    F --> I["Observation: Negative Relation<br>between Volatility and Skewness"]