Quantitative Models and Construction Methods - **Model Name**: Black-Litterman (BL) Model **Model Construction Idea**: The BL model combines market equilibrium portfolio weights with subjective investor views using Bayesian theorem, aiming to improve stability and flexibility in asset allocation[2][3][8] **Model Construction Process**: 1. **Market Equilibrium Portfolio**: The starting point is the CAPM-based market equilibrium portfolio, where asset weights are determined by market capitalization. The equilibrium returns are calculated using the utility function: $U = w^{T}\Pi - \frac{\delta}{2}w^{T}\Sigma w$ Here, $\Pi$ represents equilibrium returns, $\Sigma$ is the covariance matrix, and $\delta$ is the risk aversion coefficient[12][13][14]. Alternatively, equilibrium returns can be derived as: $\Pi = \delta\Sigma_{eq}$[14][15]. 2. **Bayesian Integration**: Bayesian theorem is applied to combine prior information (market equilibrium returns) with subjective investor views. The posterior mean and covariance matrix are calculated as: $\mu_{p} = [(\tau\Sigma)^{-1} + P^{T}\Omega^{-1}P]^{-1}[(\tau\Sigma)^{-1}\Pi + P^{T}\Omega^{-1}Q]$ $\Sigma_{p} = [(\tau\Sigma)^{-1} + P^{T}\Omega^{-1}P]^{-1}$ Here, $\tau$ represents the uncertainty of prior returns, $P$ is the matrix indicating assets involved in subjective views, $Q$ is the vector of expected returns for subjective views, and $\Omega$ is the confidence matrix for subjective views[9][10][29]. 3. **Final Asset Weights**: Using the posterior mean and covariance matrix, asset weights are optimized via mean-variance optimization: $\mathbf{w} = (\delta\Sigma_{p}^{*})^{-1}\mu_{p}$ $\Sigma_{p}^{*}$ can be calculated using two methods: - $\Sigma_{p}^{*} = \Sigma_{p} + \Sigma$ (recommended for practical use)[30][31] - $\Sigma_{p}^{*} = \Sigma_{p}$ (used in specific cases)[31][32]. - **Model Evaluation**: The BL model improves stability by starting with market equilibrium weights and allows flexible incorporation of subjective views. It avoids the sensitivity issues of traditional mean-variance models and provides intuitive results[2][8][9]. Model Backtesting Results - **BL Model**: No specific numerical backtesting results are provided in the report. Quantitative Factors and Construction Methods - **Factor Name**: None explicitly mentioned in the report. Factor Backtesting Results - **Factor Results**: None explicitly mentioned in the report.