Workflow
20210119-华西证券-Black_Litterman模型研究系列之二：应用演示
HUAXI Securities·2021-01-18 16:00
  • Model Name: Black-Litterman (BL) Model - Model Construction Idea: The BL model combines subjective views with market equilibrium returns to determine asset allocation weights[1][7] - Model Construction Process: - Calculate equilibrium returns using reverse optimization: Π=δΣwm\Pi = \delta \Sigma \mathbf{w}_{m} where $\Pi$ is the equilibrium return vector, $\delta$ is the risk aversion coefficient, $\Sigma$ is the covariance matrix of asset returns, and $\mathbf{w}{m}$ is the market capitalization weights[10] - Incorporate subjective views into the model: μp=[(τΣ)−1+PTΩ−1P]−1[(τΣ)−1Π+PTΩ−1Q]\mu_{p} = [(\tau \Sigma)^{-1} + P^{T} \Omega^{-1} P]^{-1} [(\tau \Sigma)^{-1} \Pi + P^{T} \Omega^{-1} Q] where $\mu{p}$ is the posterior mean return vector, $\tau$ is a scalar reflecting the uncertainty in the equilibrium returns, $P$ is the matrix representing the assets involved in the views, $\Omega$ is the diagonal covariance matrix of the views, and $Q$ is the vector of view returns[7] - Calculate the posterior covariance matrix: Σp∗=Σ+[(τΣ)−1+PTΩ−1P]−1\Sigma_{p}^{*} = \Sigma + [(\tau \Sigma)^{-1} + P^{T} \Omega^{-1} P]^{-1} - Determine the asset weights using the posterior returns and covariance matrix: w=(δΣp∗)−1μp\mathbf{w} = (\delta \Sigma_{p}^{*})^{-1} \mu_{p}[7] - Model Evaluation: The BL model provides a stable and reasonable asset allocation by anchoring to market equilibrium weights and adjusting based on subjective views[3][13] Model Backtest Results - BL Model, Information Ratio (IR): 0.45[2] - BL Model, Sharpe Ratio: 0.35[2] - BL Model, Annualized Return: 8.5%[2] Factor Construction and Process - Factor Name: Subjective View Matrix (P) and View Return Vector (Q) - Factor Construction Idea: The subjective view matrix (P) and view return vector (Q) represent the investor's views on the expected returns of certain assets[16][17] - Factor Construction Process: - Define the subjective views: - View 1: Automotive industry expected return of 6% - View 2: Media industry expected return of 4% - View 3: Food and beverage expected to underperform home appliances by 1% - View 4: Technology and new energy sectors expected to outperform traditional sectors by 2%[17] - Construct the view matrix (P): P=(000000000100000010000001000−10000.5−0.700.3−0.3000.20)P = \begin{pmatrix} 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & -1 & 0 & 0 \\ 0 & 0.5 & -0.7 & 0 & 0.3 & -0.3 & 0 & 0 & 0.2 & 0 \end{pmatrix}[17][19] - Construct the view return vector (Q): Q=(0.060.04−0.010.02)Q = \begin{pmatrix} 0.06 \\ 0.04 \\ -0.01 \\ 0.02 \end{pmatrix}[20][21] - Factor Evaluation: The subjective view matrix and view return vector allow for the incorporation of investor views into the BL model, providing flexibility and customization in asset allocation[23][25] Factor Backtest Results - View 1 (Automotive), Expected Return: 6%, Implied Return: 4.30%, Difference: 1.70%[24] - View 2 (Media), Expected Return: 4%, Implied Return: 5.17%, Difference: -1.17%[24] - View 3 (Food and Beverage vs. Home Appliances), Expected Return: -1%, Implied Return: -0.29%, Difference: -0.71%[24] - View 4 (Technology vs. Traditional Sectors), Expected Return: 2%, Implied Return: 2.48%, Difference: -0.48%[24]