This is a beginner project from AQR Capital Management - build a dynamic portfolio optimization framework for multi-asset classes including equity, bond, real estate, and commodity.
Traditional Markowitz model suffers from over-sensitivity regarding model parameters. The aim is to construct a dynamically rebalanced portfolio and fine-tune the model by adding sparse portfolio selection with mandate constraints.
Daily prices of four asset classes from 1990-2023 of equities (US equity, EM equity, Asia equity, Europe equity), fixed-income (high yield bond, aggregate bond), real estate (US real estate) and commodity (gold).
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$\sum_i w_i = 1, w_i>0$ are portfolio weights,$\hat{w}$ is the previous weight -
$\mu$ : mean asset returns -
$\Sigma$ : covariance matrix, portfolio volatility -
$\lambda$ : risk penalty parameter (higher$\lambda$ means lower volatility) -
$\gamma$ : portfolio turnover penalty parameter (higher$\gamma$ means lower turnover)
| Models | Return | Volatility | Sharpe | Max Drawdown | Turnovers |
|---|---|---|---|---|---|
| V1 | 0.0200 | 0.0714 | 0.2799 | -0.1691 | 0.2518 |
| V1.5 | 0.0163 | 0.0738 | 0.2216 | -0.1778 | 0.3581 |
| V2 | 0.0475 | 0.1183 | 0.4021 | -0.2044 | 0.2468 |
| V3 | 0.0479 | 0.1211 | 0.3957 | -0.2110 | 0.1499 |
| V4 | 0.0542 | 0.1411 | 0.3845 | -0.2383 | 0.1828 |
- v1: Markowitz model
- V1.5: mean-variance + winsorization
- V2: mean-variance + winsorization + notional control
- V3: mean-variance + winsorization + notional control + turnover control
- V4 (Final model): mean-variance+ winsorization + notional control + turnover control + risk control
Check the model robustness for different asset classes, different hyper-parameter values (risk control and turnover control), different backtest windows.
- Change of Sharpe and volatility with different risk penalty parameter
$\lambda$
- Performance comparison for different backtest windows
