liethon / portfolio-optimization

Dynamic portfolio optimization

Portfolio-Management

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.

Target

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.

Data

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).

Strategy Pipeline

Backtest

Models

$$\text{argmax}_w(\mu^{T}w-\cfrac{1}{2}\lambda w^T\Sigma w- \gamma \left|| w - \hat{w} \right||^2)$$

• $\sum_i w_i = 1, w_i>0$ 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)

Performance Summary

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

Risk Contribution

Optimal Portfolio Weights

Robustness Check

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