Portfolio Optimization AI Prompt

Construct an optimal portfolio from this asset universe using mean-variance optimization and robust alternatives.

Assets: {{asset_universe}}
Return estimates: {{return_estimates}}
Covariance matrix: {{covariance_matrix}}
Constraints: {{constraints}}

1. Classical mean-variance optimization (Markowitz):
   Solve: min w'Σw subject to w'μ = target_return, w'1 = 1, w ≥ 0
   - Efficient frontier: trace the set of portfolios minimizing variance for each target return
   - Identify: minimum variance portfolio (MVP), maximum Sharpe ratio portfolio (tangency)
   - Report for each portfolio: weights, expected return, volatility, Sharpe ratio

2. The problem with classical MVO:
   - Estimation error: small changes in expected returns produce large weight changes
   - Input sensitivity: MVO is an 'error maximizer' — it concentrates in assets with the most overestimated returns
   - Demonstrate: perturb expected returns by ±1% and show how weights change

3. Robust optimization alternatives:

   Maximum Sharpe Ratio with shrinkage:
   - Shrink expected returns toward a common prior (e.g. equal returns for all assets or CAPM-implied returns)
   - Ledoit-Wolf shrinkage on the covariance matrix

   Minimum Variance Portfolio:
   - Avoids using expected return estimates entirely (which are the most error-prone input)
   - min w'Σw subject to w'1 = 1, w ≥ 0
   - Historically outperforms on a risk-adjusted basis in many markets

   Risk Parity:
   - Each asset contributes equally to total portfolio variance
   - RC_i = w_i × (Σw)_i = Portfolio_variance / N
   - Implicit long duration bias (bonds are low vol); often levered to achieve return targets

   Maximum Diversification:
   - Maximize the ratio: w'σ / sqrt(w'Σw) where σ is the vector of individual asset volatilities
   - Maximizes diversification benefit relative to a weighted average of individual volatilities

4. Practical constraints:
   - Long-only: w ≥ 0
   - Weight bounds: w_i ∈ [0, 0.20] (max 20% in any single asset)
   - Turnover constraints: |w_new - w_old| ≤ budget
   - Sector constraints: sum of sector weights within bounds

5. Out-of-sample evaluation:
   - Walk-forward portfolio construction: reoptimize annually, evaluate on the following year
   - Compare all methods: realized Sharpe, realized volatility, maximum drawdown, turnover

Return: efficient frontier plot, portfolio weights for each method, sensitivity analysis, walk-forward performance comparison.