Stock Portfolio: Optimize a Portfolio Allocation Under a Risk and Budget Constraint

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## Problem You have a list of stocks, each with an `expected_return` (float, %), `risk_score` (int 1-10), and `min_investment` (int, dollars). You have a total budget `B` and a maximum allowed portfolio risk `max_risk` (weighted average of risk scores by investment fraction must be <= max_risk). Maximize total expected return. Simplified version: each stock can be selected at most once; cost = `min_investment`; return = `expected_return`; risk contribution = `risk_score`. Find the subset maximizing total return where total cost <= B and total risk score (sum, not weighted) <= max_total_risk. ```python def best_portfolio( stocks: list[dict], budget: int, max_total_risk: int ) -> float: # stocks: [{"return": float, "risk": int, "cost": int}] pass ``` **Example:** ``` stocks = [ {"return": 8.0, "risk": 3, "cost": 1000}, {"return": 12.0, "risk": 7, "cost": 2000}, {"return": 5.0, "risk": 2, "cost": 500} ] budget=2500, max_total_risk=8 Select stock 0 + stock 2: cost=1500, risk=5, return=13.0 Select stock 1 + stock 2: cost=2500, risk=9 > max. Invalid. Output: 13.0 ``` ## Follow-ups 1. This is a 2D knapsack problem. What are the DP dimensions? 2. How would you handle fractional investments (continuous knapsack)? 3. In practice, how do you model portfolio risk using covariance instead of a simple sum? 4. How does adding a short-selling constraint (minimum allocation per sector) change the optimization?

Stock Portfolio: Optimize a Portfolio Allocation Under a Risk and Budget Constraint

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