Building Efficient Portfolios
The Problem: How to Combine Assets
You have multiple assets with different returns and risks. How do you combine them to maximize returns while minimizing risk?
The Tradeoff:
- More diversification = lower risk (uncorrelated assets work together)
- But you can't own everything equally — different assets have different risk/return profiles
- You need optimization to find the best weights
This is Markowitz portfolio theory.
Diversification works best when assets have low correlation (move differently). Combining tech and defensive stocks reduces portfolio volatility below the average of individual volatilities — the magic of correlation.
Markowitz portfolio theory: optimize weights to maximize [[sharpe-ratio]] (return per unit risk)
Diversification power: combining low-correlation assets reduces portfolio vol
Optimization formula: weights ∝ Σ⁻¹ · μ (inverse covariance times mean returns)
Observation: optimized portfolio often overweights low-vol defensive stocks, underweights correlated volatile ones
Practical takeaway: Always ask — are my assets correlated? If yes, diversification gains are small