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πŸ“ˆ Quant & Trading
Portfolio Optimization
Mathematical frameworks for combining multiple assets or strategies into a portfolio that maximizes return for a given risk level (or minimizes risk for a given return). The bridge from "I have good signals" to "I have a good portfolio." Individual alpha means nothing if your portfolio construction destroys it through poor diversification or correlated bets.
2
Minutes
6
Concepts
+45
XP
1
Markowitz Mean-Variance Optimization (1952)

The original framework. Maximize expected return minus a risk penalty across all possible weight combinations.

Objective: maximize E[return] - Ξ» Γ— Var[return]

Inputs: expected returns vector, covariance matrix of returns

Output: the "efficient frontier" β€” the set of portfolios offering the best risk/return tradeoff 

Expected Return ↑
       |        * ← max Sharpe portfolio
       |      *
       |    *  ← efficient frontier
       |   *
       |  *
       | *
       +β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β†’ Risk (Std Dev)

The fatal flaw: Extremely sensitive to estimated inputs. Small errors in expected returns produce wildly different "optimal" portfolios. Garbage in, garbage out. In practice, Markowitz portfolios are unstable and often concentrate in a few assets.