Portfolio optimization

Portfolio optimization selects asset weights to pursue investment goals while respecting constraints such as risk limits, budgets, and trading rules.

Mean–variance optimization: A framework that chooses portfolios by balancing expected return against variance of returns. It formalizes the return–risk tradeoff at the heart of many portfolio choices.
Expected return: The probability-weighted average of an asset’s possible future returns. It is a central forecast input, though estimation error can strongly affect chosen weights.
Minimum-variance portfolio: The feasible portfolio with the lowest return variance, regardless of its expected return. It prioritizes risk reduction rather than balancing risk against a target or reward.
Asset allocation: The distribution of investments among asset classes, markets, or strategies. Portfolio optimization supplies quantitative methods for selecting these broad exposures.
Estimation error: The difference between an estimated quantity and its unknown true value. Small errors in expected returns or covariances can cause large changes in optimized weights.
Efficient frontier: The set of portfolios offering the highest expected return at each level of risk. Optimization traces this boundary to identify portfolios that cannot be improved on both dimensions.
Risk aversion: A preference for less uncertain outcomes when expected rewards are otherwise comparable. It determines how much expected return an investor gives up to reduce portfolio risk.
Risk parity: A portfolio construction method that allocates capital so assets contribute more evenly to total risk. It balances risk contributions instead of directly maximizing expected return for a chosen risk level.
Index tracking: The construction of a portfolio intended to follow the returns of a market index. Optimization can minimize tracking error while controlling costs and portfolio restrictions.
Turnover (finance): The rate at which assets in a portfolio are bought and sold over a period. Unstable target weights can generate excessive trading and reduce realized performance.

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