Portfolio Theory
The theoretical foundations of quantitative portfolio construction. Explore the core concepts that underpin every optimization method, from mean-variance analysis to modern risk budgeting frameworks.
Core Concepts
Portfolio theory provides the mathematical framework for understanding how rational investors should allocate capital among risky assets. The foundational insight, due to Harry Markowitz (1952), is that the risk of a portfolio depends not only on the risks of its individual components but crucially on how those components co-move. This means that diversification -- holding assets that are imperfectly correlated -- can reduce portfolio risk below the weighted average of individual asset risks, sometimes dramatically.
The concepts below form the building blocks of every portfolio optimization method. Understanding them is essential for interpreting the outputs of optimizers and for making informed decisions about which method to use for a given investment objective.
Capital Asset Pricing Model (CAPM)
The equilibrium model relating expected return to systematic risk via beta, establishing the security market line and the concept of a market risk premium.
Modern Portfolio Theory (MPT)
Markowitz's framework for constructing portfolios that maximize expected return for a given level of risk through diversification across imperfectly correlated assets.
Efficient Frontier
The set of optimal portfolios offering the highest expected return for each level of risk, forming the upper boundary of the feasible mean-variance region.
Expected Returns
Methods for estimating the expected return of assets, including historical averages, CAPM-implied returns, shrinkage estimators, and Black-Litterman views.
Volatility
Measures of asset and portfolio risk including historical volatility, exponentially weighted variance, implied volatility, and the covariance matrix.
How These Concepts Connect
Modern Portfolio Theory provides the overarching framework. Within it, expected returns and volatility (covariance) are the two fundamental inputs to any optimization. The efficient frontier is the output: the set of portfolios that are optimal in the mean-variance sense. CAPM then provides an equilibrium interpretation, showing that in a world where all investors use MPT, the market portfolio lies on the efficient frontier and expected returns are linearly related to beta.
In practice, different optimization methods (mean-variance, risk parity, CVaR, etc.) emphasize different aspects of these inputs. Mean-variance optimization uses both expected returns and covariances directly. Risk parity uses only covariances. CVaR optimization uses the full return distribution. Understanding the theoretical foundations helps in choosing the right method for the right context.