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📈 Portfolio Theory

Portfolio theory provides the mathematical framework for constructing investment portfolios that maximize expected return for a given level of risk — or equivalently, minimize risk for a given expected return.

📖 Overview

🏛️ Modern Portfolio Theory (MPT)

Introduced by Harry Markowitz in 1952, Modern Portfolio Theory revolutionized investing by showing that portfolio risk is not simply the sum of individual asset risks. Through diversification, an investor can reduce portfolio volatility without sacrificing expected return.

The key insight: what matters is not just each asset's individual risk and return, but how assets move relative to each other (correlation).

📐 The Efficient Frontier

The efficient frontier is the set of portfolios that offer the highest expected return for each level of risk:

\[ \max_{w} \quad E[R_p] = \sum_i w_i \cdot E[R_i] \]

subject to:

\[ \sigma_p^2 = \sum_i \sum_j w_i w_j \sigma_i \sigma_j \rho_{ij} \leq \sigma_{target}^2 \]

where \(w_i\) are portfolio weights, \(E[R_i]\) expected returns, \(\sigma_i\) volatilities, and \(\rho_{ij}\) correlations.

Any portfolio below the frontier is suboptimal — you could get higher return at the same risk, or lower risk at the same return.

📖 What's Inside

🔀 Diversification

The mathematical foundation of "don't put all your eggs in one basket." How combining assets with imperfect correlation reduces portfolio variance — and the limits of diversification against systematic risk.

⚖️ Asset Allocation

Strategic vs tactical allocation, glide paths, target-date strategies, and the art of rebalancing. How to decide how much of each asset class to hold.

📊 Risk Metrics

Quantitative measures of portfolio risk. From standard deviation to Sharpe ratio, each metric captures a different aspect of risk:

🔑 Key Assumptions & Limitations

MPT assumptions

Modern Portfolio Theory assumes:

  1. Rational investors who seek to maximize utility
  2. Normal distribution of returns (in practice, returns have fat tails)
  3. Known expected returns, volatilities, and correlations (in practice, these are estimated with error)
  4. Frictionless markets — no taxes, no transaction costs (LibreFolio helps you track these!)

Despite these limitations, MPT remains the foundation of institutional portfolio management and provides the vocabulary used by the entire investment industry.