Modern Portfolio Theory (MPT)

Modern Portfolio Theory (MPT)

Modern Portfolio Theory, developed by Harry Markowitz in 1952 (winning him the Nobel Prize in Economics), is a mathematical framework for constructing a portfolio of assets that maximizes expected return for a given level of risk, or equivalently, minimizes risk for a given level of expected return.

Core Principles

1. Investors are risk-averse -- they prefer less risk for the same return
2. Diversification reduces risk -- combining assets with low correlation reduces overall portfolio volatility
3. Portfolio risk is NOT simply the weighted average of individual asset risks -- correlations matter
4. An optimal portfolio exists on the efficient frontier for every risk level

The Math Behind MPT

Component	Formula	Description
Portfolio Return	E(Rp) = Σ wi * E(Ri)	Weighted average of asset returns
Portfolio Variance	σp² = ΣΣ wi * wj * σij	Accounts for covariances between all assets
Correlation	ρ = Cov(A,B) / (σA * σB)	Measures how assets move together (-1 to +1)

Key Insight: The Power of Correlation

Consider two assets, each with 15% volatility:

• If correlation = +1.0: Combined volatility = 15% (no benefit)
• If correlation = 0.0: Combined volatility = 10.6% (29% reduction)
• If correlation = -1.0: Combined volatility = 0% (perfect hedge)

Limitations

• Assumes normal distribution of returns (ignores fat tails and black swan events)
• Relies on historical data for expected returns, which may not predict the future
• Correlation between assets can increase during crises when diversification is needed most
• Does not account for transaction costs or taxes

Why It Matters

MPT remains the foundation of modern investment management. Even critics who note its limitations use its core insight: don't just pick great assets -- build great portfolios by considering how assets interact with each other.