The Efficient Frontier
Introduced by Harry Markowitz in 1952, Modern Portfolio Theory (MPT) argues that an investment's risk and return characteristics should not be viewed alone, but evaluated by how the investment affects the overall portfolio's risk and return.
The Power of Correlation
The magic of diversification stems from correlation (denoted as ρ). If you combine assets that do not move in perfect tandem (ρ < 1), the volatility (standard deviation) of the portfolio is less than the weighted average volatility of the individual assets.
Portfolio Variance Formula (2 Assets):
σp2 = w12σ12 + w22σ22 + 2w1w2Cov(1,2)
Where Cov(1,2) = ρ1,2σ1σ2
Plotting the Curve
If you plot the expected return (y-axis) against standard deviation (x-axis) for every possible combination of risky assets, a hyperbola emerges. The upper edge of this boundary is the Efficient Frontier.
- Portfolios on the frontier offer the maximum expected return for a defined level of risk.
- Portfolios below the frontier are sub-optimal (you can achieve higher return for the same risk).
- Portfolios above the frontier are unachievable with the given assets.
The Tangency Portfolio
When you introduce a risk-free asset (cash/treasuries) into the model, you can draw a straight line (the Capital Allocation Line) from the risk-free rate tangent to the Efficient Frontier.
The point of tangency identifies the Optimal Risky Portfolio (the Market Portfolio). It is the portfolio with the highest possible Sharpe Ratio.