Efficient Frontier & Sharpe Ratio

The cornerstone of modern portfolio theory: maximizing return for a given level of risk.

What is the Efficient Frontier?

The Efficient Frontier, introduced by Harry Markowitz, is a set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. Portfolios that lie below the frontier are sub-optimal because they do not provide enough return for the level of risk. Portfolios above the frontier are impossible to achieve.

For a quant, this is the fundamental concept behind portfolio construction. It demonstrates that the benefit of diversification (combining assets with low correlation) can lead to a portfolio with better risk-return characteristics than any single asset alone.

Sharpe Ratio

To find the single "best" portfolio on the frontier, we use the Sharpe Ratio.

S_p = \frac{R_p - R_f}{\sigma_p}

$R_p$ is the return of the portfolio.
$R_f$ is the risk-free rate.
$\sigma_p$ is the volatility of the portfolio.

The portfolio with the highest Sharpe Ratio is the one that provides the best return per unit of risk. It's the point on the efficient frontier that is tangent to a line drawn from the risk-free rate (the Capital Allocation Line).

Interactive Two-Asset Frontier

Observe how the correlation (

\rho

) between two assets changes the shape of the efficient frontier. A lower correlation allows for better diversification.

Correlation (ρ): 0.20