Course Progress
Part of 10 Chapters
Portfolio Optimization: Finding the Optimal Investment Mix
Portfolio Optimization: Harmony of Risk and Return
The mathematical formalization of the proverb “don’t put all your eggs in one basket” is Modern Portfolio Theory (MPT). The core is to lower overall risk by utilizing the ‘correlation’ between assets rather than focusing solely on individual asset risks.
1. The Magic of Diversification: Correlation ()
The lower the correlation between two assets (especially as it approaches -1), the significantly lower the overall portfolio volatility (risk) can be compared to the average risk of the individual assets.
Risk Reduction Effect by Asset Correlation
| Correlation (ρ) | Risk Reduction Effect | Key Meaning |
|---|---|---|
| +1.0 | None | Two assets move perfectly together (Simple sum) |
| +0.5 | Slight Diversification | Same direction but different steps |
| 0.0 | Significant Diversification | Random movement without any correlation |
| -0.5 | Strong Diversification | High probability one rises when the other falls |
| -1.0 | Complete Risk Elimination Possible | Perfectly symmetrical move in opposite directions |
2. Efficient Frontier
Among thousands of asset combinations, connecting the points that provide the highest return for the same risk level results in a curve. this is called the Efficient Frontier.
Efficient Frontier and Optimal Portfolio
Important
Portfolios located below this curve are ‘inefficient.’ This is because combinations exist that can generate higher returns for the same risk, or the same return for lower risk.
3. Three-Step Process for Optimal Allocation
The process by which a portfolio manager practically performs optimization is as follows:
Calculate expected returns for each asset and correlations between assets using historical data, etc.
Decide whether to find the minimum variance portfolio or aim for maximizing the Sharpe Ratio (return/risk).
Add realistic constraints such as limiting a specific asset weight to 30% or prohibiting short selling.
Derive specific weights (W) for each asset through a Quadratic Programming (QP) algorithm.
💡 Professor’s Tip
While Markowitz’s theory won a Nobel Prize, it is often difficult to use directly in practice due to its ‘Input Sensitivity’—being highly sensitive to estimates. To supplement this, more sophisticated techniques like the ‘Black-Litterman model’ are utilized in modern financial engineering.