A correlation matrix defines how asset classes move relative to each other — whether stocks and bonds tend to rise and fall together (+1), move independently (0), or move in opposite directions (-1). It's the key input to Cholesky decomposition, which generates realistic multi-asset returns in simulation.
A correlation matrix is a table showing the correlation coefficients between every pair of asset classes in a portfolio. Each value ranges from -1 (perfect inverse movement) to +1 (perfect co-movement), with 0 indicating no relationship. In retirement simulation, the correlation matrix is used with Cholesky decomposition to generate realistic multi-asset return scenarios.
How It Works
For a three-asset portfolio (stocks, bonds, cash), the correlation matrix is a 3×3 table:
| Stocks | Bonds | Cash | |
|---|---|---|---|
| Stocks | 1.00 | -0.10 | 0.05 |
| Bonds | -0.10 | 1.00 | 0.15 |
| Cash | 0.05 | 0.15 | 1.00 |
The diagonal is always 1 (every asset is perfectly correlated with itself). The off-diagonal values represent how each pair co-moves. A stock-bond correlation of -0.10 means they have a slight tendency to move in opposite directions — the basis of diversification.
Why It Matters for Retirement Planning
The correlation matrix determines how much risk reduction you actually get from diversification:
- Negative correlation between stocks and bonds means bonds cushion stock losses — the classic 60/40 portfolio benefit
- Zero correlation still provides diversification but less dramatically
- Positive correlation (as seen during inflationary periods) means both assets can decline simultaneously, reducing the portfolio's effective diversification
In Monte Carlo simulation, the correlation matrix feeds into Cholesky decomposition to ensure that randomly generated returns reflect these real-world relationships. Without it, the simulation would miss the portfolio-level dynamics that make asset allocation decisions meaningful.
Frequently Asked Questions
- What is the typical correlation between stocks and bonds?
- Historically, the correlation between U.S. stocks and bonds has ranged from -0.3 to +0.3, averaging near zero or slightly negative. During crises, the correlation often becomes more negative (stocks fall, bonds rise), which is precisely when diversification is most valuable. However, in inflationary environments (like 2022), stocks and bonds can become positively correlated — both falling simultaneously.
- Can I customize the correlation matrix in Retirement Lab?
- Yes, the correlation matrix is fully configurable in the pro-tier advanced settings. You can adjust the correlations between stocks, bonds, and cash to model different market regimes — for example, setting a higher stock-bond correlation to stress-test your portfolio under inflationary conditions.