Example data table
| Asset | Weight % | Annual Vol % |
|---|---|---|
| Equities | 40 | 18 |
| Bonds | 25 | 7 |
| REITs | 15 | 14 |
| Gold | 10 | 16 |
| Cash | 10 | 2 |
| Pair | Correlation | Pair | Correlation |
|---|---|---|---|
| Equities ↔ Bonds | 0.20 | Equities ↔ REITs | 0.55 |
| Equities ↔ Gold | 0.10 | Equities ↔ Cash | 0.05 |
| Bonds ↔ REITs | 0.15 | Bonds ↔ Gold | -0.10 |
| Bonds ↔ Cash | 0.35 | REITs ↔ Gold | 0.08 |
| REITs ↔ Cash | 0.03 | Gold ↔ Cash | 0.00 |
This sample portfolio shows how lower correlations can reduce total risk below the weighted average of stand-alone asset volatilities.
Formula used
Portfolio variance comes from the covariance form:
σp2 = ΣΣ wiwjσiσjρij
Here, w is the asset weight, σ is stand-alone volatility, and ρ is the correlation between two assets. The calculator converts monthly or daily inputs into annual terms first, builds the covariance matrix, and then takes the square root of variance to reach annualized portfolio volatility.
The tool also reports:
- Monthly volatility = annual volatility ÷ √12
- Daily volatility = annual volatility ÷ √trading days
- MCTR = marginal contribution to total risk
- CTR = weight × MCTR
- Diversification ratio = weighted average asset volatility ÷ portfolio volatility
How to use this calculator
- Enter a portfolio name for your scenario.
- Select whether your volatility figures are annual, monthly, or daily.
- Set the trading-day assumption if you use daily inputs.
- Enter each asset name, portfolio weight, and stand-alone volatility.
- Provide the pairwise correlations between assets.
- Keep weights totaling 100%, or turn on normalization.
- Press the calculate button to place results above the form.
- Review total volatility, covariance, and contribution tables.
- Use the CSV or PDF buttons to export the output.
FAQs
1. What does portfolio volatility measure?
It estimates how widely a portfolio’s returns may fluctuate around their average over time. Higher volatility usually signals greater uncertainty in short-term portfolio values.
2. Why are correlations important?
Correlations show how assets move together. Lower or negative correlations can reduce total portfolio risk, even when some individual holdings are volatile on their own.
3. Should weights always equal 100%?
Yes, unless you intentionally use the normalization option. A fully invested portfolio normally sums to 100%, which keeps the variance and contribution outputs consistent.
4. What is the diversification ratio?
It compares the weighted average of individual asset volatilities with the actual portfolio volatility. A higher ratio usually means stronger diversification benefits.
5. What do MCTR and CTR mean?
MCTR is marginal contribution to risk, showing how a small weight change affects portfolio volatility. CTR is the asset’s current share of total portfolio volatility.
6. Can I enter daily volatility values?
Yes. Choose the daily basis option, then set your trading-day assumption. The calculator annualizes each asset’s daily volatility before portfolio aggregation.
7. Why might a low-volatility asset raise risk?
If that asset is highly correlated with the rest of the portfolio, it may add less diversification than expected. Correlation can matter as much as stand-alone volatility.
8. Is this calculator useful for rebalancing?
Yes. You can test alternative weights, update assumptions, and compare risk contribution shares before changing allocations in a live investment portfolio.