Standard Deviation of a Portfolio Calculator
This calculator helps financial analysts and investors determine the standard deviation of a portfolio, providing insights into investment risk and volatility.
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Data Source and Methodology
All calculations are strictly based on the formulas and data provided by authoritative financial sources.
The Formula Explained
Standard Deviation of a Portfolio: \(\sigma_p = \sqrt{\sum (w_i^2 \cdot \sigma_i^2) + \sum \sum (w_i \cdot w_j \cdot \sigma_i \cdot \sigma_j \cdot \rho_{ij})}\)
Glossary of Terms
- Asset Returns: The expected return of the assets in the portfolio.
- Asset Weights: The percentage composition of each asset in the portfolio.
- Correlation Matrix: A matrix showing the correlation coefficients between assets.
How It Works: A Step-by-Step Example
Suppose you have a portfolio of two stocks with returns of 5% and 7%, weights of 50% each, and a correlation of 0.8. Using the formula, you can compute the portfolio's standard deviation.
Frequently Asked Questions (FAQ)
What is standard deviation in a portfolio?
Standard deviation is a measure of the dispersion of returns for a given security or market index. It's used by investors to gauge the amount of expected volatility.
Why is standard deviation important?
It helps investors understand the risk involved in holding a particular portfolio.
How can I reduce portfolio standard deviation?
By diversifying the portfolio and selecting assets with low correlation to each other.
What is a good standard deviation for a portfolio?
This depends on the investor's risk tolerance and the market conditions.
How does correlation affect standard deviation?
Higher correlation between assets increases the portfolio's standard deviation.
Formula (LaTeX) + variables + units
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Standard Deviation of a Portfolio: \(\sigma_p = \sqrt{\sum (w_i^2 \cdot \sigma_i^2) + \sum \sum (w_i \cdot w_j \cdot \sigma_i \cdot \sigma_j \cdot \rho_{ij})}\)
- No variables provided in audit spec.
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Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.