Calculate Variance of Portfolio

Portfolio Variance Formula:

\[ \text{Variance} = \sum(w_i^2 \times \sigma_i^2) + \sum(2 \times w_i \times w_j \times \text{Cov}_{ij}) \]

Portfolio Variance:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Portfolio Variance?

Portfolio variance is a measurement of how the aggregate actual returns of a set of securities making up a portfolio fluctuate over time. It quantifies the overall risk of the portfolio.

2. How Does the Calculator Work?

The calculator uses the portfolio variance formula:

\[ \text{Variance} = \sum(w_i^2 \times \sigma_i^2) + \sum(2 \times w_i \times w_j \times \text{Cov}_{ij}) \]

Where:

\( w_i, w_j \) — Weights of assets in the portfolio (%)
\( \sigma_i \) — Standard deviation of asset returns (%)
\( \text{Cov}_{ij} \) — Covariance between asset returns (%)

Explanation: The first term accounts for individual asset risks, while the second term accounts for how assets move together.

3. Importance of Portfolio Variance

Details: Portfolio variance helps investors understand the risk of their investment portfolio and is fundamental to modern portfolio theory and diversification strategies.

4. Using the Calculator

Tips: Enter weights as percentages (e.g., "60,40" for 60% and 40%), standard deviations as percentages, and covariance if known. For two assets, covariance can significantly impact the result.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between variance and standard deviation?
A: Standard deviation is the square root of variance. Both measure risk, but standard deviation is in the same units as returns.

Q2: How does covariance affect portfolio variance?
A: Lower or negative covariance between assets reduces overall portfolio variance through diversification benefits.

Q3: What's a good portfolio variance value?
A: There's no universal "good" value - it depends on the investor's risk tolerance. Lower variance means less risk but potentially lower returns.

Q4: Can I calculate variance for more than 2 assets?
A: Yes, but you'll need the covariance matrix for all asset pairs. This calculator simplifies for two assets.

Q5: How often should I calculate portfolio variance?
A: Regular monitoring (e.g., quarterly) is recommended, especially when market conditions change or when rebalancing your portfolio.