Calculate Standard Deviation of Portfolio

Portfolio Standard Deviation Formula:

\[ SD = \sqrt{\sum(w_i^2 \times \sigma_i^2) + \sum(2 \times w_i \times w_j \times Cov_{ij})} \]

Portfolio Standard Deviation:

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1. What is Portfolio Standard Deviation?

Portfolio Standard Deviation measures the total risk of a portfolio by accounting for individual asset risks and their correlations. It's a key metric in modern portfolio theory for understanding portfolio volatility.

2. How Does the Calculator Work?

The calculator uses the portfolio standard deviation formula:

\[ SD = \sqrt{\sum(w_i^2 \times \sigma_i^2) + \sum(2 \times w_i \times w_j \times Cov_{ij})} \]

Where:

\( w_i, w_j \) — Weights of assets in the portfolio (%)
\( \sigma_i \) — Standard deviation of each asset (%)
\( Cov_{ij} \) — Covariance between asset pairs (%)

Explanation: The formula combines the individual asset risks with their diversification benefits through covariance terms.

3. Importance of Portfolio Risk Measurement

Details: Understanding portfolio standard deviation helps investors assess risk-return tradeoffs, optimize asset allocation, and build efficient portfolios.

4. Using the Calculator

Tips: Enter weights as percentages (e.g., "60,40" for 60% and 40%), standard deviations as percentages, and covariance as a percentage value.

5. Frequently Asked Questions (FAQ)

Q1: How does correlation affect portfolio risk?
A: Lower correlation between assets reduces portfolio risk through diversification benefits.

Q2: What's the difference between covariance and correlation?
A: Covariance measures the joint variability, while correlation standardizes this measure to a -1 to +1 scale.

Q3: Can I use this for more than two assets?
A: Yes, the calculator handles multiple assets, but assumes the same covariance for all pairs.

Q4: What's a good portfolio standard deviation?
A: This depends on investor risk tolerance. Conservative portfolios typically have SD below 10%, while aggressive ones may exceed 20%.

Q5: How often should I calculate portfolio standard deviation?
A: Regular monitoring (quarterly or when making significant changes) helps maintain desired risk levels.