Calculate Standard Deviation Of Portfolio

Portfolio Standard Deviation Formula:

\[ \sigma_p = \sqrt{\sum_{i=1}^{n} w_i^2 \sigma_i^2 + 2 \sum_{i=1}^{n} \sum_{j>i}^{n} w_i w_j \rho_{ij} \sigma_i \sigma_j} \]

Asset 1

Weight (w):

(0-1)

Standard Deviation (σ):

Correlation Coefficients

Correlation between Asset 1 and Asset 2 (ρ):

(-1 to 1)

Portfolio Standard Deviation:

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1. What is Portfolio Standard Deviation?

Portfolio standard deviation is a measure of the total risk of a portfolio, considering both the individual asset risks and how they correlate with each other. It quantifies the volatility of portfolio returns and is a key metric in modern portfolio theory.

2. How Does the Calculator Work?

The calculator uses the portfolio variance formula:

\[ \sigma_p^2 = \sum_{i=1}^{n} w_i^2 \sigma_i^2 + 2 \sum_{i=1}^{n} \sum_{j>i}^{n} w_i w_j \rho_{ij} \sigma_i \sigma_j \]

Where:

\( \sigma_p \) — Portfolio standard deviation
\( w_i \) — Weight of asset i in the portfolio
\( \sigma_i \) — Standard deviation of asset i
\( \rho_{ij} \) — Correlation coefficient between assets i and j
\( n \) — Number of assets in the portfolio

Explanation: The formula accounts for both individual asset risks (first term) and how assets move together (second term). Diversification benefits occur when correlations are less than 1.

3. Importance of Portfolio Risk Measurement

Details: Understanding portfolio risk is crucial for investment decision-making, asset allocation, and risk management. A well-diversified portfolio can achieve higher returns for the same level of risk or lower risk for the same level of returns.

4. Using the Calculator

Tips: Enter weights as decimals between 0 and 1 (must sum to 1), standard deviations as percentages, and correlation coefficients between -1 and 1. Add more assets as needed for complex portfolios.

5. Frequently Asked Questions (FAQ)

Q1: Why is correlation important in portfolio risk?
A: Correlation measures how assets move together. Negative correlation provides the greatest diversification benefits, reducing overall portfolio risk.

Q2: What is a good portfolio standard deviation?
A: This depends on investor risk tolerance. Conservative portfolios might target 5-10%, while aggressive portfolios might tolerate 15-25% or higher.

Q3: How many assets are needed for proper diversification?
A: Research suggests 15-20 well-chosen stocks can provide most diversification benefits, though the exact number depends on correlation between assets.

Q4: Can this calculator handle more than 2 assets?
A: Yes, you can add multiple assets. The calculator will automatically generate the necessary correlation inputs for all asset pairs.

Q5: What are the limitations of this calculation?
A: It assumes normal distribution of returns and constant correlations, which may not hold in reality, especially during market crises when correlations tend to increase.