3 Asset Portfolio Variance Calculator

Portfolio Variance Formula:

\[ Var = w_1^2 \cdot var_1 + w_2^2 \cdot var_2 + w_3^2 \cdot var_3 + 2w_1w_2 \cdot cov_{12} + 2w_1w_3 \cdot cov_{13} + 2w_2w_3 \cdot cov_{23} \]

Weight 1 (w1):

Weight 2 (w2):

Weight 3 (w3):

Variance 1 (var1):

Variance 2 (var2):

Variance 3 (var3):

Covariance 1-2 (cov12):

Covariance 1-3 (cov13):

Covariance 2-3 (cov23):

Portfolio Variance:

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1. What Is Portfolio Variance?

Portfolio variance measures the dispersion of returns of a portfolio of assets. It quantifies the overall risk of the portfolio, taking into account both individual asset variances and the covariances between them.

2. How Does The Calculator Work?

The calculator uses the portfolio variance formula for three assets:

\[ Var = w_1^2 \cdot var_1 + w_2^2 \cdot var_2 + w_3^2 \cdot var_3 + 2w_1w_2 \cdot cov_{12} + 2w_1w_3 \cdot cov_{13} + 2w_2w_3 \cdot cov_{23} \]

Where:

\( w_1, w_2, w_3 \) — Weights of assets in the portfolio (sum should be 1)
\( var_1, var_2, var_3 \) — Variances of individual assets
\( cov_{12}, cov_{13}, cov_{23} \) — Covariances between asset pairs

Explanation: The formula accounts for both the individual risk of each asset (through variances) and how the assets move together (through covariances).

3. Importance Of Portfolio Variance

Details: Portfolio variance is a key measure in modern portfolio theory. It helps investors understand the risk-return tradeoff and optimize their portfolios for maximum return at a given level of risk.

4. Using The Calculator

Tips: Enter weights (should sum to 1 for proper normalization), variances (must be non-negative), and covariances between asset pairs. All values are unitless.

5. Frequently Asked Questions (FAQ)

Q1: Why is portfolio variance important?
A: It helps investors quantify and manage portfolio risk, enabling better diversification and risk-adjusted return optimization.

Q2: What's the difference between variance and covariance?
A: Variance measures an asset's own volatility, while covariance measures how two assets move together relative to their means.

Q3: Should weights sum to 1?
A: Yes, weights should sum to 1 (100%) to represent the full allocation of the portfolio.

Q4: Can I use this for more than 3 assets?
A: This calculator is specifically designed for 3 assets. For more assets, the formula expands with additional terms.

Q5: What are typical values for variances and covariances?
A: Variances are typically positive values, while covariances can be positive (assets move together) or negative (assets move opposite).