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Portfolio Variance Formula

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Portfolio Variance is a measure of the dispersion or spread of returns of a portfolio of investments. Check FAQs

Var p = {(w 1)}^{2} \cdot {σ 1}^{2} + {(w 2)}^{2} \cdot {σ 2}^{2} + 2 \cdot (w 1 \cdot w 2 \cdot σ 1 \cdot σ 2 \cdot p 12)

Var_p - Portfolio Variance?w₁ - Asset Weight 1?σ₁ - Variance of Returns on Assets 1?w₂ - Asset Weight 2?σ₂ - Variance of Returns on Assets 2?p₁₂ - Portfolio Correlation Coefficient?

Portfolio Variance Example

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Here is how the Portfolio Variance equation looks like with Values.

Here is how the Portfolio Variance equation looks like with Units.

Here is how the Portfolio Variance equation looks like.

0.1455 = {(0.4)}^{2} \cdot {0.37}^{2} + {(0.6)}^{2} \cdot {0.56}^{2} + 2 \cdot (0.4 \cdot 0.6 \cdot 0.37 \cdot 0.56 \cdot 0.108)

0.1455 = {(0.4)}^{2} \cdot {0.37}^{2} + {(0.6)}^{2} \cdot {0.56}^{2} + 2 \cdot (0.4 \cdot 0.6 \cdot 0.37 \cdot 0.56 \cdot 0.108)

0.1455 = {(0.4)}^{2} \cdot {0.37}^{2} + {(0.6)}^{2} \cdot {0.56}^{2} + 2 \cdot (0.4 \cdot 0.6 \cdot 0.37 \cdot 0.56 \cdot 0.108)

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Portfolio Variance Solution

Follow our step by step solution on how to calculate Portfolio Variance?

FIRST Step Consider the formula

Var p = {(w 1)}^{2} \cdot {σ 1}^{2} + {(w 2)}^{2} \cdot {σ 2}^{2} + 2 \cdot (w 1 \cdot w 2 \cdot σ 1 \cdot σ 2 \cdot p 12)

Next Step Substitute values of Variables

∴

Var p = {(0.4)}^{2} \cdot {0.37}^{2} + {(0.6)}^{2} \cdot {0.56}^{2} + 2 \cdot (0.4 \cdot 0.6 \cdot 0.37 \cdot 0.56 \cdot 0.108)

Next Step Prepare to Evaluate

∴

Var p = {(0.4)}^{2} \cdot {0.37}^{2} + {(0.6)}^{2} \cdot {0.56}^{2} + 2 \cdot (0.4 \cdot 0.6 \cdot 0.37 \cdot 0.56 \cdot 0.108)

Next Step Evaluate

∴

Var p = 0.145541248

LAST Step Rounding Answer

∴

Var p = 0.1455

Portfolio Variance Formula Elements

Variables

Portfolio Variance

Portfolio Variance is a measure of the dispersion or spread of returns of a portfolio of investments.

Symbol: Var_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Portfolio Variance

Asset Weight 1

Asset Weight 1 refers to the proportion of the portfolio's total value that the asset represents.

Symbol: w₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Asset Weight 1

Variance of Returns on Assets 1

Variance of Returns on Assets 1 measures the dispersion or variability of the asset's returns around its mean return.

Symbol: σ₁

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Variance of Returns on Assets 1

Asset Weight 2

Asset Weight 2 refers to the proportion of the portfolio's total value that the asset represents.

Symbol: w₂

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Asset Weight 2

Variance of Returns on Assets 2

Variance of Returns on Assets 2 measures the dispersion or variability of the asset's returns around its mean return.

Symbol: σ₂

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Variance of Returns on Assets 2

Portfolio Correlation Coefficient

Portfolio Correlation Coefficient measures the degree to which the returns of two assets in a portfolio move together.

Symbol: p₁₂

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Portfolio Correlation Coefficient

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How to Evaluate Portfolio Variance?

Portfolio Variance evaluator uses Portfolio Variance = (Asset Weight 1)^2*Variance of Returns on Assets 1^2+(Asset Weight 2)^2*Variance of Returns on Assets 2^2+2*(Asset Weight 1*Asset Weight 2*Variance of Returns on Assets 1*Variance of Returns on Assets 2*Portfolio Correlation Coefficient) to evaluate the Portfolio Variance, The Portfolio Variance formula is defined as a measure of the dispersion or spread of returns of a portfolio of investments. It quantifies the degree of risk associated with holding a particular portfolio. Portfolio Variance is denoted by Var_p symbol.

How to evaluate Portfolio Variance using this online evaluator? To use this online evaluator for Portfolio Variance, enter Asset Weight 1 (w₁), Variance of Returns on Assets 1 (σ₁), Asset Weight 2 (w₂), Variance of Returns on Assets 2 (σ₂) & Portfolio Correlation Coefficient (p₁₂) and hit the calculate button.

FAQs on Portfolio Variance

What is the formula to find Portfolio Variance?

The formula of Portfolio Variance is expressed as Portfolio Variance = (Asset Weight 1)^2*Variance of Returns on Assets 1^2+(Asset Weight 2)^2*Variance of Returns on Assets 2^2+2*(Asset Weight 1*Asset Weight 2*Variance of Returns on Assets 1*Variance of Returns on Assets 2*Portfolio Correlation Coefficient). Here is an example- 0.145541 = (0.4)^2*0.37^2+(0.6)^2*0.56^2+2*(0.4*0.6*0.37*0.56*0.108).

How to calculate Portfolio Variance?

With Asset Weight 1 (w₁), Variance of Returns on Assets 1 (σ₁), Asset Weight 2 (w₂), Variance of Returns on Assets 2 (σ₂) & Portfolio Correlation Coefficient (p₁₂) we can find Portfolio Variance using the formula - Portfolio Variance = (Asset Weight 1)^2*Variance of Returns on Assets 1^2+(Asset Weight 2)^2*Variance of Returns on Assets 2^2+2*(Asset Weight 1*Asset Weight 2*Variance of Returns on Assets 1*Variance of Returns on Assets 2*Portfolio Correlation Coefficient).

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Portfolio Variance Formula

Portfolio Variance Example

Portfolio Variance Solution

Portfolio Variance Formula Elements

Other formulas in Important Formulas of Investment category

How to Evaluate Portfolio Variance?

FAQs on Portfolio Variance

Variable Name