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Portfolio Standard Deviation Formula

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Portfolio Standard Deviation is a measure of the dispersion of a set of data from its mean. Check FAQs

σp = \sqrt{{(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)}

σp - Portfolio Standard Deviation?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 Standard Deviation Example

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Here is how the Portfolio Standard Deviation equation looks like with Values.

Here is how the Portfolio Standard Deviation equation looks like with Units.

Here is how the Portfolio Standard Deviation equation looks like.

0.3815 = \sqrt{{(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)}

0.3815 = \sqrt{{(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)}

0.3815 = \sqrt{{(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 Standard Deviation Solution

Follow our step by step solution on how to calculate Portfolio Standard Deviation?

FIRST Step Consider the formula

σp = \sqrt{{(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

∴

σp = \sqrt{{(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

∴

σp = \sqrt{{(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

∴

σp = 0.381498686760518

LAST Step Rounding Answer

∴

σp = 0.3815

Portfolio Standard Deviation Formula Elements

Variables

Functions

Portfolio Standard Deviation

Portfolio Standard Deviation is a measure of the dispersion of a set of data from its mean.

Symbol: σp

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Portfolio Standard Deviation

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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CGY = \frac{P c - P0}{P0}

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How to Evaluate Portfolio Standard Deviation?

Portfolio Standard Deviation evaluator uses Portfolio Standard Deviation = sqrt((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 Standard Deviation, The Portfolio Standard Deviation formula is defined as a measure of the dispersion or volatility of returns for a portfolio of assets. Portfolio Standard Deviation is denoted by σp symbol.

How to evaluate Portfolio Standard Deviation using this online evaluator? To use this online evaluator for Portfolio Standard Deviation, 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 Standard Deviation

What is the formula to find Portfolio Standard Deviation?

The formula of Portfolio Standard Deviation is expressed as Portfolio Standard Deviation = sqrt((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- 0.381499 = sqrt((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 Standard Deviation?

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 Standard Deviation using the formula - Portfolio Standard Deviation = sqrt((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)). This formula also uses Square Root (sqrt) function(s).

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Portfolio Standard Deviation Formula

Portfolio Standard Deviation Example

Portfolio Standard Deviation Solution

Portfolio Standard Deviation Formula Elements

Other formulas in Important Formulas of Investment category

How to Evaluate Portfolio Standard Deviation?

FAQs on Portfolio Standard Deviation

Variable Name