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Portfolio Standard Deviation Calculator

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✖Asset Weight 1 refers to the proportion of the portfolio's total value that the asset represents.ⓘ Asset Weight 1 [w₁]			+10% -10%
✖Variance of Returns on Assets 1 measures the dispersion or variability of the asset's returns around its mean return.ⓘ Variance of Returns on Assets 1 [σ₁]			+10% -10%
✖Asset Weight 2 refers to the proportion of the portfolio's total value that the asset represents.ⓘ Asset Weight 2 [w₂]			+10% -10%
✖Variance of Returns on Assets 2 measures the dispersion or variability of the asset's returns around its mean return.ⓘ Variance of Returns on Assets 2 [σ₂]			+10% -10%
✖Portfolio Correlation Coefficient measures the degree to which the returns of two assets in a portfolio move together.ⓘ Portfolio Correlation Coefficient [p₁₂]			+10% -10%

✖Portfolio Standard Deviation is a measure of the dispersion of a set of data from its mean.ⓘ Portfolio Standard Deviation [σp]

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Portfolio Standard Deviation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
σp = sqrt((w₁)^2*σ₁^2+(w₂)^2*σ₂^2+2*(w₁*w₂*σ₁*σ₂*p₁₂))
This formula uses 1 Functions, 6 Variables

Functions Used

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., sqrt(Number)

Variables Used

Portfolio Standard Deviation - Portfolio Standard Deviation is a measure of the dispersion of a set of data from its mean.
Asset Weight 1 - Asset Weight 1 refers to the proportion of the portfolio's total value that the asset represents.
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.
Asset Weight 2 - Asset Weight 2 refers to the proportion of the portfolio's total value that the asset represents.
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.
Portfolio Correlation Coefficient - Portfolio Correlation Coefficient measures the degree to which the returns of two assets in a portfolio move together.

STEP 1: Convert Input(s) to Base Unit

Asset Weight 1: 0.4 --> No Conversion Required
Variance of Returns on Assets 1: 0.37 --> No Conversion Required
Asset Weight 2: 0.6 --> No Conversion Required
Variance of Returns on Assets 2: 0.56 --> No Conversion Required
Portfolio Correlation Coefficient: 0.108 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σp = sqrt((w₁)^2*σ₁^2+(w₂)^2*σ₂^2+2*(w₁*w₂*σ₁*σ₂*p₁₂)) --> sqrt((0.4)^2*0.37^2+(0.6)^2*0.56^2+2*(0.4*0.6*0.37*0.56*0.108))

Evaluating ... ...

σp = 0.381498686760518

STEP 3: Convert Result to Output's Unit

0.381498686760518 --> No Conversion Required

FINAL ANSWER

0.381498686760518 ≈ 0.381499 <-- Portfolio Standard Deviation

(Calculation completed in 00.020 seconds)

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BMS College of Engineering (BMSCE), Bangalore

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Portfolio Standard Deviation Formula

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What is Portfolio Standard Deviation?

Portfolio standard deviation is a measure of the dispersion or volatility of returns for a portfolio of assets. It quantifies the extent of variability or risk associated with the portfolio's returns. The standard deviation of a portfolio takes into account both the individual volatilities of the assets within the portfolio and the correlations between them.
In simpler terms, portfolio standard deviation accounts for the volatility of each asset in the portfolio, their respective weights, and the correlation between the returns of the assets. It measures the risk of the portfolio as a whole, considering diversification effects.
To calculate the portfolio standard deviation, you need the standard deviations of the individual assets' returns, their weights in the portfolio, and the correlation coefficients between the returns of each pair of assets in the portfolio. Then, you apply the formula to compute the overall standard deviation of the portfolio.

How to Calculate Portfolio Standard Deviation?

Portfolio Standard Deviation calculator 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 calculate 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 calculate Portfolio Standard Deviation using this online calculator? To use this online calculator 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. Here is how the Portfolio Standard Deviation calculation can be explained with given input values -> 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)).

FAQ

What is 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 and is represented as σp = sqrt((w₁)^2*σ₁^2+(w₂)^2*σ₂^2+2*(w₁*w₂*σ₁*σ₂*p₁₂)) or 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)). Asset Weight 1 refers to the proportion of the portfolio's total value that the asset represents, Variance of Returns on Assets 1 measures the dispersion or variability of the asset's returns around its mean return, Asset Weight 2 refers to the proportion of the portfolio's total value that the asset represents, Variance of Returns on Assets 2 measures the dispersion or variability of the asset's returns around its mean return & Portfolio Correlation Coefficient measures the degree to which the returns of two assets in a portfolio move together.

How to calculate 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 is calculated using 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 calculate Portfolio Standard Deviation, you need 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). With our tool, you need to enter the respective value for Asset Weight 1, Variance of Returns on Assets 1, Asset Weight 2, Variance of Returns on Assets 2 & Portfolio Correlation Coefficient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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