Portfolio Variance Calculator

✖Asset Weight refers to the proportion of the portfolio's total value that the asset represents.ⓘ Asset Weight [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 refers to the proportion of the portfolio's total value that the asset represents.ⓘ Asset Weight [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 Variance is a measure of the dispersion or spread of returns of a portfolio of investments.ⓘ Portfolio Variance [Var_p]

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Formula

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Portfolio Variance

Formula

`"Var"_{"p"} = ("w"_{"1"})^2*"σ"_{"1"}^2+("w"_{"2"})^2*"σ"_{"2"}^2+2*("w"_{"1"}*"w"_{"2"}*"σ"_{"1"}*"σ"_{"2"}*"p"_{"12"})`

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")`

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Portfolio Variance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Portfolio Variance = (Asset Weight)^2*Variance of Returns on Assets 1^2+(Asset Weight)^2*Variance of Returns on Assets 2^2+2*(Asset Weight*Asset Weight*Variance of Returns on Assets 1*Variance of Returns on Assets 2*Portfolio Correlation Coefficient)
Var_p = (w₁)^2*σ₁^2+(w₂)^2*σ₂^2+2*(w₁*w₂*σ₁*σ₂*p₁₂)
This formula uses 6 Variables

Variables Used

Portfolio Variance - Portfolio Variance is a measure of the dispersion or spread of returns of a portfolio of investments.
Asset Weight - Asset Weight 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 - Asset Weight 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: 0.4 --> No Conversion Required
Variance of Returns on Assets 1: 0.37 --> No Conversion Required
Asset Weight: 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

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

Evaluating ... ...

Var_p = 0.145541248

STEP 3: Convert Result to Output's Unit

0.145541248 --> No Conversion Required

FINAL ANSWER

0.145541248 ≈ 0.145541 <-- Portfolio Variance

(Calculation completed in 00.004 seconds)

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Created by Vishnu K

BMS College of Engineering (BMSCE), Bangalore

Vishnu K has created this Calculator and 200+ more calculators!

Verified by Kashish Arora

Satyawati College (DU), New Delhi

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< 22 Investment Calculators

Portfolio Standard Deviation

Go Portfolio Standard Deviation = sqrt((Asset Weight)^2*Variance of Returns on Assets 1^2+(Asset Weight)^2*Variance of Returns on Assets 2^2+2*(Asset Weight*Asset Weight*Variance of Returns on Assets 1*Variance of Returns on Assets 2*Portfolio Correlation Coefficient))

Portfolio Variance

Go Portfolio Variance = (Asset Weight)^2*Variance of Returns on Assets 1^2+(Asset Weight)^2*Variance of Returns on Assets 2^2+2*(Asset Weight*Asset Weight*Variance of Returns on Assets 1*Variance of Returns on Assets 2*Portfolio Correlation Coefficient)

Jensen's Alpha

Go Jensen's Alpha = Annual Return on Investment-(Risk Free Interest Rate+Beta of the Portfolio*(Annual return of the market benchmark-Risk Free Interest Rate))

Compound Interest

Go Future Value of Investment = Principal Investment Amount*(1+(Annual Interest Rate/Number of Periods))^(Number of Periods*Number of Years Money is Invested)

Certificate of Deposit

Go Certificate of Deposit = Initial Deposit Amount*(1+(Annual Nominal Interest Rate/Compounding Periods))^(Compounding Periods*Number of Years)

Actuarial Method Unearned Interest Loan

Go Actuarial Method Unearned Interest Loan = (Number of Remaining Monthly Payments*Monthly Payment*Annual Percentage Rate)/(100+Annual Percentage Rate)

Equivalent Annual Annuity

Go Equivalent Annuity Cashflow = (Rate per Period*(Net Present Value (NPV)))/(1-(1+Rate per Period)^-Number of Periods)

Portfolio Expected Return

Go Portfolio Expected Return = Asset Weight*(Expected Return on Asset 1)+Asset Weight*(Expected Return on Asset 2)

Total Stock Return

Go Total Stock Return = ((Ending Stock Price-Initial Stock Price)+Dividend)/Initial Stock Price

Annuity Payment

Go Annuity Payment = (Rate per Period*Present Value)/(1-(1+Rate per Period)^-Number of Periods)

Value at Risk

Go Value at Risk = -Mean of Profit and Loss+Standard Deviation of Profit and Loss*Standard Normal Variate

Profitability Index

Go Profitability Index (PI) = (Net Present Value (NPV)+Initial Investment)/Initial Investment

Sharpe Ratio

Go Sharpe Ratio = (Expected Portfolio Return-Risk Free Rate)/Portfolio Standard Deviation

Capital Gains Yield

Go Capital Gains Yield = (Current Stock Price-Initial Stock Price)/Initial Stock Price

Treynor Ratio

Go Treynor's Ratio = (Expected Portfolio Return-Risk Free Rate)/Beta of the Portfolio

Average Return on Investment

Go Average Return = modulus(Total Value of Return)/Total Number of Returns

Information Ratio

Go Information Ratio = (Portfolio Return-Benchmark Return)/Tracking Error

Rate of Return

Go Rate of Return = ((Current Value-Original Value)/Original Value)*100

Straight Line Depreciation

Go Straight Line Depreciation = (Asset's Cost-Salvage)/Life

Portfolio Turnover Rate

Go Porfolio Turnover Rate = (Total Sales and Purchases of Shares/Average Net Assets)*100

Real Rate of Return

Go Real Rate of Return = ((1+Nominal Rate)/(1+Inflation Rate))-1

Risk Premium

Go Risk Premium = Return on Investment (ROI)-Risk Free Return

Portfolio Variance Formula

What is Portfolio Variance?

Portfolio Variancea 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.
For portfolios with more than two assets, the formula extends accordingly by adding terms for each pair of assets, considering their respective weights and correlations.
Once you have calculated the portfolio variance, you can take the square root to find the standard deviation, which gives a measure of the volatility or risk of the portfolio.

How to Calculate Portfolio Variance?

Portfolio Variance calculator uses Portfolio Variance = (Asset Weight)^2*Variance of Returns on Assets 1^2+(Asset Weight)^2*Variance of Returns on Assets 2^2+2*(Asset Weight*Asset Weight*Variance of Returns on Assets 1*Variance of Returns on Assets 2*Portfolio Correlation Coefficient) to calculate 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 calculate Portfolio Variance using this online calculator? To use this online calculator for Portfolio Variance, enter Asset Weight (w₁), Variance of Returns on Assets 1 (σ₁), Asset Weight (w₂), Variance of Returns on Assets 2 (σ₂) & Portfolio Correlation Coefficient (p₁₂) and hit the calculate button. Here is how the Portfolio Variance calculation can be explained with given input values -> 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).

FAQ

What is 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 and is represented as Var_p = (w₁)^2*σ₁^2+(w₂)^2*σ₂^2+2*(w₁*w₂*σ₁*σ₂*p₁₂) or Portfolio Variance = (Asset Weight)^2*Variance of Returns on Assets 1^2+(Asset Weight)^2*Variance of Returns on Assets 2^2+2*(Asset Weight*Asset Weight*Variance of Returns on Assets 1*Variance of Returns on Assets 2*Portfolio Correlation Coefficient). Asset Weight 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 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 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 is calculated using Portfolio Variance = (Asset Weight)^2*Variance of Returns on Assets 1^2+(Asset Weight)^2*Variance of Returns on Assets 2^2+2*(Asset Weight*Asset Weight*Variance of Returns on Assets 1*Variance of Returns on Assets 2*Portfolio Correlation Coefficient). To calculate Portfolio Variance, you need Asset Weight (w₁), Variance of Returns on Assets 1 (σ₁), Asset Weight (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, Variance of Returns on Assets 1, Asset Weight, 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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