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Fama-French Three-Factor Model Formula

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Excess Return on Asset represents the excess return of an asset over the risk-free rate. Check FAQs
Rexc=αi+βF⋅(Rmkt-Rf)+(si⋅SMB+hml+Ei)
Rexc - Excess Return on Asset?αi - Asset Specific Alpha?βF - Beta in Forex?Rmkt - Return on Market Portfolio?Rf - Risk Free Rate?si - Sensitivity of the Asset to SMB?SMB - Small Minus Big?hml - Sensitivity of the Asset to HML?Ei - Error Term?

Fama-French Three-Factor Model Example

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Here is how the Fama-French Three-Factor Model equation looks like with Values.

Here is how the Fama-French Three-Factor Model equation looks like with Units.

Here is how the Fama-French Three-Factor Model equation looks like.

23.134Edit=8Edit+0.07Edit⋅(6.5Edit-0.3Edit)+(2.5Edit⋅3.5Edit+4.5Edit+1.45Edit)
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Fama-French Three-Factor Model Solution

Follow our step by step solution on how to calculate Fama-French Three-Factor Model?

FIRST Step Consider the formula
Rexc=αi+βF⋅(Rmkt-Rf)+(si⋅SMB+hml+Ei)
Next Step Substitute values of Variables
∴ Rexc=8+0.07⋅(6.5-0.3)+(2.5⋅3.5+4.5+1.45)
Next Step Prepare to Evaluate
∴ Rexc=8+0.07⋅(6.5-0.3)+(2.5⋅3.5+4.5+1.45)
LAST Step Evaluate
∴Rexc=23.134

Fama-French Three-Factor Model Formula Elements

Variables
Excess Return on Asset
Excess Return on Asset represents the excess return of an asset over the risk-free rate.
Symbol: Rexc
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Excess Return on AssetOpen Variable
Asset Specific Alpha
Asset Specific Alpha is a measure used in finance to evaluate the performance of an investment or portfolio relative to a benchmark.
Symbol: αi
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Asset Specific AlphaOpen Variable
Beta in Forex
Beta in Forex refers to a measure of a currency pair's volatility in relation to the overall forex market.
Symbol: βF
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Beta in ForexOpen Variable
Return on Market Portfolio
Return on Market Portfolio represents the excess return of the market portfolio over the risk-free rate.
Symbol: Rmkt
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Return on Market PortfolioOpen Variable
Risk Free Rate
The Risk Free Rate is the theoretical rate of return of an investment with zero risks.
Symbol: Rf
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Risk Free RateOpen Variable
Sensitivity of the Asset to SMB
Sensitivity of the Asset to SMB refers to how the returns of that asset are influenced by movements in the small-cap minus large-cap stock factor.
Symbol: si
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Sensitivity of the Asset to SMBOpen Variable
Small Minus Big
Small Minus Big refers to a factor used in finance and investing, particularly in the context of Fama-French three-factor model or other factor models used to explain the returns of stocks.
Symbol: SMB
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Small Minus BigOpen Variable
Sensitivity of the Asset to HML
Sensitivity of the Asset to HML refers to how the returns of that asset are influenced by movements in the high book-to-market ratio minus low book-to-market ratio factor.
Symbol: hml
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Sensitivity of the Asset to HMLOpen Variable
Error Term
Error Term represents the difference between the observed values of the dependent variable and the values predicted by the regression model.
Symbol: Ei
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Error TermOpen Variable

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How to Evaluate Fama-French Three-Factor Model?

Fama-French Three-Factor Model evaluator uses Excess Return on Asset = Asset Specific Alpha+Beta in Forex*(Return on Market Portfolio-Risk Free Rate)+(Sensitivity of the Asset to SMB*Small Minus Big+Sensitivity of the Asset to HML+Error Term) to evaluate the Excess Return on Asset, The Fama-French Three-Factor Model formula is defined as an asset pricing model that expands upon the Capital Asset Pricing Model (CAPM) by considering additional factors that influence stock returns. . Excess Return on Asset is denoted by Rexc symbol.

How to evaluate Fama-French Three-Factor Model using this online evaluator? To use this online evaluator for Fama-French Three-Factor Model, enter Asset Specific Alpha (αi), Beta in Forex (βF), Return on Market Portfolio (Rmkt), Risk Free Rate (Rf), Sensitivity of the Asset to SMB (si), Small Minus Big (SMB), Sensitivity of the Asset to HML (hml) & Error Term (Ei) and hit the calculate button.

FAQs on Fama-French Three-Factor Model

What is the formula to find Fama-French Three-Factor Model?
The formula of Fama-French Three-Factor Model is expressed as Excess Return on Asset = Asset Specific Alpha+Beta in Forex*(Return on Market Portfolio-Risk Free Rate)+(Sensitivity of the Asset to SMB*Small Minus Big+Sensitivity of the Asset to HML+Error Term). Here is an example- 23.184 = 8+0.07*(6.5-0.3)+(2.5*3.5+4.5+1.45).
How to calculate Fama-French Three-Factor Model?
With Asset Specific Alpha (αi), Beta in Forex (βF), Return on Market Portfolio (Rmkt), Risk Free Rate (Rf), Sensitivity of the Asset to SMB (si), Small Minus Big (SMB), Sensitivity of the Asset to HML (hml) & Error Term (Ei) we can find Fama-French Three-Factor Model using the formula - Excess Return on Asset = Asset Specific Alpha+Beta in Forex*(Return on Market Portfolio-Risk Free Rate)+(Sensitivity of the Asset to SMB*Small Minus Big+Sensitivity of the Asset to HML+Error Term).
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