Fama-French Three-Factor Model Calculator

✖Asset Specific Alpha is a measure used in finance to evaluate the performance of an investment or portfolio relative to a benchmark.ⓘ Asset Specific Alpha [αi]			+10% -10%
✖Beta in Forex refers to a measure of a currency pair's volatility in relation to the overall forex market.ⓘ Beta in Forex [β_F]			+10% -10%
✖Return on Market Portfolio represents the excess return of the market portfolio over the risk-free rate.ⓘ Return on Market Portfolio [R_mkt]			+10% -10%
✖The Risk Free Rate is the theoretical rate of return of an investment with zero risks.ⓘ Risk Free Rate [R_f]			+10% -10%
✖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.ⓘ Sensitivity of the Asset to SMB [si]			+10% -10%
✖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.ⓘ Small Minus Big [SMB]			+10% -10%
✖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.ⓘ Sensitivity of the Asset to HML [h_ml]			+10% -10%
✖Error Term represents the difference between the observed values of the dependent variable and the values predicted by the regression model.ⓘ Error Term [E_i]			+10% -10%

✖Excess Return on Asset represents the excess return of an asset over the risk-free rate.ⓘ Fama-French Three-Factor Model [Rexc]

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Fama-French Three-Factor Model

Formula

`"Rexc" = "αi"+"β"_{"F"}*("R"_{"mkt"}-"R"_{"f"})+("si"*"SMB"+"h"_{"ml"}+"E"_{"i"})`

Example

`"23.134"="8"+"0.07"*("6.5"-"0.30")+("2.5"*"3.5"+"4.5"+"1.45")`

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Fama-French Three-Factor Model Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
Rexc = αi+β_F*(R_mkt-R_f)+(si*SMB+h_ml+E_i)
This formula uses 9 Variables

Variables Used

Excess Return on Asset - Excess Return on Asset represents the excess return of an asset over the risk-free rate.
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.
Beta in Forex - Beta in Forex refers to a measure of a currency pair's volatility in relation to the overall forex market.
Return on Market Portfolio - Return on Market Portfolio represents the excess return of the market portfolio over the risk-free rate.
Risk Free Rate - The Risk Free Rate is the theoretical rate of return of an investment with zero risks.
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.
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.
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.
Error Term - Error Term represents the difference between the observed values of the dependent variable and the values predicted by the regression model.

STEP 1: Convert Input(s) to Base Unit

Asset Specific Alpha: 8 --> No Conversion Required
Beta in Forex: 0.07 --> No Conversion Required
Return on Market Portfolio: 6.5 --> No Conversion Required
Risk Free Rate: 0.3 --> No Conversion Required
Sensitivity of the Asset to SMB: 2.5 --> No Conversion Required
Small Minus Big: 3.5 --> No Conversion Required
Sensitivity of the Asset to HML: 4.5 --> No Conversion Required
Error Term: 1.45 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Rexc = αi+β_F*(R_mkt-R_f)+(si*SMB+h_ml+E_i) --> 8+0.07*(6.5-0.3)+(2.5*3.5+4.5+1.45)

Evaluating ... ...

Rexc = 23.134

STEP 3: Convert Result to Output's Unit

23.134 --> No Conversion Required

FINAL ANSWER

23.134 <-- Excess Return on Asset

(Calculation completed in 00.020 seconds)

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< 14 Forex Management Calculators

Black-Scholes-Merton Option Pricing Model for Call Option

Go Theoretical Price of Call Option = Current Stock Price*Normal Distribution*(Cumulative Distribution 1)-(Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock))*Normal Distribution*(Cumulative Distribution 2)

Cumulative Distribution One

Go Cumulative Distribution 1 = (ln(Current Stock Price/Option Strike Price)+(Risk Free Rate+Volatile Underlying Stock^2/2)*Time to Expiration of Stock)/(Volatile Underlying Stock*sqrt(Time to Expiration of Stock))

Fama-French Three-Factor Model

Go 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)

Vasicek Interest Rate

Go Derivative of Short Rate = Speed of Mean Reversal*(Long Term Mean-Short Rate)*Derivatives*Time Period+Volatility at Time*Derivatives*Random Market Risk

Black-Scholes-Merton Option Pricing Model for Put Option

Go Theoretical Price of Put Option = Option Strike Price*exp(-Risk Free Rate*Time to Expiration of Stock)*(-Cumulative Distribution 2)-Current Stock Price*(-Cumulative Distribution 1)

Forward Rate

Go Forward Rate = Spot Exchange Rate*ln((Domestic Interest Rate-Foreign Interest Rate)*Time to Maturity)

Cumulative Distribution Two

Go Cumulative Distribution 2 = Cumulative Distribution 1-Volatile Underlying Stock*sqrt(Time to Expiration of Stock)

Position Size in Forex

Go Position Size in Forex = (Account Equity*Risk Percentage in Forex)/(Stop Loss in Pips*Pip Value in Forex)

Profit for Call Buyer

Go Profit for Call Buyer = max(0,Price of Underlying at Expiration-Exercise Price)-Call Premium

Interest Rate Parity

Go Forward Rate Constant = Spot Exchange Rate*((1+Interest Rate of Quote Currency)/(1+Interest Rate of Base Currency))

Gordon Growth Model

Go Current Stock Price = (Dividend Per Share)/(Required Rate of Return-Constant Growth Rate of Dividend)

Payoff for Call Buyer

Go Payoff for Call Buyer = max(0,Price of Underlying at Expiration-Exercise Price)

Purchasing Power Parity Theory using Inflation

Go Exchange Rate Factor = ((1+Inflation in Home Country)/(1+Inflation in Foreign Country))-1

Intrinsic Value

Go Intrinsic Value = Share Price-Base Value

Fama-French Three-Factor Model Formula

What is Fama-French Three-Factor Model?

The Fama-French Three-Factor Model is an asset pricing model that expands upon the Capital Asset Pricing Model (CAPM) by considering additional factors that influence stock returns. The three factors in the model are:

Market Risk (Mkt-RF): This is the excess return of the market portfolio over the risk-free rate.
Size (SMB - Small Minus Big): This factor represents the historical excess returns of small-cap stocks over large-cap stocks.
Value (HML - High Minus Low): This factor represents the historical excess returns of value stocks (with high book-to-market ratios) over growth stocks (with low book-to-market ratios).

How to Calculate Fama-French Three-Factor Model?

Fama-French Three-Factor Model calculator 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 calculate 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 calculate Fama-French Three-Factor Model using this online calculator? To use this online calculator for Fama-French Three-Factor Model, enter Asset Specific Alpha (αi), Beta in Forex (β_F), Return on Market Portfolio (R_mkt), Risk Free Rate (R_f), Sensitivity of the Asset to SMB (si), Small Minus Big (SMB), Sensitivity of the Asset to HML (h_ml) & Error Term (E_i) and hit the calculate button. Here is how the Fama-French Three-Factor Model calculation can be explained with given input values -> 23.184 = 8+0.07*(6.5-0.3)+(2.5*3.5+4.5+1.45).

FAQ

What is Fama-French Three-Factor Model?

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. and is represented as Rexc = αi+β_F*(R_mkt-R_f)+(si*SMB+h_ml+E_i) or 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). Asset Specific Alpha is a measure used in finance to evaluate the performance of an investment or portfolio relative to a benchmark, Beta in Forex refers to a measure of a currency pair's volatility in relation to the overall forex market, Return on Market Portfolio represents the excess return of the market portfolio over the risk-free rate, The Risk Free Rate is the theoretical rate of return of an investment with zero risks, 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, 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, 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 & Error Term represents the difference between the observed values of the dependent variable and the values predicted by the regression model.

How to calculate Fama-French Three-Factor Model?

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. is calculated using 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 calculate Fama-French Three-Factor Model, you need Asset Specific Alpha (αi), Beta in Forex (β_F), Return on Market Portfolio (R_mkt), Risk Free Rate (R_f), Sensitivity of the Asset to SMB (si), Small Minus Big (SMB), Sensitivity of the Asset to HML (h_ml) & Error Term (E_i). With our tool, you need to enter the respective value for 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 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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