Fama-french three-factor model analysis – bogleheads 1 unit electricity price india

This article describes the end-to-end process to create and maintain a portfolio. The objective is to match the desired factor loads while optimizing other factors like costs, (negative) alpha, diversification, taxes, etc. [1] The basic steps are:

finiki:Multifactor investing – a comprehensive tutorial contains numerous referenced examples throughout the article, many of which contain a detailed regression analysis. There is no need to repeat those examples here. The External links section contains an example summary, which include both the Bogleheads and Financial Wisdom Forums.

F u n d A = 60 % ( 1 × ( r m t − r f t ) + 0.6 × S M B + 0.4 × H M L ) {\displaystyle Fund_{A}=60\%(1\times (r_{mt}-r_{ft})+0.6\times {\mathit {SMB}}+0.4\times {\mathit {HML}})} F u n d B = 40 % ( 1 × ( r m t − r f t ) − 0.2 × S M B + 0.3 × H M L ) {\displaystyle Fund_{B}=40\%(1\times (r_{mt}-r_{ft})-0.2\times {\mathit {SMB}}+0.3\times {\mathit {HML}})}

F u n d A + B = ( 60 % ( 1 ) + 40 % ( 1 ) ) × ( r m t − r f t ) + ( 60 % ( 0.6 ) + 40 % ( − 0.2 ) ) × S M B + ( 60 % ( 0.4 ) + 40 % ( 0.3 ) ) × H M L {\displaystyle Fund_{A+B}=(60\%(1)+40\%(1))\times (r_{mt}-r_{ft})+(60\%(0.6)+40\%(-0.2))\times {\mathit {SMB}}+(60\%(0.4)+40\%(0.3))\times {\mathit {HML}}} F u n d A + B = 1 × ( r m t − r f t ) + 0.28 × S M B + 0.36 × H M L {\displaystyle Fund_{A+B}=1\times (r_{mt}-r_{ft})+0.28\times {\mathit {SMB}}+0.36\times {\mathit {HML}}} Regression analysis model

Define the equation: [3] r i t − r f t = α i + β i m ( r m t − r f t ) + β i s S M B t + β i h H M L t + ϵ i t {\displaystyle r_{it}-r_{ft}=\alpha _{i}+\beta _{im}(r_{mt}-r_{ft})+\beta _{is}{\mathit {SMB}}_{t}+\beta _{ih}{\mathit {HML}}_{t}+\epsilon _{it}}

Market: (Market Return – Risk Free Return) the excess return on the market, value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month t, good shares and price data at the beginning of t, and good return data for t minus the one-month Treasury bill rate (from Ibbotson Associates).

The Goodness of fit of a statistical model describes how well it fits a set of observations. In regression, the R 2 Coefficient of determination is a statistical measure of how well the regression line approximates the real data points. [9] The lower the R 2, the more unexplained movements there are in the returns data, which means greater uncertainty.

An R 2 value of 1.0 is a perfect fit. For this analysis, R 2 applies to the regression of the complete model. [note 5] When comparing several portfolios over the same number of samples, the ones with higher R 2 are explained more completely by the linear model.

The confidence levels depend on the number of data points. Refer to the Student’s t-distribution Table of selected values on Wikipedia. (Or, do it yourself using TDIST() and TINV() spreadsheet functions.) For a large number of data points, the t-distribution approaches a normal distribution. A t-value of 1 (or -1 for a negative factor) means the standard error is equal to the magnitude of the value itself.

• r f t = 4.67 {\displaystyle r_{ft}=4.67} , β i m = 0.87 {\displaystyle \beta _{im}=0.87} , ( r m t − r f t ) = 2.65 {\displaystyle (r_{mt}-r_{ft})=2.65} , β i s = 0.63 {\displaystyle \beta _{is}=0.63} , S M B t = − 8.22 {\displaystyle {\mathit {SMB}}_{t}=-8.22} , β i h = 0.50 {\displaystyle \beta _{ih}=0.50} , H M L t = − 12.04 {\displaystyle {\mathit {HML}}_{t}=-12.04} , α i = 0.05 {\displaystyle \alpha _{i}=0.05}

• ↑ A factor is a common characteristic among a group of assets. The Fama-French factors of size and book-to-market have cross-sectional characteristics. Hence, the title of the seminal paper "The Cross-Section of Expected Stock Returns" (1992). See: Factors (finance).

• ↑ The concept of regression might sound strange because the term is normally associated with movement backward, whereas in the world of statistics, regression is often used to predict the future. Simply put, regression is a statistical technique that finds a mathematical expression that best describes a set of data. Ref: Perform a regression analysis, from Microsoft.

• ↑ The residual is the difference between the actual value of the dependent variable for each sample and the estimate of the dependent variable given by the regression equation. Basically, it is the error in the regression estimate of the sample value. The regression is a "least squares" optimization, which means that the intercept and factor loadings are chosen to minimize the squared sum of all the residuals. (From forum member camontgo, via PM.)