Fama French Multi-Factor Analysis. What is it?

There are various calculations you can do with financial market data. There is Factor Analysis, Portfolio Optimization, Correlation Matrix, Covariance Matrix, VaR, CVaR, Volatility, Sharpe Ratio, and many other calculations. With the widespread popularity of Smart Beta ETFs factor-based investing has become one of the most popular investment strategies for institutional and retail investors in finding, and generating Alpha. Here is a screenshot from  ZOONOVA  showing some of the calculations.

In the above image you can see the calculations for Fama French 5 Factor Portfolio Analysis, Covariance/Correlation Matrix, and Portfolio output in “Real-Time.” Here is a link to a YouTube video that I did showing the Fama French Factor Analysis.

 Here are the definitions of the analysis.

CSharpe (95) XA

(Exp Return* − RF%) / CVaR (95)*

CSharpe (95) XP

(Curr P&L%* − RF%) / CVaR (95)*

CSharpe (99) XA

(Exp Return* − RF%) / CVaR (99)*

CSharpe (99) XP

(Curr P&L%* − RF%) / CVaR (99)*

M2 XA

(a.k.a. Modigliani, M2, M-Squared) In simple words, it measures the returns of an investment portfolio for the risk taken, relative to some benchmark portfolio. Popularly known as Modigliani Risk Adjustment Performance Measure or M2, it was developed by Nobel prize winner Franco Modigliani and his granddaughter, Leah Modigliani, in 1997. It is calculated as (Sharpe XA × SPY Volatility) + RF%.

M2 XP

(a.k.a. Modigliani, M2, M-Squared) In simple words, it measures the returns of an investment portfolio for the risk taken, relative to some benchmark portfolio. Popularly known as Modigliani Risk Adjustment Performance Measure or M2, it was developed by Nobel prize winner Franco Modigliani and his granddaughter, Leah Modigliani, in 1997. It is calculated as (Sharpe XP × SPY Volatility) + RF%.

Sharpe XA

(Exp Return* − RF%) / Volatility

Sharpe XP

(Curr P&L%* − RF%) / Volatility

SPY Variance

Variance calculated for the SPY ETF (SPDR S& P500).

SPY Volatility

Calculated as the SQRT (√) of the SPY (SPDR S& P500) Variance (see SPY Variance).

Variance

(Calculated from the COVAR Matrix) The most important quality of portfolio variance is that its value is a weighted combination of the individual variances of each of the assets adjusted by their covariances.This means that the overall portfolio variance is lower than a simple weighted average of the individual variances of the stocks in the portfolio.

Volatility

Calculated as the SQRT (√) of the Portfolio Variance (see Variance).

NOTE:

RF% = Risk-Free Interest Rate

* indicates a weighted average

Values based on 2 years of daily returns of the underlying security

Factor Analysis

Factor Analysis uses multiple linear regression to determine how much Alpha (α) is being generated for a portfolio and individual securities. It is an important statistical calculation that shows if Alpha is really being generated by a Portfolio and/or securities. In recent years, estimating Alpha over and above multiple sources of systematic risk has become the industry practice. Zoonova allows users to perform factor analysys using Fama-French factors (used by permission), ETF benchmarks or securities. The following standard tables are produced

Summary Output ("Goodness of Fit")

Multiple R

Correlation coefficient (square root of r squared): It indicates the strength of the linear relationship (i.e., a value of 1 means a perfect positive relationship and a value of zero means no relationship at all).

R Square

Coefficient of Determination. It indicates how many points fall on the regression line (e.g., 80% represents that 80% of the values fit the model).

Adjusted R Square

The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. The adjusted R-squared increases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance.

Standard Error

"Standard Error" is an estimate of the standard deviation of the error µ, and not the descriptive statistical value of the same name.

Observations

The total number of observations in the sample.

ANOVA (Analysis of Variance)

The following indicators are calculated for the regression, the residual, and the total:

df

Degress of freedom.

SS

Sum of Squares

MS

Mean square error

F

Overall F test for the hypothesis.

Significance F

Significance associated P-Value.

Value Matrix

The rows of the matrix show indicators for the Intercept and each Fama-French Factor or benchmark:

Intercept (α)

The Alpha being generated. Zoonova first calculates a daily Alpha and then shows it as an annual Alpha.

Market (Mkt-RF) β

Systematic risk factors for the market.

Size (SMB) β

"Small − big," or the amount by which small-cap stock returns are expected to exceed large-cap stock returns.

Value (HML) β

"High − low," or the amount by which the returns of high book-to-market (value) stocks are expected to exceed the returns of low book-to-market (growth) stocks.

Profitability (RMW) β

"Robust − weak", or the average return on the two robust operating profitability portfolios minus the average return on the two weak operating profitability portfolio.

Investment (CMA) β

"Conservative − aggressive," or the average return on two conservative investment portfolios minus the average return on the two aggressive investment portfolios.

Momentum (MOM) β

βMomβ (momentum) can be used as a 6th Factor. is the average return on the two high prior return portfolios minus the average return on the two low prior return portfolios: Mom = (Small High + Big High) / 2 − (Small Low + Big Low) / 2

These indicators are:

Coefficient

Least squares estimate.

Standard Error

Least squares estimate of the standard error.

t Stat

T Statistic for the null hypothesis vs. the alternate hypothesis. It indicates whether the results are significant. An absolute value of 2 or more, i.e. +2 or greater or -2 or less means that the results are significant.

P-value

P-value for the hypothesis test. It indicates the level of significance: The smaller the p-value, the higher the significance because it means that the hypothesis under consideration may not adequately explain the observation.

Lower 95%

Lower boundary for the confidence interval.

Upper 95%

Upper boundary for the confidence interval.

Cheers.