**formula for calculating the likely return on a stock market investment**. It measures this return based on a comparison of the investment to the overall risk in the market, the size of the companies involved and their book-to-market values (the inverse of the price-to-book ratio).

How do you calculate favorable and unfavorable variances?

**how to calculate favorable and unfavorable variances in excel**.

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The Fama-French Three Factor model is a **formula for calculating the likely return on a stock market investment**. It measures this return based on a comparison of the investment to the overall risk in the market, the size of the companies involved and their book-to-market values (the inverse of the price-to-book ratio).

- Calculate the average 1 month return, 2 month return,, 3 month return, …. …
- Calculate the 1 month average, 2 month average, 3 month average, …. …
- Subtract 1 month average Rf from average 1 month return, repeat until the 36th month.

- r = Expected rate of return.
- rf = Risk-free rate.
- ß = Factor’s coefficient (sensitivity)
- (rm – rf) = Market risk premium.
- SMB (Small Minus Big) = Historic excess returns of small-cap companies over large-cap companies.

Taking inspiration from the Fama French five-factor model, we can develop a multi-factor stock selection strategy that focuses on five factors: **size, value, quality, profitability, and investment pattern**.

Today, **the four factors of market, style, size, and momentum**, constitute the Fama-French 4 Factor Model.

The Fama and French model has three factors: **the size of firms, book-to-market values, and excess return on the market**. In other words, the three factors used are SMB (small minus big), HML (high minus low), and the portfolio’s return less the risk-free rate of return.

The Fama-French Three Factor model is **a formula for calculating the likely return on a stock market investment**. It measures this return based on a comparison of the investment to the overall risk in the market, the size of the companies involved and their book-to-market values (the inverse of the price-to-book ratio).

The Fama-French Portfolios are constructed from the **intersections of two portfolios formed on size**, as measured by market equity (ME), and three portfolios using the ratio of book equity to market equity (BE/ME) as a proxy for value.

Griffin (2002) demonstrates that the performance of **Fama-French country-specific** factor regression is much better than global-factor model, whereas Blanco (2012) shows that its expected outcome depends upon how the stock portfolios are formed (e.g. based on characteristics relating to risk factors).

Empirical results point out that Fama and French Three Factor Model is **better than CAPM** according to the goal of explaining the expected returns of the portfolios.

The Fama-French five-factor model includes **profitability and investment of the firm together with firm size and value to** account for additional variation in equity prices that are typically not captured by the market factor in the standard capital asset pricing model (CAPM).

- First regress each of n asset returns against m proposed risk factors to determine each asset’s beta exposures.
- Then regress all asset returns for each of T time periods against the previously estimated betas to determine the risk premium for each factor.

The Fama-French model, developed in the 1990, argued most stock market returns are explained by three factors: **risk**, price (value stocks tending to outperform) and company size (smaller company stocks tending to outperform). Carhart added a momentum factor for asset pricing of stocks.

The WML factor is computed as **the difference between the average of returns on winners portfolios** (SW as well as BW) and losers portfolios (SL and BL).

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Fama French presented their 3 factor model in order to gap the limitations posed by CAPM model. … It means that Fama French model **is better predicting variation in excess return over Rf than CAPM for** all the five companies of the Cement industry over the period of ten years.

Fama-French Market Beta is **the beta used for the Market Risk Premium** (CAPM also uses a Market Risk Premium Beta, but the FF Market Beta and CAPM Beta are not interchangeable, as CAPM uses a single beta for expected returns, whereas Fama-French uses three betas.)

Rubinstein (1973) derives an equation for the expected return in terms of an arbitrary number of co-moments. We test whether SMB and HML proxy for these co-moments.

Factor models are **financial models that use factors** — that can be technical, fundamental, macroeconomic or alternate to define a security’s risk and returns. These models are linear, as they define the securities returns to be a linear combination of factor returns weighted by the securities factor exposures.

To construct the SMB and HML factors, **we sort stocks in a region into two market cap and three book-to-market equity (B/M) groups at the end of each June**. Big stocks are those in the top 90% of June market cap for the region, and small stocks are those in the bottom 10%.

There are several approaches to construct factor mimicking portfolios. A formal approach is **to use cross-sectional regression of returns on factor loadings or firm characteristics** to estimate the return of the mimicking portfolios, henceforth denoted by the cross-sectional regression approach (CSR), (see Fama, 1976).

- Alpha = Actual Rate of Return – Expected Rate of Return. …
- Expected Rate of Return = Risk-Free Rate + β * Market Risk Premium. …
- Alpha = Actual Rate of Return – Risk-Free Rate – β * Market Risk Premium.

The Jensen’s measure, or Jensen’s alpha, is a risk-adjusted performance measure that **represents the average return on a portfolio or investment, above or below that predicted by** the capital asset pricing model (CAPM), given the portfolio’s or investment’s beta and the average market return.

2 Unlike the CAPM, the **APT does not indicate the identity or even the number of risk factors**. … While the CAPM formula requires the input of the expected market return, the APT formula uses an asset’s expected rate of return and the risk premium of multiple macroeconomic factors.

Small minus big (SMB) is a factor in the Fama/French stock pricing model that says smaller companies outperform larger ones over the long-term. High minus **low** (HML) is another factor in the model that says value stocks tend to outperform growth stocks.

To calculate the beta, we call **do(model = lm(returns ~ market_returns_tidy$returns, data = .))** .

An abbreviated form of the regression output looks like this: where the intercept is the monthly unexplained return, or alpha, and Mkt-Rf is the **market factor**.

Defined analogously to the HML factor, the profitability factor (RMW) is the difference between the returns of firms with robust (high) and weak (low) operating profitability; and the **investment factor** (CMA) is the difference between the returns of firms that invest conservatively and firms that invest aggressively.

Although the Fama-French **factors still show a strong long-term performance**, they have now experienced two lost decades during which various other factors were able to deliver. … Fama-French factors are considered a standard in academic research and their definitions are widely used in empirical studies.

**High Minus Low** (HML), also referred to as the value premium, is one of three factors used in the Fama-French three-factor model. … Along with another factor, called Small Minus Big (SMB), High Minus Low (HML) is used to estimate portfolio managers’ excess returns.