Lecture 6 Fama-French Three factor Model

The 3 systematic factor in FF models are

Firm size - book to market ratio and market index

Size Factor (SMB)

differential returns on small firm versus large firm

Carhart four-factor model

it takes into account the momentum anomaly to provide a further explanation of security return

Book-to-market ratio (value factor) ( HML)

return on high book versus low book to market firms

Why value stocks earn more on average than low book to market stock (growth stock)

- HBTM are more exposed to the market in downturn ( overcapitalised result in a difficulty to cut back capital ) e.g car manufacturer - less benefited to the market in upturn.

Growth firms can seal better with a downturn by

- deferring growth plan in booms, growth firms respond more strongly by increasing their capacity

Therefore, low book to market is more profitable /9 risk-based interpretation)

- less sensitive to downturn - more sensitive to upturn

Behavioural explanation of why value firm earn more than growth?

- low book firm doing well recently - analyst oversight recent good performance ( over-optimism )which results in a worse firm performance

HML calculation ( how much on average high book earn more than low book ?)

1/2 ( small return/H + big return/H)-1/2 ( small return/L + big return/L)

Return on small portfolio

1/3 ( small return/large + small return/medium + small return/high )

How to calculate SMB ( how much small stocks on average earn versus large stock? )

1/3 ( small return/large + small return/medium + small return/high )-1/3 (big return/large + big return/medium + big return/high)

Return on big portfolio

1/3 (big return/large + big return/medium + big return/high)

3 factors fems-french model

E( r i.t)-rf.t= ai + bi [ E(r m,t)-r f.t) +si [ E(SMB t) + hi E(HML t) bi (X1), si (X2), hi (X3) are betas of the factors - factor loadings