Fama-French 3 Factor Model

Fama-French 3 Factor Model


Extension of the Capital Asset Pricing Model (CAPM)

CAPM
Ra = Rfr +

where,
Ra = Return of the Asset
Rfr = Risk-Free Rate
βa = Beta Coefficient of the Asset
Rm - Rfr = Market Risk Premium

Fama-French 3 Factor
r = rf + β1*(rm - rf) + β2(smh) +β3(hml)

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
HML (High Minus Low) = Historic excess returns of value stocks (high book-to-price ratio) over growth stocks (low book-to-price ratio)


Small is set to $EWSC
Invesco S&P SmallCap 600® Equal Weight ETF

Big is set to $EQLW
Invesco S&P 100 Equal Weight ETF

High is set to $IUSV
iShares Core S&P US Value ETF

Low is set to $IUSG
iShares Core S&P US Growth ETF

returns selections
'returns'
'logarithmic returns' (use for realized (historical) returns)
'geometric returns' (compounded returns)

risk-free rate selections:
$DTB3
$DGS2
$DGS5
$DGS10
$DGS30

tf = primary time-frame
rtf = reference time-frame

เอกสารเผยแพร่:

// log-returns set as default

เอกสารเผยแพร่:

//plotting change

hline scale:

ln = natural logarithm

ln (3)
ln (9)
ln (27)
ln (81)
ln (248)