Module 6 — Professional Quant Topics

Factor Models — CAPM to Fama-French to Barra

Factor models, options pricing, risk, and microstructure — the curriculum interview desks expect.

Module lessons

Factor Models — CAPM to Fama-French to Barra Options and the Greeks Risk Management — VaR, CVaR, and Position Sizing Market Microstructure — How Orders Become Prices

Learning objectives

▸Run a CAPM regression and interpret α and β.
▸Understand the Fama-French three- and five-factor models.
▸Know what commercial risk models (Barra, Axioma) add.

FORMULA

CAPM

E[r_i] - r_f = β_i (E[r_m] - r_f)
β_i = Cov(r_i, r_m) / Var(r_m)

TEXT

From one factor to many

CAPM says only market risk is priced. Empirically it isn't enough — small stocks beat large, cheap stocks beat expensive, and high-momentum names continue to outperform. Fama-French formalised this as a three-factor (Mkt, SMB, HML) and later five-factor model (adding RMW and CMA). Carhart added momentum (UMD).

CODE

Time-series regression

import statsmodels.api as sm

excess_ret = strategy_ret - rf
X = ff_factors[['Mkt-RF','SMB','HML','RMW','CMA','UMD']]
X = sm.add_constant(X)
result = sm.OLS(excess_ret, X).fit()
print(result.summary())
alpha = result.params['const']  # this is your edge net of factor exposures

TEXT

Commercial risk models

Barra and Axioma decompose return into ~70 fundamental factors (country, industry, value, growth, leverage, size, liquidity, momentum, volatility…). PMs use them to constrain unwanted exposures: 'be neutral to oil price, +1 std on quality, 0 to momentum'. They turn portfolio construction into a quadratic program with factor-budget constraints.

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