Factor model

A plain CAPM-style view says a stock's return is driven by just one thing: its sensitivity to the overall market. A factor model says that is too simple. Return can depend on several things at once — how sensitive a stock is to economic growth, to interest rates, to being cheap on valuation, to being a smaller company, and more.

A factor model measures each of those sensitivities separately, and adds them up to explain — and forecast — return. Different managers pick different factors depending on what they believe drives prices, which is why the industry has ended up with many competing multi-factor indices rather than one.

Section 18.6 splits factor models into three broad kinds: Macroeconomic Factor Models (driven by GDP growth, interest rates, inflation, credit risk, liquidity and geopolitical climate — equities respond mainly to growth and inflation, fixed income mainly to rates, inflation and credit), Fundamental Factor Models (driven by company-level Quality factors — RoE, RoA, RoCE, leverage, cash flow, size — and Value factors — P/E, P/B, P/S, dividend yield), and Statistical Factor Models.

The general multi-factor equation is: Rpt = (bp1F1t + bp2F2t + ... + bpnFnt) + ept, where Rpt is the portfolio's return in period t, Fjt is the return to style factor j in period t, bpj is the portfolio's sensitivity to factor j, and ept is the portion of return the chosen factors do not explain. Building a factor portfolio means constructing a time series of the factors, estimating each asset's sensitivity to factor surprises (actual minus forecast, with a zero expected value) through regression, getting the expected-return intercept from expert or econometric estimates, and weighting constituents equally, by factor sensitivity, or as the manager decides.

Beyond portfolio construction, the workbook lists factor models as useful for attribution analysis (explaining how alpha was generated, split into sector selection, stock selection and timing), risk analysis, and decision-making before launching new products, where a manager back-tests a factor hypothesis by simulation before committing to it — or rejects the hypothesis if it fails the test.

Following the workbook's own multi-factor index example. NSE's Alpha Quality Value Low-Volatility 30 index blends four named factors — Alpha, Quality, Value and Low-Volatility — with the workbook's stated weights of 25% each.

A fund manager builds a Rs 4,00,00,000 factor-based portfolio tracking this blend. Applying the four equal weights: Rs 1,00,00,000 of the portfolio's stock selection is driven primarily by the Alpha factor's ranking criteria, Rs 1,00,00,000 by Quality metrics (such as RoE and leverage), Rs 1,00,00,000 by Value metrics (such as P/E and P/B), and Rs 1,00,00,000 by Low-Volatility ranking.

Before launch, the manager back-tests the blend by simulation over the past five years of Nifty 500 data. If the simulated factor blend would have delivered a Sharpe ratio below the plain Nifty 50's over that period, the workbook's own logic says the hypothesis should be rejected or refined, not launched as-is — factor models exist to be tested, not assumed correct.

Chapter 18, section 18.6 (Factor-based portfolios) and its sub-sections 18.6.1–18.6.3, give the macro/fundamental/statistical classification, the multi-factor equation, and the NSE four-factor index weight table. Expect a question naming a factor (say, P/E or RoE) and asking whether it belongs to the macroeconomic or fundamental factor model, and one on what attribution analysis extracts from a factor model.

• Macroeconomic factors are economy-wide (GDP, rates, inflation); fundamental factors are company-specific (Quality, Value metrics) — mixing these two lists is the most common error.
• The error term (ept) is the return the chosen factors do NOT explain — a factor model with a large residual is explaining return poorly, whatever its R-squared looks like on the factors it does include.
• Attribution analysis under a factor model splits alpha into sector selection, stock selection and timing — a specific three-way split the workbook names, not a general "skill versus luck" statement.
• A linear factor model is used for simplicity, even though the workbook notes real relationships can be non-linear (quadratic, exponential, logarithmic) — polynomial regression exists for those cases but is described as complex, which is why the linear form dominates in practice.
• Do not confuse a factor model (explains return through multiple sensitivities) with alpha-beta separation (splits return into just two pieces, market and non-market) — a factor model can sit inside the alpha-generation half of an alpha-beta-separated portfolio.