India Six-Factor Premia, Attribution & Regime Analysis
Overview
Indian equities are not a scaled copy of US markets. Large, mid, and small caps can diverge sharply around credit events; quality-oriented segments often hold up better in stress; momentum can deliver strong long-run premia but also violent drawdowns; and two funds marketed with similar labels can post very different paths once factor exposures are unpacked.
This project applies a Fama–French-style six-factor framework to India: market (MF), size (SMB5), value (HML), profitability (RMW), investment (CMA), and momentum (WML). We use monthly data over a multi-year window, align factors with Nifty style benchmarks, and run the same models on a small set of Indian equity mutual funds so you can see both index-level and fund-level results in one place.
The work is aimed at investors and researchers who want evidence, not anecdotes: Which factors earned positive long-run premia in India? How correlated are they? How much of a Nifty 200 Value or Smallcap 250 return is explained by market beta alone versus a full factor model? Do funds earn alpha after controlling for known risks? Does momentum interact with value or the market factor? And does the quality factor (RMW) still pay when the market factor is negative?
The results section below is organised by theme — market puzzles, factor premia, index and fund attribution, momentum risk, and a formal hypothesis test — with interactive charts you can explore directly in the browser.
Why factor models for India?
Single-index benchmarks (e.g. Nifty 50) hide large dispersion across cap tiers and style tilts. A mid-cap value fund and a large-cap growth fund may both be “equity” but carry different factor bets. Multi-factor models separate market beta from size, value, profitability, investment, and momentum effects so performance can be compared on a level field.
India-specific research (including work on four- and five-factor models in Indian equities) shows that classical Fama–French structures are informative but not identical to US calibrations — premia, correlations, and crash episodes differ. This study documents those differences with transparent regressions rather than relying on US factor histories as a proxy.
Factor model
For asset or index at month , excess return is modelled as:
The six factors are: MF (market), SMB5 (size), HML (value), RMW (profitability), CMA (investment), and WML (momentum). Simpler models nest inside this structure: CAPM uses MF only; a four-factor variant adds size, value, and momentum; the full six-factor specification adds profitability and investment.
Reported alphas are annualised from monthly regressions. Rolling 36-month windows show how factor exposures shift — useful for spotting style drift in indices and funds.
What you will see in the results
Market puzzles — cumulative paths for large, mid, and small caps, quality vs benchmark, momentum, fund dispersion, and volatility through major macro events (demonetisation, IL&FS, COVID).
Factor premia — summary statistics, correlations, and long-run cumulative factor returns for the Indian FF6 panel.
Index regressions — how much of each Nifty style index’s return is explained by CAPM, four-factor, and six-factor models; rolling factor exposures on a highlight index.
Momentum — WML profile, drawdowns, interaction with value and market factors, and long-only vs long–short momentum behaviour.
Funds — FF6 attribution for sample Indian equity funds, model fit across specifications, rolling factor exposures, and comparison of total return vs factor-explained performance.
Hypothesis test — whether profitability (quality) earns positive returns when the market factor is negative, with robustness checks.
Empirical results
Six-factor premia, index regressions, fund attribution, and market puzzles from the latest India factor study.
Factor summary statistics (annualised)
Long-run reward and risk for each of the six Indian factors — market, size, value, profitability, investment, and momentum. The table reports annualised mean return and volatility, Sharpe ratio, and worst peak-to-trough drawdown, all scaled from monthly factor returns (twelve months per year).
| Factor | Ann. mean | Ann. vol | Sharpe | Max DD |
|---|---|---|---|---|
| MF | 10.10% | 17.10% | 0.59 | -34.30% |
| SMB5 | 10.00% | 9.00% | 1.11 | -9.90% |
| HML | 8.60% | 14.40% | 0.60 | -27.80% |
| RMW | 3.20% | 8.70% | 0.36 | -27.10% |
| CMA | -7.30% | 9.30% | -0.78 | -53.80% |
| WML | 6.10% | 14.40% | 0.43 | -32.70% |
Factor correlation matrix
Pairwise correlations among factor returns over the full sample. Strong positive values mean factors tended to move together; values near zero suggest diversification across premia; negative values highlight hedging relationships. Colour intensity reflects the strength of each correlation.
| MF | SMB5 | HML | RMW | CMA | WML | |
|---|---|---|---|---|---|---|
| MF | 1.00 | 0.18 | 0.43 | 0.09 | -0.56 | -0.05 |
| SMB5 | 0.18 | 1.00 | 0.30 | 0.10 | -0.29 | -0.07 |
| HML | 0.43 | 0.30 | 1.00 | 0.31 | -0.42 | -0.32 |
| RMW | 0.09 | 0.10 | 0.31 | 1.00 | -0.15 | -0.29 |
| CMA | -0.56 | -0.29 | -0.42 | -0.15 | 1.00 | 0.05 |
| WML | -0.05 | -0.07 | -0.32 | -0.29 | 0.05 | 1.00 |
Cumulative factor returns
Growth of one unit invested in each factor portfolio from the start of the sample. The lines show how premia compounded over time and how drawdowns in individual factors (especially momentum) affected long-run wealth.
Cross-index model fit (R²): CAPM → FF4 → FF6
How much of each Nifty style index’s return variation is explained by increasingly rich factor models — from market-only CAPM through a four-factor specification to the full six-factor model. Taller bars mean more of the index’s moves are captured by known factor risks rather than idiosyncratic noise.
Spotlight: ^NSMIDCP
Model fit for ^NSMIDCP under CAPM, four-factor, and six-factor specifications. Rising R² from left to right indicates how much additional explanatory power size, value, momentum, profitability, and investment factors add beyond market beta alone.
Rolling 36m factor exposures — ^NSMIDCP
Time-varying factor betas for ^NSMIDCP, estimated in a 36-month rolling window. Lines above zero indicate a positive loading on that factor; shifts over time reveal style drift — for example rising size or momentum exposure during particular market phases.
Fund factor attribution (FF6)
Six-factor regressions for sample Indian equity mutual funds. Annualised alpha is return not explained by the factor model; R² measures how much of each fund’s variation is captured by market, size, value, profitability, investment, and momentum exposures; betas show the direction and magnitude of each factor bet.
| Fund | α (ann.) | R² | β MF | β SMB5 | β HML | β RMW | β CMA | β WML |
|---|---|---|---|---|---|---|---|---|
| ('Fund_A', 'NIFTYBEES.NS') | 5.00% | 0.937 | 0.934 | -0.022 | -0.029 | 0.088 | 0.110 | -0.011 |
| ('Fund_B', 'JUNIORBEES.NS') | 1.80% | 0.897 | 1.034 | 0.343 | -0.043 | -0.099 | 0.010 | 0.091 |
| ('Fund_C', 'MOM100.NS') | 0.90% | 0.881 | 1.002 | 0.728 | -0.051 | 0.087 | 0.005 | 0.014 |
Empirical findings
The sections below move from broad market patterns to factor premia, index and fund attribution, momentum risk, and a formal stress-period test — each with charts you can explore in place.
Indian market puzzles
Five stylised facts about Indian equities, shown as cumulative return paths for size tiers, quality versus the benchmark, momentum, a sample of mutual funds, and benchmark risk. Vertical markers highlight demonetisation, the IL&FS credit stress, and COVID-19; the shaded band in the quality chart marks the IL&FS episode when defensive factors often mattered most.
Puzzle 1 — Does size matter?
Puzzle 4 — Same category, different journeys
Puzzle 5 — Risk and return
Factor zoo
A CAPM-first view of Indian indices and the market factor itself. Summary cards describe the market factor’s long-run return, volatility, skewness, and residual noise; the table compares each Nifty style index’s CAPM R², market beta, and annualised alpha — how much return is left after a single market exposure.
| Index | CAPM R² | β MF | α (ann.) |
|---|---|---|---|
| ^Cnx100 | 0.958 | 0.935 | 3.10% |
| ^Nsmidcp | 0.819 | 0.995 | 4.80% |
| Smallcap.Ns | 0.128 | 0.248 | 36.90% |
| ^Nsei | 0.932 | 0.912 | 3.00% |
Factor vs style-index spreads
How closely each FF6 factor tracks a Nifty style benchmark used as a practical proxy — for example whether the value factor lines up with a value index return series. High correlation suggests the factor and the listed style index are capturing similar risks; the cumulative-return chart below compares style indices directly over the sample.
| Factor | Style proxy | Correlation |
|---|---|---|
| SMB5 | size_spread | -0.004 |
Nifty style indices — cumulative returns
Momentum deep dive
Momentum (WML) in India often earns a premium but can suffer sharp crashes. This section traces cumulative WML performance and drawdowns, lists major crash episodes, and shows how momentum co-moves with value and the market factor over rolling three-year windows. Long-only versus long–short momentum constructions illustrate how much of the story depends on the implementation choice.
WML cumulative return
Drawdown profile
| Start | End | Max DD |
|---|---|---|
| 2020-04-30 | 2023-11-30 | -32.70% |
| 2024-08-31 | 2026-05-31 | -20.00% |
| 2019-02-28 | 2019-06-30 | -11.80% |
| 2019-10-31 | 2020-02-29 | -11.00% |
| 2016-12-31 | 2017-01-31 | -6.70% |
36m rolling corr: WML vs HML
36m rolling corr: WML vs MF
Momentum strategies typically require frequent rebalancing; higher month-to-month variation in WML implies greater turnover and implementation cost in live portfolios.
Fund decomposition
A fuller picture of sample Indian equity funds: cumulative return paths, how model fit improves from CAPM through FF6, total return versus factor-explained alpha, and rolling factor exposures for each fund. Together these views show whether performance came from market timing, style tilts, or residual alpha after known factors.
Fund cumulative returns
| Fund | Total ret. (ann.) | OLS α (ann.) | FF6 R² |
|---|---|---|---|
| ('Fund_A', 'NIFTYBEES.NS') | 12.60% | 5.00% | 0.937 |
| ('Fund_B', 'JUNIORBEES.NS') | 14.50% | 1.80% | 0.897 |
| ('Fund_C', 'MOM100.NS') | 17.20% | 0.90% | 0.881 |
Rolling 36m exposures — ('Fund_A', 'NIFTYBEES.NS')
Rolling 36m exposures — ('Fund_B', 'JUNIORBEES.NS')
Rolling 36m exposures — ('Fund_C', 'MOM100.NS')
Hypothesis testing
Mean RMW is positive when market excess return (MF) is negative (quality premium in stress months). Months are classified as stressed when MF < 0. The table reports average RMW in those months, t-statistics, and p-values; asterisks mark significance at the 5% level.
| Test | Stress n | Stress mean (m) | t-stat | p-value |
|---|---|---|---|---|
| RMW factor (full FF6 panel) | 51 | 0.20% | 0.64 | 0.527 |
| RMW in bottom-quartile MF months (robustness) | 30 | 0.20% | 0.41 | 0.687 |
- Look-ahead bias if fundamentals are not lagged.
- Multiple testing across many factors inflates false positives.
- Short stress windows reduce statistical power.
- Long-only quality indices differ economically from long-short RMW.
