6A.12 Factor investing in India · M06A Events, sectors, factors

Motivation

Stocks share common sources of return beyond the market: cheapness (value), size, recent strength (momentum), profitability and stability (quality), and low volatility. These factors explain much of what fund managers sell as skill, they have long histories of positive average returns, and they have deep, long drawdowns. M04 · 4.3 covers momentum; this section covers how factors are built, what the Indian data say, and why their premia are hard to harvest.

6A.12.1Building a factor#

Setup

A characteristic $z_{i,t}$ (book-to-market, log market cap, past 11-month return, ROE, volatility) is known at the end of month $t$ . A long–short factor is formed by sorting stocks on $z_{i,t}$ , buying the top group, selling the bottom group, and holding for month $t+1$ . Fama and French (1993) use a $2 \times 3$ double sort: size at the median, value at the 30th and 70th percentiles; SMB (small minus big) averages the small-minus-big differences within each value group, HML (high minus low book-to-market) averages the high-minus-low differences within each size group. Carhart's (1997) momentum factor (WML, winners minus losers) does the same on past returns. The IIMA library builds Indian versions of all three, plus the market excess return.

Proposition 6A.19what a characteristic sort earns

Suppose $r_{i,t+1} = \beta_i m_{t+1} + \lambda_{t+1} z_{i,t} + \varepsilon_{i,t+1}$ , with $z_{i,t}$ cross-sectionally standard normal, independent of $\beta_i$ and $\varepsilon$ . The equal-weighted top-30% minus bottom-30% portfolio earns in expectation

\mathbb E[r^{LS}_{t+1}] = \mathbb E[\lambda]\cdot\frac{2\varphi(z_{0.7})}{0.3} \approx 2.318\,\mathbb E[\lambda], \tag{6A.24}

and its market beta is zero in large cross-sections.

Proof

Within the top group the average of $z$ is $\mathbb E[z \mid z > z_{0.7}] = \varphi(z_{0.7})/0.3$ (Proposition 6A.3's argument), and the bottom group's is its negative. The $\beta_i m$ terms average to $\bar\beta m$ in both groups because $\beta$ is independent of $z$ , so they cancel; the $\varepsilon$ terms average to zero.∎

A factor return is thus a premium per unit of characteristic times the characteristic spread of the portfolio, and the code (m06a_factors.py) checks this. If $\beta$ and $z$ are correlated (value stocks with higher betas, for example), the long–short has market exposure and must be regressed on the market before its alpha means anything.

6A.12.2Betting against beta#

Low volatility and quality The low-beta anomaly (the CAPM's security market line is too flat, M06 · 6.5) is explained by leverage constraints: investors who cannot borrow buy high-beta stocks instead, bidding them up (Black 1972; Frazzini and Pedersen 2014).

Proposition 6A.20betting against beta is beta-neutral

Let $r_L, r_H$ be the returns of a low-beta and a high-beta portfolio with betas $\beta_L < \beta_H$ , and let

r^{BAB} = \frac{r_L - r_f}{\beta_L} - \frac{r_H - r_f}{\beta_H}. \tag{6A.25}

Then $\beta^{BAB} = 0$ , and under the CAPM $\mathbb E[r^{BAB}] = 0$ .

Proof

Betas are linear: $\beta^{BAB} = \beta_L/\beta_L - \beta_H/\beta_H = 0$ . Under the CAPM $\mathbb E[r_j - r_f] = \beta_j(\mu_M - r_f)$ , so each leg has expected excess return $\mu_M - r_f$ and the difference is zero.∎

A positive average $r^{BAB}$ is therefore evidence against the CAPM. The long leg is levered (scaled by $1/\beta_L > 1$ ), which is exactly what constrained investors cannot do. Quality (profitability, earnings stability, low leverage; Asness, Frazzini and Pedersen's "quality minus junk", and the profitability factor RMW of Fama and French 2015) has also earned positive premia in many markets.

6A.12.3Indian factor returns, 1994–2025#

Indian factor evidence (IIMA library, release 2025-12, survivorship-bias-adjusted monthly file; statistics computed for this course; MF is the market return in excess of the 91-day T-bill rate).

Jan 1994 – Dec 2025	Mean (ann.)	Vol (ann.)	Sharpe	$t$	Max drawdown
Market (MF)	7.84%	24.41%	0.32	1.82	−75.1%
Size (SMB)	−2.52%	16.68%	−0.15	−0.85	−86.1%
Value (HML)	8.33%	20.36%	0.41	2.31	−58.8%
Momentum (WML)	13.13%	24.48%	0.54	3.03	−53.5%

Sub-period	MF	SMB	HML	WML
1994–2009, mean / Sharpe	8.94% / 0.29	−6.06% / −0.32	9.73% / 0.41	11.47% / 0.38
2010–2025, mean / Sharpe	6.74% / 0.43	1.00% / 0.07	6.93% / 0.42	14.78% / 0.90

Means are 12 times the monthly arithmetic mean; the library's own page reports a geometric WML return since 1994 of 10.65% a year (quoted in M04 · 4.3.5). Correlations of the monthly series: HML–WML −0.37, MF–SMB 0.26, MF–HML 0.22, MF–WML −0.15. Calendar 2025: SMB −19.6%, HML +11.4%, WML −5.5%, MF −4.9%.

Reading the table

Premia are small relative to their volatility. Only WML clears $t = 3$ , the threshold Harvey, Liu and Zhu argue a new factor should meet (M04 · 4.6); HML is at 2.3. With a Sharpe ratio of 0.41, it takes $(3/0.41)^2 \approx 54$ years for a true premium to reach $t = 3$ .
Size has not paid in India over this sample. The small-cap premium is negative on average, positive in only 16 of 32 calendar years, and suffered an 86% drawdown. Small-cap rallies (2014, 2017, 2023) are real but not a reliable premium.
Drawdowns are long and deep. WML lost 44% in the twelve months to November 2009 (−18% in April and −25% in May 2009 alone), the Indian counterpart of the 2009 momentum crash in M04 · 4.3.4. HML lost 34% in the twelve months to May 1999, during the technology boom.
Value and momentum hedge each other. Their correlation of −0.37 is why combined value-plus-momentum portfolios have higher Sharpe ratios than either alone.

6A.12.4Crowding and NSE factor indices#

Factor crowding When much capital follows the same signal, three things happen: the premium is competed down (McLean and Pontiff (2016) find US anomaly returns 26% lower out of sample and 58% lower after publication), the stocks in the factor portfolios move together more than fundamentals justify (Lou and Polk's "comomentum"), and an unwind by one large holder hits all the others through prices. August 2007 is the canonical episode (Khandani and Lo; case study in M13A). Indian signals of crowding: the growth of NSE factor index funds and ETFs, which rebalance on published schedules, and the valuation spread between the long and short legs.

NSE factor (strategy) indices¹: Nifty200 Momentum 30 (30 stocks from the Nifty 200 ranked on a normalised momentum score built from 6- and 12-month returns adjusted for volatility), Nifty200 Quality 30, Nifty100 Low Volatility 30, Nifty200 Value 30, Nifty Alpha 50, Nifty200 Alpha 30, and multi-factor combinations such as Nifty Alpha Quality Low-Volatility 30. These are long-only tilts: they hold the top of the sort and never short the bottom, so their returns are the market plus about half of a long–short factor plus concentration risk. Benchmark them against their parent index, not against zero.

Practitioner notes

Timing errors manufacture factor premia. Book value is known months after the fiscal year ends; Fama and French use June-end sorts with December-end book values to avoid look-ahead. The IIMA momentum signal at month $t$ uses returns from $t-11$ to $t-1$ ; using month $t$ as well adds short-term reversal (M04 · 4.3.3).
Survivorship bias is acute in India: hundreds of small companies "vanished" in the late 1990s. The IIMA library offers survivorship-adjusted files for this reason; use them.
Value in India is often state-owned and commodity companies; a value tilt is partly a sector and policy bet.