Multi factor stacking: the peak is at three

Saturday morning. Friend forwards a smart beta brochure. Five factors stacked into one fund. Value. Momentum. Quality. Size. Low volatility. The cover sells it as more screens, more rigour. He wants to know if it is worth the 1.4 pct TER.

The instinctive answer is yes. The math says wait.

Run the same Nifty 200 universe through every combination, same equal weight, same monthly rebalance, only the number of factor screens changes row to row. Value alone lands at Sharpe 0.62. Momentum alone at 0.66. Quality alone at 0.71. Stack Value and Momentum together and the Sharpe jumps to 0.91, a 0.29 lift on the back of one added screen. Add Quality on top and Sharpe edges to 0.95, a 0.04 lift. Add Size, the fourth screen, and Sharpe drops to 0.92. Add Low Volatility, the fifth, and Sharpe slides further to 0.88.

The peak is at three. The fourth pays nothing. The fifth subtracts.

The reason is correlation, not magic. Value sits at minus 0.30 with Momentum because cheap-and-ignored almost never overlaps with expensive-and-trending. The variance of the combined portfolio is governed by the cross term, two times w1 w2 sigma1 sigma2 rho, and rho being negative is what shrinks variance. Stacking those two earns the Markowitz reduction. Quality sits at plus 0.55 with Low Volatility because both screens land on the same defensive cohort. Staples, FMCG, pharma, large defensives. Stacking those is buying the same boring stocks twice through two different doors. The 5-factor portfolio looked diversified on paper. The math priced it as one bet plus three near-copies.

Three checks before signing a cheque on a multi factor fund. Ask the correlation between the named factors. Two screens that disagree is the only stack that earns the variance reduction. Treat anything past three factors as marketing rather than math. The marginal Sharpe gain disappears while turnover and crowding tax keep climbing. Avoid Quality plus Low Vol unless you actually want two defensive screens. The brochure call them two factors. The portfolio gets one.

A portfolio is not a Boolean AND of every factor in the paper. It is a small basket of bets that actually disagree with each other.

The ladder from the opening

Put the opening's numbers on one chart and the shape is plain. The big jump comes from the first pair that disagrees. After three, each extra screen costs more than it adds.

The cross term, worked by hand

Here is the formula from the opening with numbers you can check. Two sleeves, half your money in each. Sleeve one swings 18 percent a year, sleeve two 16 percent. The blend's variance is 0.5 squared times 18 squared, plus 0.5 squared times 16 squared, plus the cross term: 2 x 0.5 x 0.5 x 18 x 16 x the correlation.

At a correlation of minus 0.3, the cross term is minus 43.2 and the blend swings about 10.1 percent a year. At plus 0.55, the quality and low volatility case, the cross term is plus 79.2 and the blend swings about 15.0 percent, barely below either sleeve. Same weights, same sleeves. Only the correlation moved.

Try 0.78. That is roughly the correlation of the quarterly returns of NSE's long only momentum and value indices over the eight quarters to October 2026. The minus 0.3 in the opening describes long short factor premiums, where the market is cancelled out. Long only indices carry the market inside every sleeve, so their raw returns move together far more.

What NSE's indices show

Even at a positive correlation, the blend still helped where it mattered. Hold the Nifty200 Momentum 30 and the Nifty200 Value 30 half and half from October 2024, putting the weights back each quarter. Momentum fell about 30 percent at quarterly points and ended at 78.5. Value ended at 100.9. The blend ended at 89.5, and its worst quarterly fall was about 22 percent.

NSE also publishes the other way of building a stack. Instead of two sleeves side by side, a composite index scores every stock on two factors at once and keeps the stocks that do well on both. The Nifty Alpha Low-Volatility 30 combines a momentum style alpha score with low volatility.

On its factsheet of 30 Sep 2026, the Alpha Low-Volatility 30 had compounded at 17.71 percent a year on total return since 2005, back calculated before its 2017 launch, with five year volatility of 13.4 percent. The single factor Nifty200 Momentum 30 earned 18.30 percent with five year volatility of 19.4 percent. Almost the same long run return, about a third less swing. Two factors that disagree, not five that agree.

The free Learn module on combining factors builds both versions step by step on NSE indices, with a quiz. The posts on value and momentum disagreeing and long only factors go deeper into why a long only blend behaves differently from the research.