Multi Factor Stacking

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 brochure counts the screens