Multi-Factor Composite Equity

Overview

Every equity factor has a bad decade in it. Value spent the 2010s being wrong. Momentum crashed in 2009. Low volatility got crushed when rates rose. Quality got expensive and then derated.

The good news, and the entire reason multi-factor investing exists, is that they mostly have their bad decades at different times. Value is a bet that things which have fallen will come back. Momentum is a bet that things which have risen will keep rising. Those two are close to opposite ideas, and their returns are negatively correlated. When one is bleeding, the other is often thriving.

Put them together and something quite pleasant happens. The combined portfolio has a higher Sharpe ratio than either sleeve on its own, not because the combined return is higher, but because the volatility drops sharply. That is diversification doing exactly what it is supposed to do, and in factor land it is one of the few genuinely free lunches available.

The catch is that the way you combine them matters enormously, and there is one right answer and one very common wrong answer.

Thesis (why the edge exists)

The edge is not a new anomaly. It is the mathematics of combining imperfectly correlated bets.

If you have four signals, each with a modest information ratio, and they are close to uncorrelated with each other, the blended signal has an information ratio meaningfully higher than any of them alone. This is the same principle that makes a diversified stock portfolio less risky than a single stock, applied one level up, to strategies rather than securities.

The individual factor premia exist for the reasons discussed elsewhere: behavioural biases, structural constraints and risk compensation. The composite does not create a new premium. It harvests the existing ones more efficiently by removing a large amount of the timing risk.

There is also a defensive argument. You do not know which factor will work next decade. Nobody does. Timing factors has proved extremely difficult, with a long list of respected researchers arguing convincingly on both sides. A blend is what you build when you accept that you cannot time them.

Strategy logic

The key decision, and the one that separates a good implementation from a mediocre one, is how you combine.

The wrong way: portfolio blending. Build a value portfolio, a momentum portfolio, a quality portfolio and a low-vol portfolio, then hold 25 percent of each. This feels natural and it is worse. The problem is cancellation: your value sleeve buys a cheap stock that your momentum sleeve is shorting. You pay the spread on both trades, you carry the risk of both positions, and your net exposure to that stock is zero. You have spent money to hold nothing.

The right way: signal blending. Compute all four scores for every stock first, average them into a single composite score, then build one portfolio from the composite. Now the stock that is cheap but falling gets a mediocre composite score and simply does not make the book. You never trade it. You end up owning the stocks that look good on several dimensions at once, which is both cheaper and, empirically, better performing.

The mechanics:

• Compute each factor score for every stock.
• Convert each to a z-score within its sector, so a bank is compared to banks.
• Winsorise the extremes so one broken data point cannot dominate.
• Average the four z-scores into a composite.
• Rank on the composite. Long the top, short or exclude the bottom.

Parameters (knobs)

• Which factors. Value, momentum, quality, low volatility is the standard four. Adding more increases the risk of overfitting faster than it increases diversification.
• Factor weights. Equal weight is the honest default and it is very hard to beat out of sample. Any deviation should be justified before you look at the returns, not after.
• Sleeve construction. Each sleeve is a composite in its own right (value is three ratios, quality is a dozen). Keep each one simple.
• Neutralisation level. Sector-neutral z-scores at minimum. Full risk-model neutralisation on the final book if you have one.
• Rebalance frequency. Monthly is the common choice; the momentum sleeve wants speed and the value sleeve does not care, so monthly is a reasonable compromise.
• Long-only versus long-short. Long-only with a tracking-error budget is the deployable version for most people. Long-short is cleaner in theory and hostage to borrow in practice.

Portfolio construction

Signal blend first, then optimise.

Once you have the composite score, feed it into a portfolio optimiser with a risk model, maximising expected score subject to constraints: tracking error versus benchmark, sector limits, single-name caps, turnover penalty, and liquidity limits.

The turnover penalty inside the optimiser matters more here than almost anywhere else, because the composite includes a fast-moving momentum sleeve pulling against slow-moving fundamental sleeves. Left unconstrained, you will trade far more than the signal justifies.

Report the exposure of the final book to each factor. You will frequently find that the optimiser, chasing risk reduction, has quietly killed your value exposure. That is the risk model doing its job and destroying your strategy at the same time.

Costs, capacity and turnover

Signal blending is genuinely cheaper than portfolio blending, and this is one of its underrated advantages. Because the offsetting trades never happen, turnover falls, sometimes by a third or more relative to running the sleeves separately.

Expect blended turnover in the 60 to 120 percent per year range, driven mostly by the momentum sleeve. The value and quality sleeves barely move.

Capacity is good. The composite naturally favours reasonably sized, reasonably liquid companies, since a stock has to score decently on several dimensions to make the book, and total junk rarely does.

The cost that matters most is not slippage, it is management fee and complexity. If you build a sophisticated four-factor composite and it delivers a Sharpe of 0.6 before costs where a simple two-factor value-and-momentum blend delivers 0.55, the extra machinery is not earning its keep.

Backtest design checklist

• Build the sleeves separately and test them first. If your value sleeve is broken, the composite will hide it. Every sleeve must stand on its own before it goes into the blend.
• Compare signal blending against portfolio blending. Run both. Seeing the turnover and return difference is the most instructive experiment in this whole strategy.
• Weight sensitivity. Test 25/25/25/25 against a range of alternatives. If the results are wildly sensitive to the weights, you are looking at noise, and your "optimal" weights are fitted to the past.
• Missing data policy. Be explicit. A stock with no quality score should not silently receive a zero, because zero is a neutral z-score and that is a real decision you are making by accident.
• Correlation matrix of the sleeves. Print it. If your value and quality sleeves are 0.7 correlated, you have two factors that are really one factor and your diversification is imaginary.
• The 2018 to 2020 window. Multiple factors underperformed together. Test it. Diversification across factors is much weaker than the long-run correlations suggest during a coordinated factor drawdown.

Common failure modes

• Portfolio blending instead of signal blending. The classic, expensive mistake.
• Weight overfitting. With four factors and a historical sample, some weighting will look brilliant. It will not repeat.
• Correlated sleeves. Quality, low volatility and profitability overlap heavily. Three sleeves that are really one sleeve give you the illusion of diversification without the substance.
• Coordinated factor drawdowns. The assumption that the factors zig and zag independently is a long-run average, not a guarantee. They can all lose money at once, and they have.
• Crowding. Every one of these factors is available in a cheap ETF. You are not early.
• Complexity for its own sake. A composite of ten factors is not better than a composite of three. It is just harder to debug and easier to overfit.

Variants

• Value and momentum only. The simplest and, on some evidence, the most robust blend. The two most negatively correlated factors, both with the longest evidence base.
• Defensive composite. Quality plus low volatility, long-only. Aims at a smoother equity exposure rather than at maximum alpha.
• Factor timing overlay. Tilt sleeve weights based on factor valuation spreads or momentum of the factor itself. Intellectually appealing, extremely hard to do well, and a graveyard of good intentions.
• Integrated optimisation. Skip the explicit composite and put all four scores into the optimiser's objective directly, with a risk model, letting it find the trade-off. More elegant, much more of a black box.
• Long-only smart beta. Overlay the composite on a benchmark with a tight tracking-error budget. Boring, cheap, capacious, and the version that actually holds most of the world's factor money.

Our notes and suggestions

If you build only one thing from this whole theme, build this, but build it in the right order: sleeves first, individually, honestly tested, then the blend.

Then run the single experiment that teaches the most: construct the same strategy twice, once by averaging the signals and once by averaging four separate portfolios, and compare the turnover and the net return. The gap between those two is a real, repeatable, purely structural edge that costs you nothing but a bit of thought, and it is available to anyone who understands why it exists.

Be sober about the rest. Not one of these four factors is a secret. The composite's advantage is not that it knows something the market does not, it is that it is diversified and patient. That is a modest, honest edge, and modest honest edges are the only kind that last.