Multi-factor portfolios: mixing versus integrating, factor correlations and the evidence on factor timing

What you will learn

• Why factors are combined at all: the role of low or negative correlation between factor returns.
• The difference between mixing single-factor sleeves and integrating factors at stock level.
• How to estimate the tracking error and information ratio of a factor combination.
• What the published evidence says about timing factors, and a cautious rule for using valuation spreads.

Explanation

Why combine factors

Each factor has long bad periods (lesson 2: the value drawdown; lesson 3: the momentum crash), but their excess returns over the market move differently. Historically, value and momentum excess returns have been negatively correlated in most long samples, while quality and low volatility have often been positively correlated with each other and negatively with value. Correlations change, so treat any number as an estimate. The two-asset volatility formula from the course "ETF Investing" applies directly; for a 50/50 combination

TE = sqrt(0.25 × TE1² + 0.25 × TE2² + 2 × 0.25 × ρ × TE1 × TE2)

where tracking error (TE) is the annualised standard deviation of the return difference against the market-cap benchmark and ρ (rho) is the correlation of those differences. The information ratio (IR) is the expected excess return divided by TE; it tells you how much reward you get per unit of regret.

Mixing versus integrating

Mixing means holding separate single-factor funds, for example 50 % value ETF and 50 % momentum ETF: transparent, easy to rebalance, weights of your choice. The weakness: the value fund may hold a cheap stock with terrible momentum while the momentum fund holds an expensive stock with strong momentum. The positions partly cancel, and you pay two sets of turnover for exposure that nets out.

Integrating means scoring each stock on all factors at once and selecting stocks that are good on average or on all. MSCI's Diversified Multiple-Factor indices and many "multi-factor" ETFs do this, usually with an optimiser and constraints on sector, country and stock weights. Integration delivers more combined exposure per unit of turnover, but it is less transparent, the constraints matter a lot, and a bad period is harder to explain because you cannot see which sleeve caused it. A common compromise: integrated quality-and-value (slow signals) plus a separate momentum sleeve (a fast signal with different rebalancing needs).

The evidence on factor timing

Timing means increasing a factor when it looks "cheap" and reducing it when it looks "expensive". The main signal is the valuation spread: how much cheaper the long side of a factor is than its short side, compared with its own history. Two findings from the published debate (2016–2019, Research Affiliates versus AQR) are worth remembering:

• Valuation spreads predict long-horizon factor returns to some degree, especially at extremes.
• The gain after costs is small, timing signals are themselves correlated with value ("timing" often just means buying more value), and a simple diversified multi-factor portfolio was hard to beat.

A defensible rule: do not time; at most, let an extreme spread (the widest 10 % of its history) be a reason not to abandon a factor, never a reason to leverage it.

Worked example

Hypothetical example. Two single-factor ETFs on the same parent index. Assumed long-run numbers (not forecasts): value sleeve expected excess return 2.0 % per year with TE 6 %; momentum sleeve 3.0 % with TE 8 %; correlation of their excess returns −0.3. Fees, spreads and taxes are excluded.

Step 1 – single-sleeve information ratios: value 2.0 / 6 = 0.33; momentum 3.0 / 8 = 0.375.

Step 2 – expected excess return of a 50/50 mix: 0.5 × 2.0 % + 0.5 × 3.0 % = 2.5 %.

Step 3 – tracking error of the mix:

TE² = 0.25 × 0.0036 + 0.25 × 0.0064 + 2 × 0.25 × (−0.3) × 0.06 × 0.08 = 0.0009 + 0.0016 − 0.00072 = 0.00178, so TE = 4.2 %.

Step 4 – information ratio of the mix: 2.5 / 4.2 = 0.59, far above either sleeve alone. Sensitivity: with ρ = 0 the TE is 5.0 %; with ρ = +0.5 it is 6.1 %.

Step 5 – stock-level view. Four stocks with z-scores (value, momentum): P (+1.5, −1.5), Q (−1.5, +1.5), R (+0.8, +0.7), S (−0.8, −0.7). A mix holds P (via value) and Q (via momentum); an integrated average-score rule ranks R first (+0.75), P and Q at 0, S last. Integration concentrates on R and avoids paying turnover for P and Q, whose exposures cancel.

Common mistake

Practice activity

On paper: you consider a 50/50 mix of a quality ETF (expected excess 1.5 %, TE 4 %) and a low-volatility ETF (expected excess 1.0 %, TE 7 %). You estimate their excess-return correlation at +0.6. (a) Calculate the mix's expected excess return, TE and information ratio. (b) Compare the IR with the quality sleeve alone. (c) Decide whether the mix is worth the extra product.

Key takeaways

• Combining factors works through low or negative correlation of their excess returns; always check the correlation assumption.
• Mixing is transparent but wastes turnover on offsetting positions; integrating is more efficient but less transparent and optimiser-dependent.
• Information ratio, not raw excess return, is the right measure of a combination.
• Factor timing on valuation spreads has weak evidence after costs; use spreads to stay disciplined, not to trade.

Next step

Lesson 9 shows how to measure the factor exposure of your own portfolio with a simple regression and how to read the loadings.