Strategy #0000000018 · Value and multifactor investing
Multifactor portfolios and alpha combinations
Turn distinct signals into a portfolio with explicit weights and risk controls.
A multifactor portfolio combines value, momentum, quality, low-risk or other defined signals. It may weight factor portfolios or first combine stock-level scores.
Diversification depends on covariance and costs; adding more signals does not ensure robustness.
Three ways in
Understand the story. Then inspect the risk.
Start with a familiar situation, check the payoff, then test how the numbers change.
The idea · in two minutes
Jack does not treat every new factor as a separate source of return
Jack has value, momentum and quality strategies. If all three buy the same technology stocks, three labels may conceal one concentrated bet. He starts with the return streams of the factor portfolios, not just their ranking tables.
Equal weights are simple; covariance-aware methods manage estimated risk, while score integration combines standardised stock ranks. Rose warns that optimising weights and testing them on the same history mistakes noise for stable correlation.
Jack separates training, validation and test periods in time, includes turnover costs and checks losses under stress. Diversification is not a permanent property of factor names; it depends on uncertain correlations and estimated weights.
- Value factorAssumed one-period value-factor return, for a weighted arithmetic example.
- Momentum factorAssumed one-period momentum-factor return; factor returns can be correlated.
- 50／50 組合扣成本0.5×4% + 0.5×2% − 0.2% assumed cost = 2.8%.
Illustrative research examples only. They are not live signals or a recommendation.
The mechanics · payoff and exposure
Define each factor portfolio, then fix a weighting rule before evaluating the combined portfolio.
Rₖ is the next-period return of a defined factor portfolio; wₖ is known at formation; TC includes trading, borrow and execution costs. Covariance optimisation may use w ∝ Σ⁻¹μ, but expected returns μ and covariance Σ are estimates.
Greeks: the directional intuition
- Correlation
- Measures sensitivity to implied volatility.
- Estimation error
- Measures sensitivity to implied volatility.
- Turnover
- Measures sensitivity to implied volatility.
- Crowding
- Measures sensitivity to implied volatility.
Define each factor portfolio, then fix a weighting rule before evaluating the combined portfolio.
Practical context · published observations
50/50 factor mix: read the record with its caveats.
The chart uses the published figures or explicitly labelled study inputs below. A historical index or model replay is not the same as an investor’s realised account return.
數字為明列假設。真正的風險比較要用同期因子報酬序列、交易成本和樣本外期間，並揭露槓桿與基準。 Source ↗ · Methodology ↗
Change assumptions and inspect the scenario
Inputs illustrate the strategy mechanics; they are not live quotes, forecasts or investment advice.
Variants · same family, different risk levers
Factor combinations differ in how they integrate signals and set weights.
Combining factor return streams differs from combining stock characteristics into one score.
| Related strategy | Relationship | What changes | New cost or risk |
|---|---|---|---|
| Equal-weight factor combination | Equal factor returns | Assigns equal weights to defined factor portfolios without forecasting an optimal mean. | Different factor volatilities mean equal weight is not equal risk. |
| Composite characteristic score | Integrated stock score | Combines standardised stock ranks into one selection score. | Scaling, missing values and outliers can determine the final ranking. |
| Covariance-aware allocation | Risk optimisation | Uses factor-return covariance for a risk budget or minimum-variance mix. | Covariance error can create concentrated or rapidly changing weights. |
| Value and momentum | Cross-factor mix | Combines value and momentum exposures with historically different return patterns. | Their correlation changes across markets and samples. |
| Learning strategies | Machine-learned weights | Learns weights across strategy or alpha streams. | More flexibility invites overfitting; use walk-forward and a final holdout. |
| Vote / ensemble strategy | Signal voting | Uses direction votes or consensus across several signals. | Signal dependence and vote thresholds affect the result. |
| Cost-aware alpha combination | Cost-constrained blend | Includes expected turnover and trading costs in selection and weights. | Cost models can understate market impact in stressed liquidity. |
| Regime-dependent factor rotation | State-conditioned allocation | Changes factor weights under pre-defined macro or market states. | State variables arrive with lags and thresholds can be selected after the fact. |
Large alpha libraries contain highly dependent signals; regularisation, costs and a genuinely untouched test period are essential.
Read beyond the summary
References
Primary sources and research used to describe the strategy and its limits.
- 01Asness, Moskowitz & Pedersen (2013), Value and Momentum Everywhere.research
- 02Kakushadze & Yu (2017), How to Combine a Billion Alphas.research
- 03Novy-Marx & Velikov (2016), A Taxonomy of Anomalies and Their Trading Costs.research
- 04Chen & Zimmermann, Open Source Cross-Sectional Asset Pricing.dataset
- 05Kakushadze & Serur (2018), 151 Trading Strategies, §§3.6, 3.20.source