The strategy uses 20-day momentum signals, singular value decomposition for principal portfolios, and predicts future returns. Positions are taken in the top three portfolios, equally weighted, and rebalanced every 20 days.
ASSET CLASS: stocks | REGION: United States | FREQUENCY:
Monthly | MARKET: equities | KEYWORD: Principal
I. STRATEGY IN A NUTSHELL
The strategy trades 25 double-sorted Fama-French size-value portfolios using 20-day momentum signals. Signals are standardized and ranked across assets to create a prediction matrix, which forecasts 20-day-ahead returns by multiplying expected returns at t+1 by signals at t, estimated over the past 120 periods. Singular value decomposition (SVD) is applied to extract singular vectors, forming principal portfolios. The top three principal portfolios are selected, with equal positions across them. The strategy is rebalanced every 20 days.
II. ECONOMIC RATIONALE
The strategy’s effectiveness stems from singular vectors, which capture the largest covariation between momentum signals and future returns. These vectors form principal portfolios that exploit cross-predictability and joint signal-return dynamics. By ranking portfolios based on predictability, the strategy isolates the most profitable combinations. It delivers consistent performance both in-sample and out-of-sample, across various horizons, universes, and momentum lookbacks, demonstrating robust and repeatable return predictability.
III. SOURCE PAPER
Principal Portfolios [Click to Open PDF]
Bryan T. Kelly, Yale SOM, AQR Capital Management, LLC, National Bureau of Economic Research (NBER); Semyon Malamud, Ecole Polytechnique Federale de Lausanne, Centre for Economic Policy Research (CEPR), Swiss Finance Institute; Lasse Heje Pedersen, AQR Capital Management, LLC, Copenhagen Business School – Department of Finance, Centre for Economic Policy Research (CEPR)
<Abstract>
We propose a new asset-pricing framework in which all securities’ signals are used to predict each individual return. While the literature focuses on each security’s own-signal predictability, assuming an equal strength across securities, our framework is flexible and includes cross-predictability-leading to three main results. First, we derive the optimal strategy in closed form. It consists of eigenvectors of a “prediction matrix,” which we call “principal portfolios.” Second, we decompose the problem into alpha and beta, yielding optimal strategies with, respectively, zero and positive factor exposure. Third, we provide a new test of asset pricing models. Empirically, principal portfolios deliver significant out-of-sample alphas to standard factors in several data sets.
IV. BACKTEST PERFORMANCE
| Annualised Return | 7.2% |
| Volatility | 10% |
| Beta | N/A |
| Sharpe Ratio | 0.72 |
| Sortino Ratio | N/A |
| Maximum Drawdown | N/A |
| Win Rate | N/A |
