Patrick Kiefer and Michael Nowotny

Crypto lacks accounting data, so the Fama-French playbook of sorting assets by firm characteristics does not apply. Statistical factor extraction tools like PCA are natural alternatives for reducing noise and dimensionality. However, PCA concentrates factors based on the ability to explain variance and is blind to whether a factor portfolio has a high Sharpe ratio or otherwise performs well.

In this article, we use a variation of Risk-Premium PCA (Lettau & Pelger, 2020) (RP-PCA) to form cryptocurrency portfolios. Relative to PCA, RP-PCA favors components that have high average returns along with high variance. The result is a set of factors that sacrifice minimal explained variance while improving Sharpe ratios and other performance statistics.

The RP-PCA derived crypto tangency and minimum-variance portfolios have higher Sharpe ratios both in and out of sample than standard PCA, equal-weighted and value-weighted market portfolios, as well as BTC buy-and-hold strategies. We corroborate the stability of this performance with out-of-sample tests over a grid of estimation and walk-forward windows. We also confirm stability across a variety of covariance and mean shrinkage estimation techniques, episodic backtests and bootstrap inference. Interpretations and future work are discussed.

Data

We obtain individual trade records from Binance Vision, the exchange's public historical data repository, for 30 cryptocurrencies quoted against USDT over the period January 2021 to December 2025. Each trade record includes a transaction price, a quantity, and a binary aggressor flag indicating which counterparty initiated the trade. We use these signed trades to estimate effective bid-ask spreads following the Glosten and Harris (1988) price impact decomposition, which builds on the theoretical framework of Glosten and Milgrom (1985). Returns are winsorized at the 1st and 99th percentiles. Further details on the spread estimation and mid-price recovery procedure are provided in the Data Appendix.

PCA and RP-PCA

We implement uncentered PCA on the 30 cryptocurrency returns using singular value decomposition (SVD), with certain modifications described below. PCA yields a primary, long-only "market" factor, together with a series of trailing, orthogonal "long-short" factors.

We also implement RP-PCA, the risk-premium principal component analysis introduced by Lettau and Pelger (2020). Unlike standard PCA, RP-PCA directly incorporates mean returns into the optimization problem. The effect is to rearrange the components to favor factors capturing both high mean returns and high variance.

We modify the baseline RP-PCA procedure by separating the decomposition into several steps. In the first step, we estimate the sample covariance matrix. We then estimate and add the mean return vector, scaled by an RP-PCA penalty parameter, to the covariance estimate. In the final step, we apply a eigendecomposition (via SVD) to this resulting composite matrix. This breakdown allows modularity in the estimation of moments which we make use of in the out-of-sample procedure.

PCA and RP-PCA results for the full sample are reported jointly. We also report the walk-forward out of sample (OOS) Sharpe ratios for comparison. A detailed description of the walk-forward implementation and additional OOS results are reported in the robustness section.

The tangency and minimum variance portfolios are formed from the top five components of each decomposition model, following Barillas and Shanken (2018). The RP-PCA tangency Sharpe ratio exceeds that of PCA by a substantial margin. RP-PCA's second factor is optimized for high mean returns and high variance, resulting in a dominant Sharpe ratio contribution. Equal-weighted and value-weighted market returns and BTC buy-and-hold strategies are presented as benchmarks.

The efficient frontier plots the risk-return (volatility vs. mean return) pairs that are optimal among all achievable combinations in the given asset universe, including the RP-PCA top 5 component, PCA top 5 component and market portfolio universes.

In-Sample Portfolio Statistics (w OOS comparison)

Component Reweighting

RP-PCA reorders the principal components relative to standard PCA. The first components under each method are nearly identical, both capturing a broad, level-like market factor. The second RP-PCA component, however, recombines elements of the standard PCA decomposition in a way that concentrates high mean return and high variance into a single factor — this is the mechanism through which RP-PCA achieves its superior Sharpe ratio.

Explained Variance