Beyond market capitalization: efficiency and benchmark design in cryptocurrency indices

Abstract

This paper examines whether alternative weighting schemes improve the risk–return profile and the degree of alignment with a capitalization-weighted benchmark (CW) in cryptocurrency indices. Using a static universe of 27 liquid cryptocurrencies, we build seven indices—cap-weighted, capped cap-weighted, diversity-weighted, equal-weight, inverse-volatility, minimum-variance, and maximum-diversification—plus buy-and-hold strategies in Bitcoin and Ethereum. Indices are constructed from daily CoinGecko prices between 2018 and 2024 with monthly rebalancing. We compare annual returns, volatility, Sharpe and Calmar ratios, beta and tracking error versus the cap-weighted index, and concentration measures (HHI and Top-5 weight), both over the full sample and across distinct market phases. Results show that the cap-weighted index is extremely concentrated and delivers the weakest risk-adjusted performance among diversified strategies, whereas enhanced and full replication approaches (especially equal-weight and inverse-volatility) achieve higher Sharpe ratios while keeping betas close to one and tracking error at moderate levels. Minimum-variance and maximum-diversification portfolios roughly double the Sharpe ratio of the cap-weighted benchmark and mitigate drawdowns in bear markets, however their low beta and high tracking error indicate that they behave more like quantitative active strategies than pure market indices. These findings are robust to reasonable changes in concentration caps and covariance-estimation windows, and they suggest that cap-weighted cryptocurrency indices are a poor proxy for the risk–return profile faced by a diversified investor.