Operational Risk for Hedge Funds: The Chi-Score

Benford’s law is an observation about the frequency distribution of leading non-zero digits in numerical data. The law suggests that, in naturally occurring numbers, the leading non-zero digits follow a non-uniform distribution. In this paper, as the first to apply Benford’s law to hedge funds, we develop a univariate measure, called the Chi-score, to represent the degree of hedge fund return conformity to Benford’s law. The lower the score, the more a fund’s return data conforms to Benford’s law. We document that more conforming hedge funds are associated with favorable fund characteristics, better risk-return profiles, and higher survival rates. These funds tend to charge higher incentive fees, have more managerial investments, and impose more flexible share restrictions. Additionally, more conforming funds are associated with higher levels of adequate fund governance and better-quality return data. Our findings are further confirmed through a list of hand-collected hedge funds with documented fraud charges or operational failures. These problematic funds generally display farther deviations from Benford’s law than other funds do. Investors and regulators can use the Chi-score to quantitatively assess hedge fund operational risk.