The Statistical Limits of Realised Variance as a Benchmark for Delta-Hedged Option Strategies

This paper examines the econometric limitations of using realised variance as a benchmark for evaluating the performance of delta-hedged option strategies. We show that the statistical precision of realised variance estimators depends critically on the asymptotic regime, whether infill or long-span, and that many standard practices in volatility trading implicitly conflate these frameworks. When the horizon is fixed, realised variance is a noisy estimate of integrated variance, with confidence intervals that remain wide regardless of sampling frequency unless high-frequency data and noise-robust estimators are used. By contrast, inference on long-run variance rates under ergodicity is consistent but refers to different population quantities. We derive approximate sampling errors and confidence intervals for variance estimators under realistic market conditions, and clarify the relation between model free implied variance and single-strike implied volatilities in determining delta-hedged profit and loss. The results highlight why traders' intuitive benchmarking of realised variance against implied volatility often leads to a false sense of precision and performance. Our findings reconcile econometric consistency with market practice, providing a framework for statistically valid evaluation of volatility-trading strategies.