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The assessment of risk based on historical data faces many challenges, inparticular due to the limited amount of available data, lack of stationarity,and heavy tails. While estimation on a short-term horizon for less extremepercentiles tends to be reasonably accurate, extending it to longer timehorizons or extreme percentiles poses significant difficulties. The applicationof theoretical risk scaling laws to address this issue has been extensivelyexplored in the literature.  This paper presents a novel approach to scaling a given risk estimator,ensuring that the estimated capital reserve is robust and conservativelyestimates the risk. We develop a simple statistical framework that allowsefficient risk scaling and has a direct link to backtesting performance. Ourmethod allows time scaling beyond the conventional square-root-of-time rule,enables risk transfers, such as those involved in economic capital allocation,and could be used for unbiased risk estimation in small sample settings.  To demonstrate the effectiveness of our approach, we provide various examplesrelated to the estimation of value-at-risk and expected shortfall together witha short empirical study analysing the impact of our method.

A novel scaling approach for unbiased adjustment of risk estimators