  The assessment of risk based on historical data faces many challenges, in
particular due to the limited amount of available data, lack of stationarity,
and heavy tails. While estimation on a short-term horizon for less extreme
percentiles tends to be reasonably accurate, extending it to longer time
horizons or extreme percentiles poses significant difficulties. The application
of theoretical risk scaling laws to address this issue has been extensively
explored in the literature.
  This paper presents a novel approach to scaling a given risk estimator,
ensuring that the estimated capital reserve is robust and conservatively
estimates the risk. We develop a simple statistical framework that allows
efficient risk scaling and has a direct link to backtesting performance. Our
method 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 examples
related to the estimation of value-at-risk and expected shortfall together with
a short empirical study analysing the impact of our method.
