Volatility as a risk measure has been criticized and dismissed on various grounds. Yet, volatility is the dominating risk measure in the investment management industry. Volatility is typically calculated as the arithmetic standard deviation of returns. At the same time, it is industry practice...

Ex post volatility is defined as dispersion of ex post portfolio returns over the measurement period. Ex post volatility takes into account the variability in asset returns and changes of asset weights over time due to trading and drift. Ex ante volatility, on the other hand, is defined as...

Deriving estimators from historical data is common practice in applied quantitative finance. The availability of ever larger data sets and easier access to statistical algorithms has also led to an increased usage of historical estimators. In this research note, we illustrate how to assess the...

In this research note, we compare S&P 500 volatility figures calculated with the popular “square-root-n rule” to volatility figures derived from time-aggregated daily returns and try to reconcile the differences with popular time-series models featuring serial correlation in returns or...

In this research note, we explain how to correctly calculate contributions to ex post returns and ex post volatility and tracking error. The calculations are performed on a realistic portfolio, i.e. a portfolio in which the asset weights change over time due to active management and passive...