Preliminary remarks on the key figures

The performance of a security, especially in comparison to others, is considered an important decision-making criterion and there is also a generally accepted calculation method for absolute performance. However, a comparison of securities based solely on their absolute performance is not meaningful.

Rather, the two components of performance or return and risk must always be taken into account, as this is the only way to make a "fair" comparison. However, there is a whole range of key figures for measuring risk. In addition to the classic measure, volatility, the tracking error, (Jensen) beta and, of course, measures of downside risk such as VaR and expected shortfall should also be mentioned here.

As a result, there is a whole range of key figures for risk-adjusted performance measurement, most of which are derived from one of the various capital market models of portfolio theory.

The following is a selection of the best-known and most frequently used key figures in this area.

Some key figures, including the Sharpe ratio and Treynor ratio as well as outperformance and stability of outperformance, are always calculated on the basis of annualized performance or standard deviation/volatility. In order to carry out this annualization, a normal distribution of returns is assumed. Since in practice - and also in textbooks such as Performance Analysis in Practice, 2nd edition, Fischer - absolute performance is the preferred method of calculation, this is also the default setting in tables and formulas. However, the normal distribution assumption is usually not even approximately fulfilled for the absolute performance. For shares and funds, the assumption of a log-normal distribution, i.e. normal distribution of the logarithms, is often at least approximate, so that the use of logarithmic returns (compounded returns) is preferable from a financial mathematical point of view. It is therefore possible to calculate all of the relevant key figures on this basis.