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...

In this research note, we will discuss a specific asymmetrical model and build an attribution framework which allows relating the effects of asymmetry on Alpha and Beta relative to a benchmark model, the single-index model with its symmetric Alpha and Beta. We explain the difference between two...

We discuss the problems associated with changing individual correlation values in a valid correlation matrix and outline a solution for calculating upper and lower bounds within which correlations can be modified, such that the resulting correlation matrix is still valid. We illustrate two...

We highlight important and specific characteristics of default risk and methodological implications. In a simulation contrasting independent, Gaussian and Clayton copulas, we also show that joint default probabilities might be a hidden source of risk in conventional portfolio models of default

We are said to live in an “Alpha-centric” world, in which investors supposedly focus on “Alpha”. This demand is met by active investment managers – “Alpha hunters”. This note does presents two conceptual arguments why Alpha does not automatically result in superior risk-adjusted...

We try to reconcile the popular opinion that the Financial Crisis has fundamentally altered equity risk characteristics with empirical data. Our analysis based on Extreme Value Theory suggests that equity tail risks have remained remarkably stable. This means that the loss dynamics of S&P 500...

Tail risk refers to the shape of the left tail of the distribution of investment returns. Return distributions are traditionally described in terms of their first for moments: mean return, volatility, skewness and kurtosis. Attribution is a descriptive approach used in portfolio analysis to...

Correlations play an important role in the construction of investment portfolios. In this research note, we explain why the manipulation of a valid correlation matrix is challenging. We also propose three methods to perform the following tasks: 1) Increase all correlations such that they...