These two measures, developed in 2010, are mixing beta (i.e. relation between an asset and a benchmark) and skewness (i.e. how two assets are related between themselves during extreme negative returns of the first asset).
Beta Coskewness measures how much an asset, within a portfolio, has historically reacted to extreme benchmark negative returns. An asset with a positive beta coskewness provides portfolio protection when the benchmark has extreme negative returns. Positive beta coskewness is good.
Beta Cokurtosis measures how much an asset, within a portfolio, has historically reacted to extreme benchmark returns. An asset with negative beta cokurtosis provides portfolio protection when the benchmark has extreme positive or negative returns. Negative beta cokurtosis is good.
In the example below, the benchmark is the S&P500 and the graph displays the beta coskewness for each fund in the portfolio. This means during S&P500 extreme negative returns, the funds BlueTrend and MAN AHL are protecting the heavy S&P500 losses.
The Beta Coskewness and Beta Cokurtosis measures are available in AlternativeSoft platform.