How to explain non-additive measures, Part 2: Incremental contribution
Interactive decomposition with atoti
This article is the second part of a series of tutorials about interactive analytics in in atoti’s dynamic pivot tables. Check out Part 1: Pro-rata allocation if you wish to read what non-additive measures are and why we may want to have them decomposed.
Solution #2: Incremental contribution
In the previous post we were decomposing a non-additive measure into additive components. There’s another perspective on the contribution analysis when you don’t want to allocate the top-level number down to additive components, but you want to evaluate incremental, aka marginal impact of a contributor — computing the impact of a scenario if that contributor is hypothetically removed:
In the following example, the “VaR Incremental BookHierarchy” measure shows the impact of the sub-portfolios on the firm-level VaR “as if the portfolio was removed”. For example, for the business line “Equities” it is +15.414, meaning that this portfolio has a positive +15.414 impact on the firm-level VaR.
UPDATE: The GIFs and code snippets in this article are based on an older version of atoti. We have released much smoother and even more functional dashboards and widgets with the latest version of atoti. Check out this link to see the documentation of the latest version of atoti.
To test that, let’s visualize the plain version of the “VaR” measure — not the incremental one. If we filter out the “Equities” and compute the “VaR” it goes from -593,129 to -608,543 which is exactly 15.414 lower (-593k — (-609k))!
To implement this behavior in atoti, we will use exclude_self=True parameter of the siblings aggregation. The following measure will aggregate positions being “siblings” of a sub-portfolio, and will ignore positions belonging to the current sub-portfolio:
Now let’s compute VaR from the sibling’s aggregation:
To finalize the incremental calculation, we’ll compute VaR above the current book and subtract the calculation excluding current sub-portfolio:
You can find a notebook implementing this example in the atoti gallery: Value at Risk: A simple way to monitor market risk with atoti.
Conclusion
In this post, we discussed how to use parent and sibling relationships in atoti to implement contributory measures and explain non-additive measures. I hope the described techniques can help you build powerful analytic applications!
