When to Aggregate Greeks Across Underlyings and Instruments

Summary

The document explains that whether portfolio Greeks can be combined depends on what each Greek measures and whether positions share a common risk factor. Sensitivities to a shared factor, such as interest rates across equity positions, can be aggregated to assess exposure to that factor.

By contrast, adding underlying-specific measures such as delta across distinct equities is generally not meaningful because the quantities refer to different risk drivers. Aggregation can make sense across multiple instruments tied to the same underlying, for example when assessing an overall delta hedge or combining vega by maturity bucket. The response gives conceptual guidance rather than a normalization formula, and it does not address cross-asset conversion conventions or portfolio-wide nonlinear risk measures.

Key ideas

• Aggregate sensitivities when positions share a common risk factor, such as interest rates.
• Underlying-specific measures like equity delta generally should not be summed across distinct underlyings.
• Greeks from different instruments referencing the same underlying can be combined.
• Portfolio delta hedging and bucketed vega are examples of useful within-underlying aggregation.

Tags

# Greeks across different underlying


# Greeks across different underlying












To monitor risk of a client portfolio, does it make sense to accumulate Greeks across different underlying? If yes, how can Greeks be normalized across different underlying?

## Answer by Quantuple (score 1)

https://quant.stackexchange.com/a/25250

It depends on what kind of 'Greek' and 'underlying' you are referring to.

Aggregating the sensivity of various equity positions (e.g. options, futures) to interest rates could for instance make sense if you want to evaluate the sensitivity to that common risk factor.

On the other hand, aggregation of underlying-dependent quantities (such as Delta) across distinct underlyings, does not make sense, at least in the equity world.

That being said, aggregation across a different positions/instruments written on a given underlying asset does of course make sense (e.g. macro hedging of the Delta, or bucketed Vegas).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.