Interpreting Marginal Risk Contributions in Long-Short Portfolios
Summary
The document poses implementation and interpretation questions about marginal risk contributions in a long-short portfolio. It describes legacy code that applies a marginal volatility formula using each instrument’s sided U.S. dollar notional as its weight. The author asks what units the derivative of portfolio volatility with respect to those weights has, reasoning that dollar units in both quantities might make the derivative unitless.
It also asks whether a positive derivative identifies a risk contributor and a negative derivative a risk reducer, given that the code reports positive values for long positions and negative values for short positions. Finally, it questions whether signed dollar notionals are appropriate weights in the calculation. The document supplies no answer, covariance inputs, formula details, or worked example, so it cannot establish whether the observed signs reflect portfolio risk effects or the chosen position convention. Resolving the questions requires specifying how portfolio volatility is defined and how weights and position signs enter that definition.
Key ideas
- The document asks how to interpret marginal volatility derivatives when portfolio weights are signed dollar notionals.
- It questions whether the derivative has units when both volatility and weights are expressed in dollar terms.
- It observes that the code reports positive derivatives for long positions and negative derivatives for short positions.
- It asks whether signed dollar notional is an appropriate input weight for marginal risk calculations.
- No formula details or answer are provided, so the risk interpretation remains unresolved.
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# Marginal Risk Contribution Implementation Questions
# Marginal Risk Contribution Implementation Questions
Sorry if this is too obvious to you. The marginal risk contribution mentioned here is the same as in this post Marginal Risk Contribution Formula .
I understand the concepts and derivation on the formula. But I got some questions from some legacy codes I'm working on. Original writer isn't available anymore. Will appreciate if anyone can shed some lights.
Calculation from the codes is pretty much following the formula mentioned in above link. There are two particularities.
- The portfolio is a long-short portfolio.
- The calculation uses each symbol's sided US dollar notional as weight $w_{i}$.
My questions are:
- What's the unit of calculated results $\frac{\partial{\sigma}}{\partial{w_{i}}}$? Notice that the weights used in calculating $\sigma$ are also the sided US dollar notional. I'm guessing since the unit of $\sigma$ is US dollar notional, weight $w_{i}$ is US dollar notional, so $\frac{\partial{\sigma}}{\partial{w_{i}}}$ is unitless?
- What does it mean when $\frac{\partial{\sigma}}{\partial{w_{i}}}$ is positive or negative? My guess is since it's partial derivative, if $\frac{\partial{\sigma}}{\partial{w_{i}}} > 0$, then symbol $i$ is risk contributor and if $\frac{\partial{\sigma}}{\partial{w_{i}}} < 0$, then symbol $i$ is risk reducer? However, I noticed the calculated results have all negative $\frac{\partial{\sigma}}{\partial{w_{i}}}$ for short positions and positive $\frac{\partial{\sigma}}{\partial{w_{i}}}$ for long positions. This seems odd. There seems nothing obviously wrong with the calculation. Just wondering if there is some conceptual things deeper than what I realized.
- Is it proper to use each symbol $i$'s sided dollar notional as weights $w_{i}$ in $\frac{\partial{\sigma}}{\partial{w_{i}}}$? If not, what should be used for $w_{i}$?
Thank you a lot for some clarifications.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.