# Variance Allocation and Shapley Value

arXiv: https://arxiv.org/abs/1606.09424 · HTML: https://mlsanity.com/paper/1606.09424/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2016.

## Built on by (most cited first, 4 of 4)

- [Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process Models](https://mlsanity.com/paper/2305.15167/) (2023)
- [Explain Variance of Prediction in Variational Time Series Models for Clinical Deterioration Prediction](https://mlsanity.com/paper/2402.06808/) (2024)
- [Reinforcement Learning Paycheck Optimization for Multivariate Financial Goals](https://mlsanity.com/paper/2403.06011/) (2024)
- [Explaining Risks: Axiomatic Risk Attributions for Financial Models](https://mlsanity.com/paper/2506.06653/) (2025)

## Abstract (arXiv)

Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of n possibly dependent random variables. This criterion, the Shapley value, requires to translate the problem into a cooperative game. The Shapley value has nice properties, but, in general, is computationally demanding. The main result of this paper shows that in our particular case the Shapley value has a very simple form that can be easily computed. The same criterion is used also to allocate the standard deviation of the sum of n random variables and a conjecture about the relation of the values in the two games is formulated.