Marginal Volatility Contribution of an Asset to a Portfolio

Summary

The document addresses how to describe one asset’s volatility in relation to a portfolio that contains several correlated assets. The answer identifies the quantity as the asset’s marginal volatility contribution and expresses it as the asset’s own standard deviation multiplied by its correlation with the portfolio. This links the asset’s standalone risk to how closely its returns move with the combined portfolio.

The formula is useful for understanding why an asset’s effect on portfolio risk cannot be inferred from its weight or standalone standard deviation alone. Correlation with the portfolio matters. The post does not explain how to construct correlated Monte Carlo draws, derive the expression, or distinguish marginal volatility from a weighted risk contribution or a full variance allocation. Its brief answer therefore clarifies one risk measure but does not provide a complete simulation procedure.

Key ideas

• The asset’s marginal volatility contribution depends on its standalone volatility and its correlation with the portfolio.
• An asset’s weight alone does not determine its relationship to portfolio volatility.
• The answer identifies a marginal measure rather than giving a full Monte Carlo workflow.
• A complete portfolio risk allocation requires additional definitions and calculations.

Tags

# Isolating single assets standard deviation in a portfolio accounting for correlation


# Isolating single assets standard deviation in a portfolio accounting for correlation












I am running a simple Monte Carlo analysis in Excel using mean return, standard deviation and the =NORMINV(RAND(),mean,std dev) method. I have a correlation matrix that I use to compute the portfolio variance for varying weights of 16 assets.

I would like to compute the standard deviation of a single asset after accounting for correlations with the portfolio. For example using the data in the attached picture, if I wanted to run a Monte Carlo analysis on asset 1 after accounting for the correlations with assets 2 and 3 in portfolio 1, what would me steps be? The mean return would simply be the weight of the asset in the portfolio times the assets return but what would the standard deviation of the asset be, the standard deviation of the portfolio times the weight of the asset?

## Answer by Kiwiakos (score 1)

https://quant.stackexchange.com/a/19591

If I understand correctly what you are after is the marginal volatility contribution of a single asset to the portfolio.

This is given by $$ \sigma(X_j;X) = \sigma(X_j)\ \rho(X_j, X) $$

See here for details.

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