Scaling Active Portfolio Positions to a Risk Budget

Summary

The document asks how to size overweights and underweights in a ten-asset portfolio relative to benchmark weights. The investor has views on four assets and wants to scale active positions so their risk contributions are balanced, while keeping the remaining six assets mostly unchanged. They also ask how to target a specified level of active risk without running a full portfolio optimization.

It frames two practical choices: scale positions according to their contribution to portfolio risk, or use a predicted covariance matrix to set active weights against an ex ante risk budget. However, the document is a question and provides no answer, worked example, implementation, or evidence that establishes which approach is preferable. Any method would need to account for correlations among active positions and the benchmark portfolio; matching individual risk contributions alone may not produce the desired total active risk. The proposed approach and its behavior therefore remain unresolved.

Key ideas

• Active weights can be considered relative to benchmark holdings.
• A covariance matrix can estimate the risk of active positions.
• Equalizing individual risk contributions may not control total active risk when assets are correlated.
• The document asks how to reach a specified active risk budget while leaving other holdings mostly unchanged, but does not provide a solution.

Tags

# Portfolio construction: Over/underweighting assets with a given active risk budget


# Portfolio construction: Over/underweighting assets with a given active risk budget












I am trying to refresh my knowledge of portfolio risk calculation but would like to get a second opinion on the best approach.

I have a set of 10 assets that together make up the benchmark and I have the benchmark weights available. I also have a lot of historical data so I would be able to estimate a predicted covariance matrix on that basis.

Within these 10 assets I have a view on 4, 2 asset I would like to overweight, 2 asset I would like to underweight. Not all assets have the same contribution to portfolio risk, so I would want to do some scaling to keep many active calls balanced.

The simple approach would be to scale the position by the contribution to portfolio risk, such that my underweights and overweight have the same contribution?

I am also looking at a more sophisticated approach where I control the overall level of active risk ex ante. Is there a straightforward way to rebalance these two assets with, say, a 2% active risk budget without running a full optimisation?

Also any ideas on how to avoid broader rescaling / rebalancing of the other 6 assets I want to keep mostly untouched would be appreciated

I am looking for an implementation in python

Thanks!!

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