Combining Allocation and Security Selection Risk in Multi-Asset Funds
Summary
The document asks whether ex-ante active risk from asset allocation can be combined with ex-post active risk from security selection to estimate a multi-asset portfolio’s total tracking error. It raises the key issue that simply adding risk measures assumes a relationship between the sources of active return, and asks whether their correlation should be treated as zero or one.
The response suggests a factor-based bridge: estimate security factor sensitivities, aggregate them into portfolio exposures, compare those exposures with the benchmark, and relate the resulting differences to realized tracking error. It recommends checking explanatory reliability on a validation sample distinct from the data used to build the model. This is a proposed approach rather than a fully specified risk formula or empirical demonstration. Its usefulness depends on whether the chosen factors and exposure estimates capture the portfolio’s realized active returns well enough.
Key ideas
- Adding allocation and security selection risk requires assumptions about how their active returns co-move.
- A factor model can translate portfolio and benchmark holdings into comparable factor exposures.
- Aggregated exposure differences can be evaluated against realized tracking error.
- Validate the proposed relationship on returns not used to fit the model.
- The suggestion depends on the factor model explaining active return variation adequately.
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Full text
# Total risk from asset allocation and security selection # Total risk from asset allocation and security selection My company's multi-asset fund has been using risk metrics methodology to calculate ex-ante VaR and tracking error for years. Due to hardware limitation, the calculation only reflects active risk from asset allocation (e.g. O/W S&P 500 by 2ppt), assuming our portfolio managers largely replicate the benchmarks. However, my boss is concerned about the active risk from security selection. He tasked me to explore whether it is possible to combine the ex-ante active risk from asset allocation with the ex-post active risk from security selection to estimate the total risk and tracking error. My question is whether this addition makes sesnse? What is the assumed correlation between the two active risk measures(i.e. 1 to be prudent or 0 to be realistic)? Kindly advise if you have any ideas or come across any literature on this. Thanks ## Answer by Fr1 (score 1) https://quant.stackexchange.com/a/41528 If you don’t find any better codified solution in literature, I think you could try to run a factor analysis of the securities in your portfolio, aggregate the factor sensitivities into the portfolio sensitivities to factors, and see how you are exposed to factors and what is the exposure of the reference benchmark. Then you can try to see how that works on a validation sample of returns (different from the sample used) to check whether it is reliable enough in explaining ex post tracking error. If so, you have a closed-form expression to map the risk factors sesntivities, so that you build a bridge between ex ante portfolio composition vs benchmark and ex post differential returns, provided that your model is good enough. This is a suggestion in case you do not find anything you like more in past literature, so search literature before.
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