Component VaR Aggregation Across Assets and Accounts

Summary

The document addresses how component value at risk (VaR) should be combined across assets and accounts. It confirms that, when the component VaRs are calculated consistently for the full portfolio, their sum equals the portfolio VaR. Accordingly, the listed asset-level components can be summed to recover total portfolio VaR.

The answer qualifies aggregation at the account level: grouping components calculated for the entire portfolio does not necessarily give the VaR contribution of an account considered as its own subportfolio. Asset weights differ when the portfolio is restricted to a subset, so account-level component VaR requires a separate calculation using that subset’s composition. The response gives no formulas or assumptions about the VaR model, confidence level, horizon, or allocation method, so its additivity claim should be understood within the component VaR framework assumed by the question.

Key ideas

• Consistently calculated asset component VaRs sum to total portfolio VaR.
• Components can be grouped by account as arithmetic sums, but that does not necessarily produce standalone account VaR.
• A subset portfolio has different asset weights from the full portfolio.
• Account-level component VaR should be recalculated for the account’s own portfolio.

Tags

# Component VaR is additive but at what level


# Component VaR is additive but at what level












I have a portfolio data as

```
Account     Symbol      ComponentVaR
Acc1        MSFT        CV1
Acc2        GOOG        CV2
Acc1        FUT1        CV3
Acc2        FUT2        CV4
```

So, are following calculations correct.

```
Account     ComponentVaR
Acc1        CV1+CV3
Acc2        CV2+CV4
```

And portfolio VaR can be CV1+CV2+CV3+CV4

## Answer by chjortlund (score 1)

https://quant.stackexchange.com/a/15840

Yes and no :-)

Portfolio VaR = CV1 + CV2 + CV3 + CV4 is correct.

To safeguard my answer, I looked this up from thinxlabs.com

> The individual component VaRs from the assets in the portfolio should add up tho the total portfolio VaR. The equation is as follows.

But you need to calculate another VaR for each account, if you want to use CV on those. The reason is that the asset weight, is not the same for a given asset when you look at a subset of the portfolio.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.