Interpreting Vega Aggregated Across Asset Classes
Summary
The document considers whether a hedge fund can meaningfully sum vega exposures across asset classes such as equities and credit. Its central point is that aggregate sensitivities are not exact measures of portfolio risk unless the underlying risk factors move in a sufficiently coherent way. Even aggregated equity delta lacks a single realistic market factor that directly translates the total into portfolio profit and loss.
Summing vega can still provide a broad indication of exposure or help compare a portfolio over time. It is more informative when the positions’ volatility factors tend to move together, as may be the case for similar equities. Cross-asset aggregation is more approximate because volatility correlations can be below perfect and cross effects or higher-order impacts are omitted. The discussion offers conceptual guidance, not a formal proof or a specific aggregation formula; the usefulness of the result depends on the intended purpose and the assets being combined.
Key ideas
- Summed sensitivities are not generally exact measures of portfolio profit and loss across distinct risk factors.
- Aggregate vega is more informative when the relevant volatility factors tend to move together.
- Cross-asset vega sums omit imperfect correlation and interactions between positions.
- An aggregate measure can still help describe broad exposure or compare a portfolio over time.
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Full text
# How to calculate the multi-asset class portfolio vega? # How to calculate the multi-asset class portfolio vega? I am viewing a risk report of a hedge fund and the portfolio vega seems to be a plain summation of the vegas of the different asset classes the fund invests in (i.e. Equity, Credit etc) As far as I know, vega is additive when referring to the same underlying with a similar maturity, therefore, the assumption of the hedge fund is too simplifying? Is there any kind of 'mathematical' proof regarding why this is wrong? And the main question, what is the 'correct' way to do this? ## Answer by Ivan (score 1) https://quant.stackexchange.com/a/41490 Well if you go there, can one ever really aggregate risk exposures to different risk factors ? Not really, even something as simple as equity deltas can't really be aggregated, because there is no one realistic risk factor that when multiplied by such aggregate delta will give you your P&L. What those measures do instead is give a broad understanding of the quantum of risk being run. They are only as good as the coherence of the individual factors they are summing up. In that sense an aggregate equity vega is relatively informative, because equity volatilities will tend to move together. If on top of that your portfolio is made up of similar equities (say similar market caps in the same sector), then our aggregate measure is likely to be quite informative. Now, whether an aggregate vega over different asset classes is informative is up to the person who is aggregating them. I guess the important thing here is whether this is meant to be a precise reflection of risk run (it isn't), or a broad indication meant to help compare the portfolio at different points in time, for example (it probably is ok for that). ## Answer by Magic is in the chain (score 0) https://quant.stackexchange.com/a/41488 So they would have computed the vega of each asset class by shifting the vol of each position by, say 1bp, and then summed the results across the asset classes. It uses simplyifying assumptions in that it does not take into account the fact that the vols of the different positions will have less than perfect correlation (and the cross and higher order impacts between the different positions). What position would give rise to vega in credit btw? Correlation?
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