# 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?

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).

• thanks for your response. I am aware of ways to 'combine' the risk of multiple risk factors. For example, there is the approach of stressing a single risk factor and then applying the beta of the other risk factors available in the portfolio to calculate their stress amount. What is the main point here (and I modified the title of the question to make it more clear) is whether there is a 'correct' way to do this. Aug 29, 2018 at 7:26
• I don't know if there is a correct way to do this, but the beta approach you mention is a very reasonable one. One possible implementation is to choose a base asset and a reference bump, say +1 vol point for the SPX, and sum all vegas after scaling each vega by the beta of the vol moves of the related asset to that of SPX vol moves. The next question is obviously finding a period for betas that is relevant to your particular application.
– Ivan
Aug 29, 2018 at 17:43
• thanks, yeah that would make sense - I was just hoping, though, that there is some kind of market standard for that.... Aug 30, 2018 at 13:41

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?