Aggregating Portfolio Greeks and Other Risk Measures
Summary
The answer explains which portfolio risk report fields can be scaled by position size and netted across trades. Most sensitivities, including Greeks, typically scale with notional, but aggregation needs care: unlike-for-like positions should be combined, and market or contract reference data generally should not be netted. Some summaries, such as weighted averages, may still be meaningful.
It highlights risks that simple addition can hide. Delta aggregation across different underlyings assumes relationships between those assets; rho should distinguish curves, currencies, and curve tenors; and vega should preserve differences across volatility products, expiries, and moneyness. Notionals in different currencies need conversion before aggregation. VaR and expected shortfall also do not generally aggregate by summing standalone values, so portfolio risk should be recalculated. The advice is qualitative and does not provide formulas or a specific portfolio example; conventions can also depend on the risk report and instrument definitions.
Key ideas
- Most position sensitivities scale with notional and can often be aggregated across comparable trades.
- Market data and contract characteristics should not be netted as though they were position exposures.
- Aggregating risk across underlyings, currencies, curves, or volatility types can conceal important differences.
- Interest rate sensitivities should retain tenor detail when curve shape risk matters.
- Portfolio VaR and expected shortfall should be recalculated rather than estimated by summing individual trade figures.
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# Aggregate Greeks calculations # Aggregate Greeks calculations My question is simple and slightly amateur but I wanted to get a good foundation on aggregate Greeks calculations. For delta, I understand the delta values for a spread would be first multiplied by the quantity or trade size and then summated. This would mean a long call or put would be multiplied by a positive trade size and a short call or put by a negative trade size. Does this same logic apply for theta, gamma, vega, and rho? Is there any case, for example with theta, where the absolute value of the trade size (irrespective of whether it’s a long or short call/put) is used before summating the values for the spread? I appreciate the help. ## Answer by Dimitri Vulis (score 3) https://quant.stackexchange.com/a/60386 Most, but not all, columns on the typical risk report will double if you double the notional ; and can be also netted for two different trades. Moneyness (how far the is the option from being at the money) is usually expressed as how much the underlying needs to move, so it does not depend on the notional. Market data (implied vol, interest rates, yields, prices, etc) and indicative data (coupon rates, time to expiry/maturity, expiry/maturity date) do not depend on the notional. Don't net them or peope will point at you and laugh. However some summary statistics (like average or weighted average) of a portfolio may sometimes make sense. Netting bond accrueds as amounts in the reporting currency makes (a little) sense, while netting them as a percentage of the notional does not. If you're netting deltas and similar greeks across multiple positions, be careful when netting across different underlyings, i.e. assuming that the undelyings are correlated. Likewise, when netting interest rate risk (rho), do not blindly add up the sensitivities to different interest rate curves and currencies. Netting the sensitivities to all the tenors of one curve to obtain the sensitivity to a parallel shift is generally OK, but be careful not to obscure situations where a portfolio is not sensitive to a parallel shift, but is sensitive to a change in the slope or convexity of a curve - provide a way to drill down into interest rate sensitivities by tenor bucket and/or report sensitivities to principal components of the curve. Likewise, when netting vega of a portfolio of different kinds of volatility products, do not assume that all implied vols are perfectly correlated, but provide a way to see the sentivities to different kinds of vols (e.g. caplets v swaptions), and provide a way to drill down into vega broken down by moneyness, time to expiry, and possibly other dimensions. Likewise, be careful when netting notionals (or equivalent notionals), and in particular don't net any amounts expressed in different currencies without converting them to one reporting currency. Value at Risk (VaR), Expected Shortfall (ES), etc will double if you double the notional ; but the VaR of two different trades is less likely to be close to the sum than to the square root of the sum of the squares, or something else yet. The only way to get it right is to recalculate the VaR for the portfolio. "Net VaR" is bad. Probably among the less useful things I've ever seen on a risk report were the par values of the underlying common equity, scaled by equivalent notiona, and netted by the equity.
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