Method for an additive decomposition of hypothetical P&L by risk factor

External question — Quantitative Finance Stack Exchange Author: la_fonction_capetienne Original post: https://quant.stackexchange.com/questions/85875 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I have a historical-scenario hypothetical P&L calculated by RiskMetrics. I want to decompose the total into additive contributions from: Interest rates FX Equity Volatility Inflation Credit/spreads Other or interaction effects The standard decomposition by riskType is not additive. For example: Total hypothetical P&L = -1,414,260.65 Sum of risk types = -1,369,309.27 Residual = -44,951.38 The hierarchical-factor decomposition also does not necessarily reconcile with the total. What is the standard quantitative methodology for producing an additive hypothetical-P&L decomposition?. BTW I am using RiskManager (Riskmetrics)

External answer — Quantitative Finance Stack Exchange Author: Deniz Kara Original post: https://quant.stackexchange.com/a/85877 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. the usual way to get an additive decomposition is to define the factors as mutually exclusive P&L components rather than simply summing RiskMetrics' riskType results. one practical approach is sequential revaluation: start from the base portfolio, revalue after applying the historical shock for factor A, then factor B, etc. The contribution of each factor is the incremental P&L. The ordering matters because of interactions, so you can either assign interactions to a separate residual bucket or use a Shapley-value decomposition to allocate them across factors. If you need the decomposition to reconcile exactly, the cleanest approach is essentially: Total P&L = rates + FX + equity + volatility + inflation + credit + other/interaction with the interaction term explicitly included, or allocated among the factors using Shapley values. A standard riskType aggregation generally won't guarantee this reconciliation because the factors aren't necessarily independent in the underlying repricing.

External answer — Quantitative Finance Stack Exchange Author: Dimitri Vulis Original post: https://quant.stackexchange.com/a/85878 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I'm not familiar with Riskmetrics. Generally, building a good P&L attribution / explanation (PAA) - leaving little unexplained P&L (UPL) - takes some effort. There are several books and book chapters (see Good references on PNL explain? citing some examples ). See also PnL Explained Using Scenario(Full Reval Model) , Explain daily P&L by risk factor for a portfolio of bonds and FX forwards , and Interest rate swap Profit and loss attribution . We can't tell why your PAA leaves too much unexplained not knowing even what financial instruments / products you're asking about. Maybe you're ignoring some gammas or cross-gammas? Who knows, given your question? You can try asking Riskmetrics, but in my experience, vendor tech support is seldom helpful. But here are 2 pieces of general advice: the best practice, is to have 3 methodologies every day: risk-theoretical P&L (RTPL - Taylor series approximation of the P&L); brute force "cumulative" or "waterfall" or "progressive"; brute force "independent" or "restore" or "component slide". I don't know what "hierarchical-factor decomposition" means, but if it means "cumulative", then it should not leave UPL. If it does, then something's seriously broken, and you need to figure this out. But if it means "independent", then it's normal to have some UPL, but you need to analyze how much UPL would be "too much". I don't know whether Riskmetrics does all 3. If it doesn't, then you should implement your own. Whenever you have a pricing model trying to explain an observable price (rate, spread, etc), as opposed to just pricing to model, there's likely to be some mismatch between the observed price and the model price. You need to monitor this discrepancy as part of the ongoing performance monitoring (OPM) of the pricing model, and raise alarm if it is "too large", but it's not UPL. Example 1: consider a (very simple) model that predicts the USD price of American/Global Depositary Receipts (ADR/GDR) based on the local currency price of the underlying stock, and the USD/local currency exchange rate. Their product is likely not to match exactly the observed ADR/GDR price for various reasons. So your explanation can attribute the P&L to the underlying stock price, to the FX rate, and to the model-observable discrepancy. Note how even in this simple example, a change in the underlying stock price triggers a change in the FX rate sensitivity, and vice versa, which you should ideally explain as well. Example 2. consider a model that predicts the price of a high-yield bond based on risk-free interest rates and the bond issuer's credit spread. Again, there is likely to be some idiosyncratic spread between this model price and the observable bond price, and your explanation will likely attribute the change in the model price to the changes in rates, credit spreads, passage of time, the idiosyncratic spread, and the cross-gammas between them.