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P&L Attribution - judging the weatherman

A light hearted what, why, how description of P&L attribution

Acuity Derivatives

on 11 March 2013

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Transcript of P&L Attribution - judging the weatherman

Judging the weatherman P&L Attribution (P&LA) P&LA Who is the Risk Models generating sensitivities VAR model generating P&L distribution Trade Activity generating P&L changes ....this is both New Trades and Trade Lifecycle events P&LA provides a critical product control function of decomposing and analyzing P&L and its variance:

in relation to portfolio risks and
in relation to portfolio trade events.
in relation to the VaR predicted P&L distribution. First, terminology - or is "is" what "is" is? Attribution
Explain Risk
Explain vs
Reval Flash vs
Actual vs Buy&Hold P&L Unexplained
Backtest They mean the same thing to me Attribution vs Explain? Though sometimes Explain is used to mean P&L due to market moves
Attribution is P&L due to everything else (e.g. new trades, funding, CVA etc) P&L Attribution (P&LA) Weathermen? Risk-Based P&L Explain is based on a Taylor Expansion; Risk-based Explain vs Revaluation? Revaluation on the other hand
involves a repricing and has 2 flavours. 1. Component Slide or
Bump1-Reset1-Bump2-Reset2... The position is revalued with only one actual market data change applied and the P&L due to this attributed. The market data is then reset to the prior day's values; and the position revalued with some other actual market data change applied. ... and so on Component slide may help identify P&L due to the change in a specific underlying e.g. Credit Spread curves but will not distinguish between 1st order and 2nd+ order effects of that change
eg. credit spread delta vs credit spread gamma 2. Progressive Slide or
Bump1-Bump2-Bump3.. The position is revalued with each actual market data change applied sequentially - without reset. And the P&L at each step due to all preceding changes attributed. ... and so on Progressive slide similarly will not distinguish between the 1st order and 2nd+ order effects of a change in an underlying e.g. Credit Spread curves ... this means that the incremental P&L attributed at each step will be sensitive to the order in which the market data changes are applied

Even though the end cummulative P&L is invariant. With all market data changes applied, cummulative incremental P&L should match the market driven Buy & Hold P&L. ... as you've just re-played the EOD valuation in incremental steps Also, because of the lack of reset between bumps; Progressive slide will include in the incremental P&L captured at each bump, the cross effects between the current market change being applied and the previous market changes applied e.g. cross gamma, vanna etc. Using prior day (T-1) sensitivities and the actual market data change to predict and attribute the P&L expected from changes in specific market data. Flash P&L is a Front Office (FO) view on predicted P&L.

Usually calculated using prior day T-1 sensitivities;

may rely on unofficial closing market data and exclude other official P&L components e.g. CVA change, Funding, Transfer pricing etc. Flash vs Actual P&L? Flash P&L - especially when available at book/market close - offers an early warning indicator of where official Actual P&L is likely to be.

The benchmark for analyzing P&L Attribution is Actual P&L. Actual P&L is the official EOD P&L run and involves a full revaluation of closing positions using closing market data; and includes all P&L components.
Subset of Actual P&L that includes components of P&L due to market movements, trade changes or lifecycle events affecting the start of day (SOD) positions is the Buy & Hold P&L

i.e. P&L due to holding a bought SOD position. Buy&Hold P&L For any given position i made up of n trades: Unexplained P&L? When aggregating Unexplained P&L across positions that are either not risk or methodology homogenous, a sum of absolutes is appropriate. This assumes that all n trades are risk homogenous and that their P&L attribution is calculated using the same P&LA methodology and valuation is done with consistent models and market data. Value at Risk (VaR) describes probabilistically the potential loss of a given portfolio of risky positions over a holding period of time for a given confidence interval. Backtesting VaR? The daily Buy & Hold P&L recorded over the holding period is used to test the predictive capability of the VaR model i.e. did the frequency of Buy & Hold losses above the VaR amount materially exceed or lag the frequency predicted by the VaR model. VS ....Prediction "Reality Check" P&L Attribution is your Unexplained P&L are your eyeballs Don't hide your eyeballs Don't hide Unexplained P&L ...tells you if you are missing relevant risk factors ...tells you if your risk model is "iffy" ...tells you if your Buy & Hold P&L deserves confidence ...Buy & Hold P&L tells you if your VaR is "iffy" Scoring the Weatherman.... Risk Classification Use Classification rules to determine what risk factors are applicable for a given position. Classification is dynamic - risk factors for a near expiry ATM exotic option are not the same for the same option deep ITM or at inception. Fast Forward
I Speak Fluent P&LA Eg. a near expiry ATM exotic option may require: Market Driven P&L Attribution Using T-1 Sensitivities and market data change from prior day, generate a Risk Based P&L Attribution for as many Taylor risk factors as possible. P&L due to higher order risk factors and cross factors can be estimated by combining Component Slide and Progressive Slide revaluations. Trade Lifecycle P&L Attribution With the (closing) market data constant, attribution is the difference between the valuation before an event is applied and after applying the event. Impact of event on the trade position(s) may include:
the status of the trade (e.g. from active to non-active),
the terms of the trade (e.g. a change in the notional) or
the product type of the trade (e.g. from an Option to an Underlying). Sample P&L Attribution Sub Items Your Weatherman Scoring Toolkit Monitor Unexplained P&L and use to: review risk factors for completeness. review risk models for correcteness. review trade lifecycle booking for completeness. Use Buy & Hold P&L with confidence to: backtest your VaR model. Measuring without Gotchas Homogeneity Be careful combining attribution across model families - especially for those "bastard" greeks "SABR vega does not play with Black vega". GM-Senior-USD-ModRe is not GM-Senior-USD-NoRe. Be careful combining attribution calculated with different curve families. Netting If the Unexplained P&L is not from Homogenous attribution you CANNOT NET it down! "Delta" from a Component Slide revaluation includes Gamma and Speed effects that Risk-based explain Delta does not . Be careful combining attribution calculated using different P&LA methodologies. Double Counting eg. ΔS1.ΔS2 vs ΔS2.ΔS1 Be careful not to double count attribution - especially with attribution due to cross factors. Adjustments A major source of errors and ...umm.. vanishing Unexplained P&L. Adjustments to one, require Adjustments to one or both of the other two. Adjustments are a necessary evil because mistakes do occur but.... are open to abuse and should be carefully monitored and audited. ... especially by Regulators. theta-delta-gamma (and vega for options) for material underlyings would be a minimum Taylor expansion for non-linear books. Fast Forward
I Speak Fluent P&LA Fast Forward
I Speak Fluent P&LA Fast Forward
I Speak Fluent P&LA Fast Forward
I Speak Fluent P&LA Fast Forward
I Speak Fluent P&LA Fast Forward
I Speak Fluent P&LA Fast Forward
I Speak Fluent P&LA Actual
P&L Risk P&L
Attribution Thank you....
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