Backtesting VaR with Hypothetical and Actual Profit and Loss

Summary

This discussion explains two profit-and-loss measures used in value-at-risk backtesting. Hypothetical or clean P&L revalues the positions held at the prior day’s close using market data observed on the current day. It holds positions static, so the result isolates how their value would have changed without subsequent trading activity.

Actual or dirty P&L adds the effect of trading activity to the hypothetical measure. The question asks how actual P&L can be used when some accounting classifications are not typically sold, but the answer says that regulators known to the respondent prefer hypothetical or clean P&L. It does not explain a practical procedure for producing actual P&L when instruments are held, nor does it survey regulatory rules across jurisdictions. The distinction is useful for understanding what a VaR backtest is comparing, but specific regulatory requirements should be checked separately.

Key ideas

• Hypothetical P&L revalues prior-day positions using current-day market data while keeping positions static.
• Actual P&L includes the effects of trading activity in addition to hypothetical P&L.
• The answer reports a preference for hypothetical or clean P&L among regulators known to the respondent.
• The discussion does not establish a universal regulatory rule or explain treatment across all accounting classifications.

Tags

# Backtesting of VaR estimates


# Backtesting of VaR estimates












Regulators want to backtesting `VaR` estimates based on both `Risk theoretical PnL` and `Actual PnL`. My question is how can Backtesting of VaR be done with `Actual PnL`? Typically, financial instruments are classified as `Amortised cost basis, FVTOCI and FVTPL`, so for first 2 groups Bank would not or unlikely sell the instrument, so actual PnL data will not be available.

Could you please provide some insight how Backtesting with Actual PnL is done in practice?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/77737

I don't know about all regulators, but as far as I know, they prefer to backtest vakue at Risk "VaR" against "Hypothetical/Clean P&L" (HPL), rather than "Actual/Dirty P&L" (APL).

HPL is calculated by revaluing positions held at the end of prior day, using market data actually observed from the current day, to measure portfolio value changes that wwould have occurred if the positions didn't change, using static positions, buy-and-hold, not taking account the actual trading activity, cancelled, amended, or modified trades. Mark to market everything. The P&L is the change in mark to market.

APL is HPL plus the effect of the trading activity.

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