P&L attribution challenge in FRTB compliance

FRTB’s P&L attribution test requirements are based on two metrics:

  1. Mean unexplained daily P&L (ie: risk theoretical P&L minus hypothetical P&L) over the standard deviation of hypothetical daily P&Lratio1

N is number of trading days in the month. Ratio1 has to be between -10% to +10%.

  1. The ratio of variances of unexplained daily P&L and hypothetical daily P&L.

rati2

Ratio2 has to be less than 20%.

These ratios are calculated monthly and reported prior to the end of the following month. If the first ratio is outside of the range of -10% to +10% or if the second ratio were in excess of 20% then the desk experiences a breach. If the desk experiences four or more breaches within the prior 12 months then it must be capitalized under the standardized approach. The desk must remain on the standardized approach until it can pass the monthly P&L attribution requirement and provided it has satisfied its backtesting exceptions requirements over the prior 12 months.

The real challenge:

Let’ look at variance(P&LRisk – P&LHypo)

Volatility of P&LRisk  = σ(P&LRisk)

Volatility of P&LHypo  = σ(P&LHypo)

Then variance(P&LRisk – P&LHypo) = σ2(P&LHypo) + σ2(P&LRisk) – 2×ρ × σ(P&LRisk) × σ(P&LHypo)

For simplicity let us assume that σ(P&LRisk) = σ(P&LHypo). Then

ratio3

As per FRTB guidelines,  (2-2 ×ρ) < 20%

This implies ρ>90%

The following article explains these challenges from the practical perspective:

FRTB Compliance – Implementation Challenges http://www.garp.org/#!/risk-intelligence/culture-governance/compliance/a1Z40000003PBRnEAO/frtb-compliance-implementation-challenges

 

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