RAS Risk ManagementMarket Risk Capital

Amit Sinha, James Wang & Tolga Sezer

August, 2012

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Agenda

Market Risk Capital: Definition and Requirements

Backtesting Methodology

RAS VaR Backtesting

From VaR to MRC: The Tail-Loss Penalty

RAS MRC Summary

Conclusion

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Part I

Market Risk Capital: Definition and Requirements

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MRC: Definition and Requirements

Basel II & VaR-based Risk Capital

Basel II sets the regulatory standard for risk-based capital requirements.

Market Risk Capital is derived from the VaR (internal model approach)and tail-loss penalty.

Internal Model Approach means that the institutions shall be able to usetheir in-house VaR models, but are required to conduct extensivebacktesting to validate their performance.

Tail-loss penalty are based on the losses of a portfolio historically beyondwhat the in-house VaR model would have predicted.

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Market Risk Capital

Definition:

MRCt = max(VaRt(C ),K1

60

t−1∑i=1

VaR(i)(C )) (1)

where VaR numbers are expressed in absolute values and K is themultiplier, the K-factor.MRC is equal to the maximum of today’s VaR and average VaRestimated over previous 60 trading days times the multiplier. TheK-factor is a function of the tail-loss, the part of losses whichexceeds our VaR.

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Market Risk Capital

Requirement:

VaR and hypothetical PnL backtest in order to measure whatthe tail-losses for any portfolio would have been historically.

A penalty-factor function, which incorporates the tail-lossesidentified in the backtesting, which results in a K-factor.

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Part II

Backtesting Methodology

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Backtesting Methodology

A conceptualization of the backtesting routine for any given day

On a specific date (Portfolio Date), we take the actual portfolio positions.

Using 1000 days prior to Portfolio Date, we calculate the 10-day VaR atT3.

The VaR is compared to the cum. 10-day PnL after T3.

We report if there is a breach and if so the extend of the breach.

Next, we move one day back to T2 and do the analysis again for thesame portfolio.

Once we reach our backtesting horizon, we do the same routine for thenext portfolio.

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Part III

RAS VaR Backtesting

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RAS VaR Backtesting

10-day VaR (95%) vs 10-day cumulative PnL: RAS Portfolio as of 2012-01-20

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RAS VaR Backtesting

10-day VaR (99%) vs 10-day cumulative PnL: RAS Portfolio as of 2012-01-20

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Part IV

From VaR to MRC: The Tail-Loss Penalty

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The Tail-Loss Penalty

K-factor: How do we penalize tail losses?

Basel II sets forth following K-factor rule:Condition to calculate multiplier:

KBasel.II = 2. if N <= 3 (2)

= 2 + 0.2(N − 3), if 3 < N <= 4 (3)

= 3 + 0.2(N − 4), if 5 <= N <= 9 (4)

= 4.0, if 10 < N (5)

N here is the number of breaches identified in the backtesting.

This approach only concerns itself with the frequency of breaches.

The magnitude of breach, i.e. the tail loss, is disregarded.

The factors are set without empirical underpinnings.

The penalty factor is floored at 2 and capped at 4.

Critique: Extreme tail-loss risks will be underpenalized and smallerbreaches will be overpenalized.

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The Tail-Loss Penalty

K-factor: Alternative approach

The Blanco-Ihle Approach (BI, henceforth) (Dowd,K 2010: ’MeasuringMarket Risk’)

TailLosst = {(Lt−VaRt)/VaRt

0 if Lt>VaRtLt<VaRt (6)

Tail-loss is defined as the % breach compared to the VaR estimateconditional upon a breach.

If the 10-day cumulative loss is greater than the estimated VaR, then thevalue is the % deviation. Otherwise the value is zero.

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The Tail-Loss Penalty

K-factor: Two ways of deriving the K-factor from the tail-loss

The first way is to take the maximum of tail-losses ever recorded in thedataset as the basis for the K-factor:

KBI .max = 1 + max(TailLosst) (7)

The second way is to take the average size of tail-losses of all recordedbreaches in the dataset as the basis for the K-factor:

KBI .mean = 1 +1

NΣNi=1(TailLosst) (8)

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The Tail-Loss Penalty

Conclusion

KBasel.II is not very realistic as a tail-loss penalty.

There is a very high risk of understating or overstating tail-risk whenusing KBasel.II .

KBI . is a more accurate and realistic approach if one has extensive dataavailable.

With KBI .max we would assume a single extreme event as the basis for thepenalty, which is very punitive.

KBI .mean is a more balanced approach as it takes the average size of alltail-loss occurances as the basis.

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Part V

RAS MRC Summary

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RAS MRC Summary

Examples of Portfolio Backtestings

Portfolio of 2012-01-20K-Factor (Basel II) K-Factor (Blanco-Ihle Max) K-Factor (Blanco-Ihle Mean)

VaR (USD) 1,398,275 1,398,275 1,398,275# of breaches 4 4 4

K-factor 3 1.92 1.15MRC 4,194,825 2,684,688 1,608,016

Portfolio of 2012-02-11K-Factor (Basel II) K-Factor (Blanco-Ihle Max) K-Factor (Blanco-Ihle Mean)

VaR (USD) 2,373,537 2,373,537 2,373,537# of breaches 4 4 4

K-factor 3 6.22 3.56MRC 7,120,611 14,763,400 8,449,792

In the first example, the KBasel.II clearly overstates the tail-risk.

It overstates because empirically, the realized losses were less than 3times higher than the estimated VaR.

The second portfolio has more cash exposure. KBasel.II understates thetail-risks, as cash positions can have significant tail risks.

However, the KBI .max is too punitive as it takes the 2008 liqudity crisisevent as the basis for the factor.

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RAS MRC Summary

RAS MRC and Capital Charges for Jan-Apr and May-Jul

K-Factor (Blanco-Ihle Mean) K-Factor (Blanco-Ihle Max) K-Factor (Basel.II)MRC Factor Cap. Charge MRC Factor Cap. Charge MRC Factor Cap. Charge

Jan – Apr 1,987,167 1.84 90,021 4,888,880 7.86 221,714 5,695,849 3.76 251,326May – Jul 2,325,435 1.05 94,525 2,683,682 1.7 104,377 7,783,110 4 299,991

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Part VI

Conclusion

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Conclusion

Tail-losses are significant and need to be take account for on top of VaR.

While VaR is lower in Q1, RAS has bigger tail-risks in Q1 ...

... relative to Q2 and

... relative to what KBasel.II would imply.

The KBasel.II would be understating risk due to the cap on the factor.

The Blanco-Ihle approach - together with extensive data mining - enablesus to capture tail-risks more accurately.

It would be very punitive if the KBI .Max approach was used, especially forcash positions.

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