Toward a Unified Theory of Risk Management

Aaron BrownAQR Capital ManagementQuant Congress USAJuly 9, 2008

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Disclaimer

The opinions expressed in this presentation are those of the presenter. They do not necessarily reflect the views of his employer nor any other entity.

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History

• Prehistoric: Risk takers manage risk and return together—evolve into front office risk managers

• Early modern: Analysts compile statistics and produce standardized analyses—evolve into back office risk managers

• Mid 1980s: Trading organizations integrate into banks, senior management demands independent, firmwide risk management—middle office risk managers are invented

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Front Office Risk

• Risk is good, it creates opportunities

• Actual losses are bad because they reduce your capital for taking advantage of future opportunities

• Kelly criterion

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Back Office Risk

• Risk is bad, it costs money

• Potential losses are bad because you need to reserve expensive capital or pay for hedges

• Standardized, verifiable metrics

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Middle Office Risk

• Risk is neither good nor bad, it’s a dial you set to the appropriate level to accomplish your goals

• Miscalibration is bad, neither actual nor potential losses matter in the long run

• Economic capital

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Comparison

Time FocusQuantile Focus

Risk is relative to:

Risk management

means:

Front Office Present Left tail WealthDecisions

under uncertainty

Back OfficeBackward

lookingWorst case Benchmark

Risk measurement and reporting

Middle OfficeForward looking

Entire distribution

Risk is absolute

Risk management

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Front Office Unification Model

• James Bond makes all the risk decisions

• Middle office constraints are generally annoying and counterproductive (M), but sometimes helpful (Q, Felix)

• Back office should tell the public whatever is necessary to keep 007 in operation

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Back Office Unification Model

• Police gather some evidence and arrest criminals

• Prosecutors direct investigators and handle legal issues

• CSI analyzes data gathered by others, integrates it with external data and expert knowledge, and cracks the case

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Middle Office Unification Model

• Lois Lane makes pursues profit (stories) but inevitably incurs excessive risk

• Superman comes to the rescue

• Clark Kent prepares the story for publication

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Organizing Principle

• Front office: Kelly criterion

• Back office: Utility theory

• Middle office: Option pricing

• Differ in everyday experience, but can become identical under extreme conditions

• Symmetry breaking

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Interactions

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Baseball

PlayersOwners /

ManagementReporters /

Scorers

Front Office Only important partSometimes help,

sometimes get in the way

Fantasy baseball players

Back Office Undisciplined troublemakers

More disciplined troublemakers, but don’t appreciate the

game

Great sportswriters, analysts, novelists,

only reason it matters

Middle OfficeGood when they pay

attention to quantitative principles

Moneyball

Good when they pay attention to quantitative principles

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Where does this leave us?

• Unification is only possible in the context of a strategy

• Economic capital is the only existing concept that spans front, middle and back offices

• Unification requires economic capital to become real

• Are we in a risk-based economic system?