Toward a Unified Theory of Risk Management Aaron Brown AQR Capital Management Quant Congress USA July 9, 2008

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.

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

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

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

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

Comparison Time Focus Quantile Focus Risk is relative to: Risk management means: Front Office Present Left tail Wealth Decisions under uncertainty Back Office Backward looking Worst case Benchmark Risk measurement and reporting Middle Office Forward looking Entire distribution Risk is absolute Risk management

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

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

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

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

Interactions Senior Management Front Office Market Middle Office Back Office Stakeholders

Baseball Players Owners / Management Reporters / Scorers Front Office Only important part Sometimes 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 Office Good when they pay attention to quantitative principles Moneyball

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?