Toward a Unified Theory of Risk Management

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

2. 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.

3. 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

4. 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

5. 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

6. 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

7. Comparison

8. 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

9. 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

10. 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

11. 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

12. Interactions Senior Management Front Office Market Middle Office Back Office Stakeholders

13. Baseball

14. 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?