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Risk Budgeting Martyn Dorey 2nd December 2002 Aon Consulting Limited is regulated by the Financial Services Authority for investment business

Risk Budgeting (RB) Agenda • What is risk budgeting? • Why do it? • What is the Output from risk budgeting? • What are the benefits? • Conclusion

What is risk • Romans and Renaissance • Uncharted water = uncertainly • Not fatalism • Fatalism • Select fund managers • Fear of regret

What is risk budgeting • Attempt to balance • Active/passive management • Matching/non-matching asset classes

Why do it? • Consistency in advice • Cheap ALM tool? • Some structure to advice

Published work in the market • Watsons: Risk budget paper presented to institute • BGI risk budget paper in Journal of Portfolio Management • Portfolio Risk & Working Party

General impressions of work • Difficulties of justification remain • How to fit with ‘way in which we do things’

Watsons • Kicked off the concept • Reception pensive • Conceptually fit two efficient frontiers over each other Active Passive AA

BGI • Similar • Introduces optimisation • Assumes managers independent • Deals with active & passive separately • Separate maths for active and passive optimisation • Active is growth/value

Comments • Optimise against liabilities in an integrated fashion • Express solution as variation in funding level • Understand correlations between managers and trade-off • Hard bit is philosophy & calibration

Funding level at risk (FAR) • Assume that the funding level is like a statisticians bell curve Average in the middle 100% funded

(FAR) • Tails are linked to funding levels 105% funded 95% funded 100% funded

(FAR) • The area adds up to 100% Whole area adds up to 100% 105% funded 95% funded 100% funded

(FAR) • Area represents a probability 95% funded 10% chance 100% funded

(FAR) • This scheme has a 10% chance of being less than 95% funded Asset mix one 95% funded 10% chance 100% funded

(FAR) • What can you tell me about this scheme? Asset mix two 95% funded 1% chance 100% funded

What is this spread then? Tracking error = assets - liabilities Mismatching different returns from benchmark If you know how asset returns will differ you know how funding levels will differ you know how contribution rates will vary

Things that affect spread • Current funding level • Amortisation period • Asset classes held • Active/passive mix • Definition of benchmark

How do we calculate risk? Ye olde way

Relative covariance Optimising Cinch Optimising Silly

Thinking in another dimension - é ù 16 10 H = ê ú - 10 25 ë û é ù 0 . 75 = B ê ú 0 . 25 ë û - é ù 3 . 8125 11 . 4375 ~ H = ê ú - 11 . 4375 34 . 3125 ë û - é ù 1 1 = RelCorr ê ú - 1 1 ë û

Case study • Client liability benchmark • 40% Gilts • 40% MFR UK Equities • 20% Cash • Only look at a few asset classes

Case study - (risk) Scenario1 100% Property 5.5% 90% OS Equities 4.6% 80% 70% UK Equities 38.3% 60% % Asset Alloc 50% Corporate AA 5.5% 40% Index Linked Gilts 0% 30% 20% FI Gilts 34.1% 10% Cash 12.2% 0% 0.3 1.6 2.9 4.2 5.4 6.7 8.0 9.3 10.5 11.8 13.1 14.4 15.6 16.9 18.2 Risk vs Benchmark % The spread of returns (as standard deviation) around the liability benchmark

Scenario1 100% Property 5.5% 90% OS Equities 4.6% 80% 70% UK Equities 38.3% 60% % Asset Alloc 50% Corporate AA 5.5% 40% Index Linked Gilts 0% 30% 20% FI Gilts 34.1% 10% Cash 12.2% 0% 103.9 101.9 99.8 97.7 95.6 93.4 91.2 89.0 86.8 84.5 82.2 79.9 77.6 75.2 72.9 Funding level @ risk % 95% probability of the funding level being above x% Case study - (funding level)

Implementing ALM • Client liability benchmark • 40% Gilts • 40% MFR UK Equities • 20% Cash • ALM says….. • 20% Cash • 40% FI • 30% UK Equity • 10% OS Equity

Happiness • Objective modelling • Model upside & downside • varying manager skill • varying tracking error (TE) • identify optimum TE

Happiness Optimum risk Tracking error Manager skill What is the right level of risk?

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