00 Economic Capital: “The Heart of Decision Making”- Asia Banker Summit 2011 Portfolio Optimization, Replication & Response Surface Modeling into the Risk Process Chicago | London | Singapore

11 QRM Proprietary and Confidential © 2011 Efficient ERM calculations facilitated by powerful approximation techniques based on Replicating Portfolios Response Surface Modeling Portfolio Optimizer provides clients with the ability to turn risk analysis into strategic decisions Presentation Overview

22 QRM Proprietary and Confidential © 2011 Definition of Replicating Portfolio: a portfolio that generates the same cash flows as the source (reference) portfolio under all possible scenarios Ideally, matching period-specific cash flows is more accurate than cumulative cash flows In general, the process of determining the appropriate replicating portfolio is a “best fit” process that requires the use of a suitable optimization routine Replicating portfolio should contain the smallest number of instruments that replicate the source portfolio cash flows Always possible to add more instruments, but these add marginal information Often Replication can be an iterative process, gradually increasing the universe of possible instruments until the fits are sufficiently accurate Replicating Portfolios Generate Same Cash Flows but with Fewer/Simpler Instruments

33 QRM Proprietary and Confidential © 2011 RP is an approach that can be used to include assets & liabilities that have not previously been covered Often business units use distinct modeling platforms and models Conversion to a single platform is difficult both logistically and “politically” Replicate with same instruments as source portfolio to intelligently stratify portfolios Useful when aggregating data based on risk metrics A replication routine to mimic cash flows through a variety of forecasts allows for quicker processing and decision making E.g., Economic capital simulations may be computed on RP more efficiently Replicating Portfolios Can Facilitate Enterprise Risk Calculations

44 QRM Proprietary and Confidential © 2011 Distilling a complex portfolio into hedgeable instruments facilitates communication with traders Improves intuition and makes portfolio more transparent RP is an approach that can be used to “synthesize” complex instruments Useful when processing time is crucial Also works for instruments or structures that the Framework cannot yet model Synthesized instrument can be priced if each of the replicating instruments is itself priced Replicating Portfolios Can Facilitate Hedging Strategies

55 RP Results for Universal Life: Along Any Particular Path, Cash Flow Mismatch is Small QRM Proprietary and Confidential © 2011 RP fits cash flows from Universal Life policies

66 Identify Outlier Path/Period Replicating Portfolio Values and Qualify Fit QRM Proprietary and Confidential © 2011 Easy to see outliers, harder to identify how often outliers occur

77 Cumulative Distribution of Replication Error Clearly Identifies Global Goodness of Fit QRM Proprietary and Confidential © 2011 Cumulative distribution clearly indicates that about 90% of path/periods are fit exactly

88 QRM Proprietary and Confidential © 2011 Market value sensitivity analysis is computationally expensive, especially when there are a large number of scenarios under consideration Computation time is exacerbated by any of the following: Complexity of the instruments Size of the portfolio Number of scenarios … or any combination! Although fitting response surfaces require some “pre-run” scenarios (exact number depends on the problem), ultimately further scenarios are processed very quickly Response Surface Models Fit Market Value “Surface” in Terms of Risk Factors

99 QRM Proprietary and Confidential © 2011 VaR is the perfect candidate for RSM Particularly when the portfolio has structured transactions Great way to leverage 400 scenarios into 10,000! Regulatory capital standards rely on VaR as measure of required capital Insurance Solvency II standard is predicated on VaR for each risk “module” Basel II Advanced Market Risk Approach uses VaR for trading portfolios Response Surface Modeling Can Improve VaR Calculation times & Accuracy Dramatically

10 QRM Proprietary and Confidential © 2011 Example: Cumulative Distribution of Market Value Changes for a CMO 2000 full valuations for VaR scenarios Pricing MethodNo RSMRSM Number of full valuations VaR 95% - 85,967, ,225, full valuations for training scenarios only

11 Using RP, RSM or just running multiple scenarios (stochastically or deterministically), clients can leverage the Framework to study the space of possibilities Along each path, the Framework enforces modeling consistency across all of the relevant risk factors Results in the production of a tremendous amount of information By focusing on a few risk measures, clients are able to summarize the vast amount of simulation data into risk metrics, for example: Liquidity profiles, gap cash flows, earnings at risk Market value sensitivities, Value at Risk Losses, economic capital, regulatory capital Management relies on these risk metrics to make business decisions as well as to monitor past decisions Scenario Analysis Allows Clients to Study Complex Model Spaces QRM Proprietary and Confidential © 2011

12 Risk metrics summarize a distribution into a single number that is easier for senior management to digest However, Risk Metrics Typically Only Provide Part of the Picture QRM Proprietary and Confidential © 2011 Difference between Quantile and Mean MeanQuantile

13 Construct the efficient frontier and assess compositional differences vis-à-vis current portfolio Identify which portfolios to invest in and where to divest Modify origination strategies to improve portfolio risk adjusted return Quantify which assets are best for securitization depending on whether the objective is to minimize funding cost or reduce risk Define optimal hedging strategies to: Keep bank’s exposures within policy limits Find economic hedges without compromising too much income Find optimal balance sheet structure to maximize return to shareholders while maintaining liquidity ratio constraints QRM’s Portfolio Optimizer Was Designed to Provide Answers to Many Strategic Questions QRM Proprietary and Confidential © 2011

14 Efficient Frontier Analysis Highlights Effect of Capital Constraints on Optimal Portfolio QRM Proprietary and Confidential © 2011 Basel May Reduce Attainable Returns Some Optimal Portfolios are Not Affected by Basel Current portfolio is sub-optimal Expected Return Standard Deviation (Return)

15 If you would like a copy of the full version of this presentation or any additional information please contact: or Thank you for your attention Please enjoy the Asian Bankers Summit! Additional QRM information QRM Proprietary and Confidential © 2011

16 World Headquarters: 181 West Madison Street, 41st Floor Chicago, IL (312) London Office: 288 Bishopsgate Suite 4.04 London, EC2M 4QP +44 (0) Singapore Office: 6 Battery Road #18-07 Singapore QRM Proprietary and Confidential © 2011